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Unified, Verifiable Neural Simulators for Electromagnetic Wave Inverse Problems (2404.00545v1)

Published 31 Mar 2024 in physics.optics, cs.LG, and eess.IV

Abstract: Simulators based on neural networks offer a path to orders-of-magnitude faster electromagnetic wave simulations. Existing models, however, only address narrowly tailored classes of problems and only scale to systems of a few dozen degrees of freedom (DoFs). Here, we demonstrate a single, unified model capable of addressing scattering simulations with thousands of DoFs, of any wavelength, any illumination wavefront, and freeform materials, within broad configurable bounds. Based on an attentional multi-conditioning strategy, our method also allows non-recurrent supervision on and prediction of intermediate physical states, which provides improved generalization with no additional data-generation cost. Using this O(1)-time intermediate prediction capability, we propose and prove a rigorous, efficiently computable upper bound on prediction error, allowing accuracy guarantees at inference time for all predictions. After training solely on randomized systems, we demonstrate the unified model across a suite of challenging multi-disciplinary inverse problems, finding strong efficacy and speed improvements up to 96% for problems in optical tomography, beam shaping through volumetric random media, and freeform photonic inverse design, with no problem-specific training. Our findings demonstrate a path to universal, verifiably accurate neural surrogates for existing scattering simulators, and our conditioning and training methods are directly applicable to any PDE admitting a time-domain iterative solver.

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References (45)
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[4] Qin, Z. et al. Deep tissue multi-photon imaging using adaptive optics with direct focus sensing and shaping. Nature Biotechnology 2022 40:11 40, 1663–1671 (2022). URL https://www.nature.com/articles/s41587-022-01343-w. [5] Zhao, X. et al. Imaging through scattering media via spatial-temporal encoded pattern illumination. Photonics Research, Vol. 10, Issue 7, pp. 1689-1694 10, 1689–1694 (2022). URL https://opg.optica.org/viewmedia.cfm?uri=prj-10-7-1689&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=prj-10-7-1689https://opg.optica.org/prj/abstract.cfm?uri=prj-10-7-1689. [6] Lalau-Keraly, C. M., Bhargava, S., Miller, O. D. & Yablonovitch, E. Adjoint shape optimization applied to electromagnetic design. Optics Express, Vol. 21, Issue 18, pp. 21693-21701 21, 21693–21701 (2013). URL https://opg.optica.org/viewmedia.cfm?uri=oe-21-18-21693&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-21-18-21693https://opg.optica.org/oe/abstract.cfm?uri=oe-21-18-21693. [7] Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). 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Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. 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URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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URL https://opg.optica.org/viewmedia.cfm?uri=prj-10-7-1689&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=prj-10-7-1689https://opg.optica.org/prj/abstract.cfm?uri=prj-10-7-1689. [6] Lalau-Keraly, C. M., Bhargava, S., Miller, O. D. & Yablonovitch, E. Adjoint shape optimization applied to electromagnetic design. Optics Express, Vol. 21, Issue 18, pp. 21693-21701 21, 21693–21701 (2013). URL https://opg.optica.org/viewmedia.cfm?uri=oe-21-18-21693&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-21-18-21693https://opg.optica.org/oe/abstract.cfm?uri=oe-21-18-21693. [7] Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. 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URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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URL https://www.nature.com/articles/nphoton.2015.140. Lalau-Keraly, C. M., Bhargava, S., Miller, O. D. & Yablonovitch, E. Adjoint shape optimization applied to electromagnetic design. Optics Express, Vol. 21, Issue 18, pp. 21693-21701 21, 21693–21701 (2013). URL https://opg.optica.org/viewmedia.cfm?uri=oe-21-18-21693&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-21-18-21693https://opg.optica.org/oe/abstract.cfm?uri=oe-21-18-21693. [7] Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. 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URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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[19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). 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[26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. 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International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) 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Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. 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URL https://opg.optica.org/viewmedia.cfm?uri=oe-21-18-21693&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-21-18-21693https://opg.optica.org/oe/abstract.cfm?uri=oe-21-18-21693. [7] Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. 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URL https://www.nature.com/articles/nphoton.2015.140. Zhao, X. et al. Imaging through scattering media via spatial-temporal encoded pattern illumination. Photonics Research, Vol. 10, Issue 7, pp. 1689-1694 10, 1689–1694 (2022). URL https://opg.optica.org/viewmedia.cfm?uri=prj-10-7-1689&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=prj-10-7-1689https://opg.optica.org/prj/abstract.cfm?uri=prj-10-7-1689. [6] Lalau-Keraly, C. M., Bhargava, S., Miller, O. D. & Yablonovitch, E. Adjoint shape optimization applied to electromagnetic design. Optics Express, Vol. 21, Issue 18, pp. 21693-21701 21, 21693–21701 (2013). URL https://opg.optica.org/viewmedia.cfm?uri=oe-21-18-21693&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-21-18-21693https://opg.optica.org/oe/abstract.cfm?uri=oe-21-18-21693. [7] Molesky, S. et al. Inverse design in nanophotonics. Nature Photonics 2018 12:11 12, 659–670 (2018). URL https://www.nature.com/articles/s41566-018-0246-9. [8] Yu, N. & Capasso, F. 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URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. 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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). 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URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nature Materials 2014 13:2 13, 139–150 (2014). URL https://www.nature.com/articles/nmat3839. [9] Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). 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Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. 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Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). 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URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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[13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). 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Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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[14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. 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Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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[14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) 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Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). 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URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. 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[32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. 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URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yee, K. S. Numerical solution of initial boundary value problems involving maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation 14, 302–307 (1966). [10] Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). 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Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. 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[19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. 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URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Su, L. et al. Fully-automated optimization of grating couplers. Optics Express 26, 4023 (2018). [11] Kuznetsov, A. I. et al. 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. 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Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. 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Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. 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[32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. 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URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.
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URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). 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URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Kuznetsov, A. I. et al. Roadmap for optical metasurfaces. ACS Photonics (2024). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.3c00457. [12] McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. McClung, A. et al. Multifunctional 2.5d metastructures enabled by adjoint optimization. Optica, Vol. 7, Issue 1, pp. 77-84 7, 77–84 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-1-77&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-1-77https://opg.optica.org/optica/abstract.cfm?uri=optica-7-1-77. [13] Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Devaney, A. J. Inverse-scattering theory within the rytov approximation. Optics Letters, Vol. 6, Issue 8, pp. 374-376 6, 374–376 (1981). URL https://opg.optica.org/viewmedia.cfm?uri=ol-6-8-374&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-6-8-374https://opg.optica.org/ol/abstract.cfm?uri=ol-6-8-374. [14] Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M., Waller, L., Ren, D., Chowdhury, S. & Liu, H.-Y. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). 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[20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). 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URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). 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URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. 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Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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  14. Multi-layer born multiple-scattering model for 3d phase microscopy. Optica, Vol. 7, Issue 5, pp. 394-403 7, 394–403 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=optica-7-5-394&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=optica-7-5-394https://opg.optica.org/optica/abstract.cfm?uri=optica-7-5-394. [15] An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. 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URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. 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URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. An, S. et al. A deep learning approach for objective-driven all-dielectric metasurface design. ACS Photonics 6, 3196–3207 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.9b00966. [16] Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. 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International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. 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URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J. & Fan, J. A. Global optimization of dielectric metasurfaces using a physics-driven neural network. Nano Letters 19, 5366–5372 (2019). URL https://pubs.acs.org/doi/abs/10.1021/acs.nanolett.9b01857. [17] Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Yao, K., Unni, R. & Zheng, Y. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.
  17. Intelligent nanophotonics: merging photonics and artificial intelligence at the nanoscale. Nanophotonics 8, 339–366 (2019). URL https://pubmed.ncbi.nlm.nih.gov/34290952/. [18] Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Nadell, C. C., Padilla, W. J., Huang, B. & Malof, J. M. Deep learning for accelerated all-dielectric metasurface design. Optics Express, Vol. 27, Issue 20, pp. 27523-27535 27, 27523–27535 (2019). URL https://opg.optica.org/viewmedia.cfm?uri=oe-27-20-27523&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=oe-27-20-27523https://opg.optica.org/oe/abstract.cfm?uri=oe-27-20-27523. [19] Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. 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URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hegde, R. S. Deep learning: a new tool for photonic nanostructure design. Nanoscale Advances 2, 1007–1023 (2020). URL https://pubs.rsc.org/en/content/articlehtml/2020/na/c9na00656ghttps://pubs.rsc.org/en/content/articlelanding/2020/na/c9na00656g. [20] So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.
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URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. 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Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. So, S., Badloe, T., Noh, J., Rho, J. & Bravo-Abad, J. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). 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[30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. 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Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.
  20. Deep learning enabled inverse design in nanophotonics. Nanophotonics 9, 1041–1057 (2020). URL https://www.degruyter.com/document/doi/10.1515/nanoph-2019-0474/html. [21] Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Inampudi, S. & Mosallaei, H. Neural network based design of metagratings. Applied Physics Letters 112, 241102 (2018). URL /aip/apl/article/112/24/241102/35352/Neural-network-based-design-of-metagratings. [22] Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Martin, O. J. F. & Blanchard-Dionne, A.-P. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. 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U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. 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  22. Teaching optics to a machine learning network. Optics Letters, Vol. 45, Issue 10, pp. 2922-2925 45, 2922–2925 (2020). URL https://opg.optica.org/viewmedia.cfm?uri=ol-45-10-2922&seq=0&html=truehttps://opg.optica.org/abstract.cfm?uri=ol-45-10-2922https://opg.optica.org/ol/abstract.cfm?uri=ol-45-10-2922. [23] Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. 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URL https://www.nature.com/articles/nphoton.2015.140. Liu, D., Tan, Y., Khoram, E. & Yu, Z. Training deep neural networks for the inverse design of nanophotonic structures. ACS Photonics 5, 1365–1369 (2018). URL https://pubs.acs.org/doi/abs/10.1021/acsphotonics.7b01377. [24] Gao, L., Li, X., Liu, D., Wang, L. & Yu, Z. A bidirectional deep neural network for accurate silicon color design. Advanced Materials 31, 1905467 (2019). URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). 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Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. 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URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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URL https://onlinelibrary.wiley.com/doi/full/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/abs/10.1002/adma.201905467https://onlinelibrary.wiley.com/doi/10.1002/adma.201905467. [25] Jiang, J., Chen, M. & Fan, J. A. Deep neural networks for the evaluation and design of photonic devices. Nature Reviews Materials 2020 6:8 6, 679–700 (2020). URL https://www.nature.com/articles/s41578-020-00260-1. [26] Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). 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URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lim, J. & Psaltis, D. Maxwellnet: Physics-driven deep neural network training based on maxwell’s equations. APL Photonics 7 (2022). URL /aip/app/article/7/1/011301/2835095/MaxwellNet-Physics-driven-deep-neural-network. [27] Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. 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URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. 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[29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. 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[32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. 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A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. 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High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. 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International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). 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[42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. 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Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). 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Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Chen, M. et al. High speed simulation and freeform optimization of nanophotonic devices with physics-augmented deep learning. ACS Photonics 9, 3110–3123 (2022). URL https://pubs.acs.org/doi/full/10.1021/acsphotonics.2c00876. [28] Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). 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URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.
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Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Guermond, J.-L. & Minev, P. High-order adaptive time stepping for the incompressible navier–stokes equations. SIAM Journal on Scientific Computing 41, A770–A788 (2019). URL https://doi.org/10.1137/18M1209301. [29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. 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Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. 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URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. 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Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. 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[29] Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Um, E. S., Harris, J. M. & Alumbaugh, D. L. 3d time-domain simulation of electromagnetic diffusion phenomena: A finite-element electric-field approach. Geophysics 75 (2010). URL https://api.semanticscholar.org/CorpusID:26433652. [30] Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. Journal of biomedical optics 20, 111208 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26259511/. [39] Park, Y. K., Depeursinge, C. & Popescu, G. Quantitative phase imaging in biomedicine. Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Wang, X., Guo, W., Li, C., Lan, J. & Sui, W. Introducing time-dependant sources for solving time-domain schrödinger equation using fdtd method. INEC 2010 - 2010 3rd International Nanoelectronics Conference, Proceedings 746–747 (2010). [31] Vaswani, A. et al. Attention is all you need. Advances in Neural Information Processing Systems 30 (2017). [32] Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). 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URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. (eds) Ultra-fast metalens optimization using conditional physics-augmented deep learning surrogate solvers. (eds Chang-Hasnain, C. J., Alù, A. & Zhou, W.) High Contrast Metastructures XIII, Vol. PC12897, PC128970P. International Society for Optics and Photonics (SPIE, 2024). URL https://doi.org/10.1117/12.3005029. [34] Hughes, T. W., Williamson, I. A. D., Minkov, M. & Fan, S. Wave physics as an analog recurrent neural network. Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). 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URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. Chang-Hasnain, C. J., Alù, A. & Zhou, W. 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Science Advances 5, eaay6946 (2019). URL https://www.science.org/doi/abs/10.1126/sciadv.aay6946. [35] Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. [37] Yoon, J. et al. Label-free characterization of white blood cells by measuring 3d refractive index maps. Biomedical optics express 6, 3865 (2015). URL https://pubmed.ncbi.nlm.nih.gov/26504637/. [38] Park, H. et al. Three-dimensional refractive index tomograms and deformability of individual human red blood cells from cord blood of newborn infants and maternal blood. 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Nature Photonics 2018 12:10 12, 578–589 (2018). URL https://www.nature.com/articles/s41566-018-0253-x. [40] Piggott, A. Y. et al. Inverse design and demonstration of a compact and broadband on-chip wavelength demultiplexer. Nature Photonics 2015 9:6 9, 374–377 (2015). URL https://www.nature.com/articles/nphoton.2015.69. [41] Yoon, S. et al. Recent advances in optical imaging through deep tissue: imaging probes and techniques. Biomaterials Research 26 (2022). URL /pmc/articles/PMC9587606//pmc/articles/PMC9587606/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC9587606/. [42] Helmchen, F. & Denk, W. Deep tissue two-photon microscopy. Nature Methods 2005 2:12 2, 932–940 (2005). URL https://www.nature.com/articles/nmeth818. [43] Feuchtinger, A., Walch, A. & Dobosz, M. Deep tissue imaging: a review from a preclinical cancer research perspective. Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Hansen, M. S. & Kellman, P. Image reconstruction: an overview for clinicians. Journal of magnetic resonance imaging : JMRI 41, 573 (2015). URL /pmc/articles/PMC4276738//pmc/articles/PMC4276738/?report=abstracthttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC4276738/. [36] Okawa, S. & Hoshi, Y. A review of image reconstruction algorithms for diffuse optical tomography. Applied Sciences 2023, Vol. 13, Page 5016 13, 5016 (2023). URL https://www.mdpi.com/2076-3417/13/8/5016/htmhttps://www.mdpi.com/2076-3417/13/8/5016. 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Histochemistry and cell biology 146, 781–806 (2016). URL https://pubmed.ncbi.nlm.nih.gov/27704211/. [44] Gigan, S. et al. Roadmap on wavefront shaping and deep imaging in complex media. Journal of Physics: Photonics 4, 042501 (2022). URL https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9https://iopscience.iop.org/article/10.1088/2515-7647/ac76f9/meta. [45] Horstmeyer, R., Ruan, H. & Yang, C. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140. Ronneberger, O., Fischer, P. & Brox, T. U-net: Convolutional networks for biomedical image segmentation. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 9351, 234–241 (2015). URL https://link.springer.com/chapter/10.1007/978-3-319-24574-4_28. [33] Lupoiu, R., Mao, C., Shao, Y., Chen, M. & Fan, J. A. 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  45. Guidestar-assisted wavefront-shaping methods for focusing light into biological tissue. Nature Photonics 2015 9:9 9, 563–571 (2015). URL https://www.nature.com/articles/nphoton.2015.140.

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