Flat optics for analog computing: from fundamental mechanisms to advanced meta-processors

Abstract: As the explosive growth of visual data increasingly strains the latency and energy limits of conventional electronic computing, optical analog computing has re-emerged as a disruptive paradigm for zero-power, speed-of-light information processing. Propelled by the unprecedented wave-manipulation capabilities of optical metasurfaces, this field is undergoing a rapid transition from macroscopic physical optics to ultra-compact, on-chip meta-processors. This Review examines the fundamental mechanisms of metasurface-empowered optical computing spanning Fourier-domain, nonlocal spatial-domain, and interferometric architectures that perform mathematical operations, with a particular focus on spatial differentiation and edge detection as representative computing tasks. By emphasizing recent breakthroughs, we highlight the evolution of meta-processors from static, linear regimes to dynamically reconfigurable, nonlinear, and quantum-assisted multidimensional platforms. We also envision how the synergy of AI-driven inverse design and the integration of analog meta-front-ends with optical neural networks will synergistically revolutionize next-generation intelligent machine vision.

• The paper demonstrates a mathematical framework that maps prescribed optical transfer functions to metasurface designs for precise spatial differentiation and Laplacian filtering.
• It details multiple architectures, including Fourier-domain systems, nonlocal spatial filtering, and interferometric platforms, to enable compact and efficient optical computing.
• It explores advanced meta-processors featuring parallel multiplexing, dynamic reconfigurability, and quantum-assisted operations to enhance integration with AI hardware.

Flat Optics for Analog Computing: Mechanisms, Architectures, and Emerging Meta-Processors

Introduction and Context

The exponential escalation of visual data in machine vision, AI, and autonomous systems has outpaced the processing bandwidth and energy efficiency of conventional electronic hardware. Optical analog computing, which directly manipulates information carried by photons, offers unparalleled bandwidth, inherent massive parallelism, and low energy dissipation, making it inherently suitable for front-end ultrafast information processing. Recently, the development of optical metasurfaces has been transformative, as their subwavelength-scale control over amplitude, phase, polarization, and dispersion allows for the realization of sophisticated transfer function engineering in truly flat, compact, and integrable platforms.

Mathematical Underpinnings: Transfer Function Engineering

Optical analog computing in flat optics is best described as the physical realization of a mathematically prescribed transfer function (OTF), matched to a desired operator, such as spatial differentiation. Utilizing the LSI framework, mathematical operations like 1D/2D spatial differentiation and Laplacian filtering are analytically mapped to required transfer functions in the spatial frequency domain. For instance, a first-order derivative $H(k_x) \propto ik_x$ mandates an odd transfer function, entailing specific amplitude zero-crossings and $\pi$ phase discontinuity, typically necessitating symmetry breaking at the device level or angular selection. Second-order differentiation, $H(k_x) \propto -k_x^2$ or the 2D Laplacian, demands an isotropic parabolic profile, naturally synthesized with symmetric structures and resonant architectures. The vectorial Jones formalism extends these mappings to polarization-multiplexed operators.

Mechanisms and Device Architectures

Fourier-Domain Systems

Traditional 4$f$ spatial filtering is realized via cascaded lenses and a spatially structured metascreen encoding the OTF. Architectural advances have driven progressively more compact implementations: from transmissive/reflective $4f$ systems utilizing nanoantenna arrays to all-dielectric and high-index architectures supporting more efficient and programmable responses [Silva et al., Science 2014]. Single-layer metasurfaces now conflate Fourier transformation and transfer function modulation, achieving compactness without sacrificing mathematical expressivity, as evidenced by single-layer Huygens' metasurfaces and meta-imagers for all-optical convolution [Wang et al., Nat. Commun. 2022; Fu et al., Light Sci. Appl. 2022].

Nonlocal Spatial-Domain Filtering

Eliminating lens-induced spatial propagation, the Green's function approach implements the transfer function directly in the angular response of unstructured interfaces, thin-film stacks, or metasurfaces. This spans non-resonant (Brewster effect, thin slabs, multilayer absorbers) and resonant routes (plasmonic SPPs, guided-mode resonances, high-index Mie or quasi-BIC resonators). Recent high-NA, polarization-multiplexed Laplacian differentiators [Cotrufo et al., Nat. Commun. 2023; Zhou et al., Adv. Funct. Mater. 2025] operationalize broadband, isotropic edge detection in ultra-thin monolithic platforms.

Interferometric Difference Platforms

Spin-orbit interaction–based interferometric architectures generate lateral beam displacements in different polarization channels, mapping finite-difference approximations to spatial derivatives. Geometric-phase and Pancharatnam–Berry metasurfaces execute these with extreme efficiency and spectral bandwidth, advanced further by exploiting intrinsic birefringence and spin-orbit coupling effects in natural crystals [Zhou et al., Sci. Adv. 2020; Yang et al., Optica 2024].

Spiral Phase and Phase Contrast

Phase objects require isotropic, phase-sensitive edge filters, realized by spiral phase metasurfaces implementing the 2D Fourier-space generalization of the Hilbert transform (Riesz transform). Hybrid devices that combine focusing and spiral phase are single-shot, label-free phase imagers for biological and transparent specimen imaging [Huo et al., Nano Lett. 2020; Kim et al., Adv. Funct. Mater. 2022].

Advanced Meta-Processors: Parallelism, Reconfigurability, Nonlinearity, and Quantum Integration

Parallel Multiplexing

Multi-DOF architectures leverage polarization, spin, wavelength, momentum, and spatial channels to perform simultaneous, crosstalk-free mathematical operations (e.g., simultaneous 1st/2nd/3rd order differentiation, convolution, and Laplace operation). Recent dual-polarization and hybrid spin-wavelength architectures have attained ultra-broadband edge detection across ambient lighting scenarios [Tanriover et al., Nat. Commun. 2023; Zhou et al., Adv. Funct. Mater. 2025; Yu et al., Light Sci. Appl. 2026].

Dynamically Reconfigurable Computation

Hybrid photonic platforms embedding PCMs (VO$_2$, Sb$_2$S$_3$/Se$_3$), liquid crystals, or graphene enable nonvolatile and reversible switching between edge-detection and bright-field modalities with high spatial resolution—even permitting active multi-modal imaging or continuous kernel tuning [Cotrufo et al., Nat. Commun. 2024; Yang et al., Light Sci. Appl. 2025]. Mechanical and environmental stimuli (such as mechanical strain or humidity) further extend reconfigurability to sensor-integrated applications.

Nonlinear and Quantum-Assisted Meta-Optics

Metasurfaces supporting nonlinear interactions (SHG, SFG, third-order Kerr, etc.) add intensity-dependent, wavelength-shifting, or up-conversion modalities for computational imaging. These nonlinear meta-processors synthesize Volterra kernels, enabling edge detection at up-converted harmonics, with experimental platforms now supporting high conversion efficiency and multi-diffraction-channel outputs [Cotrufo et al., Nanophotonics 2025; Molina et al., Adv. Mater. 2024].

Quantum-assisted metasurfaces leverage photon entanglement and nonlocal quantum switching to isolate weak phase signals in extreme-noise or photon-starved regimes. Notably, metasurface-enabled quantum phase distillation demonstrates rapid, noise-immune pure phase imaging with unprecedented signal-to-noise suppression—even in the presence of amplitude signals two orders higher than the phase signal [Yang et al., Nano Lett. 2025].

Implications and Outlook

Theoretical

These advances redefine the fundamental bounds of optical analog computers: metasurfaces achieve compact, loss-minimized, high-NA, and high-throughput computation at the speed of light. The synthesis of arbitrarily complex mathematical operators—including time-differentiated and angular spectrum derivatives—transcends prior physical limitations. The seamless integration with AI-driven inverse design will further expand the feasible OTF basis and facilitate global-optima device discovery [Chu et al., Nano Lett. 2023; Swartz et al., Sci. Adv. 2024].

Practical

Practically, the fusion of analog meta-optics with digital post-processing—especially as a programmable or reconfigurable front-end for ONNs—reduces computational overhead, power consumption, and data bottlenecks. These architectures will play a pivotal role in next-generation machine vision systems, autonomous robotics, and in vivo biomedical imaging, transitioning from isolated prototypes toward robust, manufacturable, and system-integrated hardware.

Future Directions

Future developments are set to focus on:

• Expansion of control dimensions (spatiotemporal, spectral, polarization, spatial modes) for truly multidimensional and fully programmable computation.
• Highly nonlinear and quantum-ready architectures supporting entanglement-resilient, photon-efficient image analysis.
• Embedding these analog layers in end-to-end optoelectronic and all-optical deep learning systems, where meta-processors act not just as hand-crafted convolutional kernels but also as trainable, differentiable front-end operators [Qiu et al., Optica 2026; Liang et al., J. Appl. Phys. 2026].

Conclusion

Metasurface-based analog optical computing offers a compelling route for ultrafast, low-power, and integrable information processing platforms. By systematically combining advances in transfer function engineering, resonant photonics, spin-orbit control, parallel multiplexing, and quantum/nonlinear photophysics, these systems promise a disruptive reconfiguration of physical intelligence architectures, driving the co-evolution of AI hardware toward greater speed, efficiency, and functional density (2604.16849).