Metasurface Diffractive Optical Networks

• Metasurface-based diffractive optical networks are coherent processors that use trainable, subwavelength phase masks to map input fields to desired outputs.
• They employ phase-only encoding, diffractive propagation, and multiplexing (polarization, wavelength) to perform tasks like multi-task classification and sensing.
• Demonstrated applications include high-accuracy object recognition, adaptive optics, and optical encryption with passive, energy-efficient operation.

Searching arXiv for recent and foundational papers on metasurface-based diffractive optical networks. Metasurface-based diffractive optical networks are coherent optical processors in which subwavelength metasurfaces serve as trainable diffractive layers, so that local optical modulation and free-space propagation jointly implement a computational mapping between an input and an output field-of-view. In this framework, metasurfaces composed of a two-dimensional array of millions of meta-units can realize precise control of optical wavefront with subwavelength resolution, and can therefore function as constitutive layers of optical neural networks, diffractive deep neural networks, spectropolarimetric encoders, or hybrid opto-electric front ends (Tsai et al., 2022, Kulce et al., 2020, Qiu et al., 27 Jul 2025). Reported realizations span object recognition, multi-task classification, permutation operations, wavefront sensing, spectropolarimetry, super-resolution direction-of-arrival estimation, and inverse-designed multifunctional optics from the visible to terahertz and microwave regimes.

1. Architectural foundations

The basic architectural element is a metasurface layer modeled as a thin transmissive mask with trainable local response. In the simplest phase-only form, a layer is written as $T(x,y)=e^{i\phi(x,y)}$ with unit amplitude, while polarization-dependent or vectorial designs use Jones-matrix descriptions or separate phase functions for different channels. A single-layer (“singlet”) optical neural network places one metasurface between an input plane and an output plane; multilayer variants use cascaded metasurfaces separated by free-space gaps, and examples include doublets, bilayers, three-layer stacks, and five-layer diffractive networks (Tsai et al., 2022, Tian et al., 23 Jun 2025, Behroozinia et al., 2024).

The physical realization depends on wavelength and multiplexing strategy. Near-infrared “smart glass” implementations used amorphous silicon nanopillars on silica with a square lattice of period $750$ nm and height $1\,\mu$m, together with isotropic and birefringent meta-unit libraries that provided $\sim2\pi$ phase modulation and polarization multiplexing (Tsai et al., 2022). Visible on-chip multiplexed diffractive neural networks used TiO$_2$ pillars on quartz with $p=400$ nm and $H=600$ nm, later bonded through a $100\,\mu$m OCA spacer to a CMOS sensor with $0.8\,\mu$m pixels (Luo et al., 2021). Terahertz arrangeable diffractive neural networks used high-resistivity silicon nanofins at $0.291$ THz, with each diffractive layer implemented as an $750$0 array of nanofins over an aperture of approximately $750$1 (Tian et al., 23 Jun 2025). Spectropolarimetric diffractive optical networks employed anisotropic Si nanobricks with periodicity $750$2 nm and height $750$3 nm, while spin-multiplexed nonlocal metasurfaces used crescent-shaped silicon nanopillars in a hexagonal lattice with period $750$4m and height $750$5 nm (Qiu et al., 27 Jul 2025, He et al., 15 Jun 2026).

A recurring design pattern is phase-only encoding with subwavelength sampling. In the terahertz arrangeable network, pixel size $750$6m ensured sub-wavelength sampling $750$7 across the layer (Tian et al., 23 Jun 2025). In the visible on-chip platform, the single-channel neuron density was $750$8, and with two polarization channels the effective density became $750$9 (Luo et al., 2021). This suggests that metasurface implementations derive their practical expressive power not only from network depth but also from the very high areal density of trainable optical neurons.

2. Propagation physics and capacity

Forward propagation is generally formulated by alternating local metasurface modulation and scalar diffraction. A common expression is

$1\,\mu$0

or, in angular-spectrum form,

$1\,\mu$1

with equivalent Rayleigh–Sommerfeld formulations also used extensively (Tian et al., 23 Jun 2025, Tsai et al., 2022). For polarization-multiplexed visible metasurfaces, the local response can be written with a diagonal Jones matrix,

$1\,\mu$2

where $1\,\mu$3 and $1\,\mu$4 are independently designed for orthogonal polarizations (Luo et al., 2021).

Pancharatnam–Berry phase and related geometric-phase mechanisms are central in several metasurface diffractive networks. In the terahertz arrangeable network, rotating each nanofin by angle $1\,\mu$5 provided an abrupt geometric phase $1\,\mu$6 covering $1\,\mu$7 (Tian et al., 23 Jun 2025). In the spin-multiplexed nonlocal metasurface, the cross-polarized channel used

$1\,\mu$8

while the co-polarized channel exploited the momentum-space transfer function

$1\,\mu$9

which approximates a Laplacian high-pass filter for optical edge detection (He et al., 15 Jun 2026). In the spectropolarimeter, wavelength- and helicity-dependent phase control combined propagation phase and geometric phase through

$\sim2\pi$0

(Qiu et al., 27 Jul 2025)

The theoretical capacity of coherent diffractive networks has been analyzed in terms of the dimensionality of the implementable linear transformations. For a network with $\sim2\pi$1 trainable surfaces, input field $\sim2\pi$2, output field $\sim2\pi$3, and layer neuron counts $\sim2\pi$4, the achievable solution-space dimension is

$\sim2\pi$5

If each layer has the same number of neurons, $\sim2\pi$6, then

$\sim2\pi$7

This linear growth with depth, մինչև saturation at the field-of-view limit, was connected to depth advantages in statistical inference, learning, and generalization (Kulce et al., 2020). A related scaling law appeared in all-optical permutation networks, where the permutation approximation error dropped precipitously once the total number of trainable meta-atoms satisfied $\sim2\pi$8; for a $\sim2\pi$9 permutation, roughly $_2$0k was required (Mengu et al., 2022).

3. Training and inverse design methodologies

Training is ordinarily performed by differentiating through the optical forward model. In object-recognition singlets, the forward pass starts from the complex amplitude of the coherently illuminated object, applies the metasurface phase mask, propagates to the output plane, and integrates intensities over class-specific detection zones. The class probabilities are then defined by normalized zone energies,

$_2$1

and optimized with cross-entropy,

$_2$2

optionally with an auxiliary contrast term to maximize inter-zone contrast and robustness (Tsai et al., 2022). The trainable variables are the per-meta-unit phases, updated with Adam after computing $_2$3 by the chain rule through the diffraction integral (Tsai et al., 2022).

Multi-task and fabrication-aware variants extend this basic recipe. The arrangeable diffractive neural network introduced a weighted multi-task loss

$_2$4

and for two tasks

$_2$5

with $_2$6 selected empirically to bias performance between MNIST and Fashion tasks (Tian et al., 23 Jun 2025). Tri-channel wavelength-multiplexed classifiers used

$_2$7

with best-performing weights $_2$8 in the reported end-to-end optimization framework (Behroozinia et al., 2024).

Several works moved beyond direct phase optimization. The phase correlation method for multiplexed metasurfaces replaced joint optimization of multiple channel phases with learned mappings such as $_2$9 and $p=400$0, where small multilayer perceptrons reduced the multi-channel problem to a single-channel inverse design over the “master” phase profile (Xiang et al., 2024). The diffractive meta-neural network for super-resolution direction-of-arrival estimation pre-trained “mini-metanets” that mapped geometric parameters $p=400$1 to multi-frequency Jones-matrix responses, and then backpropagated through both angular-spectrum propagation and the differentiable surrogate models (Yang et al., 7 Sep 2025). Three-task multiplexed metasurfaces similarly used surrogate ANNs to predict $p=400$2 from $p=400$3, then trained geometry directly with Adam, initial learning rate $p=400$4, decay by $p=400$5 every $p=400$6k steps, batch size $p=400$7, and approximately $p=400$8 epochs (Behroozinia et al., 2024).

Robustness is commonly injected during training. Smart-glass classifiers included random perturbations to model nonuniform illumination, misalignment of object, metasurface, and detector, and distance fluctuations (Tsai et al., 2022). Diffractive permutation networks used a “vaccination” strategy, perturbing lateral shift, axial displacement, and in-plane rotation on each mini-batch, with

$p=400$9

to enforce misalignment tolerance (Mengu et al., 2022). Hybrid wavefront sensors and spectropolarimeters also injected detector noise, fabrication variability, quantization, and dynamic-range effects during end-to-end training (Jimenez et al., 18 Feb 2026, Qiu et al., 27 Jul 2025).

4. Multiplexing, reconfiguration, and multifunctionality

Metasurface-based diffractive optical networks use multiple physical degrees of freedom to exceed the single-task, single-channel behavior of conventional diffractive processors. Polarization multiplexing is among the most direct strategies. Near-infrared object-recognition smart glass employed birefringent meta-unit libraries with different phase shifts $H=600$0 and $H=600$1 for orthogonal polarizations, enabling one metasurface to route different recognition tasks to different outputs (Tsai et al., 2022). Visible on-chip multiplexed diffractive neural networks and bilayer multi-task classifiers further exploited polarization channels under the same wavelength, while maintaining phase-only operation at the network-design stage (Luo et al., 2021, Behroozinia et al., 2024).

Wavelength multiplexing extends this principle across spectral channels. Bilayer TiO$H=600$2 metasurfaces were used to encode up to three parallel tasks at $H=600$3 nm, $H=600$4 nm, and $H=600$5 nm under fixed $H=600$6-polarization, with channel filtering at the detection plane (Behroozinia et al., 2024). The phase-correlation method likewise targeted dual-wavelength classification at $H=600$7 nm and $H=600$8 nm under the same polarization, converting a multi-wavelength phase-design problem into a reduced single-channel optimization (Xiang et al., 2024). Spectropolarimetric diffractive optical networks generalized multiplexing further by encoding both spectrum and Stokes parameters into a single-shot intensity fingerprint on a CMOS sensor (Qiu et al., 27 Jul 2025).

Reconfiguration need not require active meta-atoms. The arrangeable diffractive neural network achieved task switching by reordering two pre-trained metasurface layers: Task 1 used the sequence $H=600$9 and Task 2 used $100\,\mu$0, so that layer rearrangement alone changed the effective mapping without re-fabrication (Tian et al., 23 Jun 2025). The diffractive magic cube network pushed mechanical reconfiguration much further by combining permutation, rotation, and translation of three cascaded phase-only metasurface layers. In that system, up to $100\,\mu$1 non-independent mechanical states were available as “potential channels,” and the training objective jointly optimized a selected subset of channels for holography, focusing, or orbital angular momentum generation (Feng et al., 2024).

Spin multiplexing and hybrid preprocessing provide another route to multifunctionality. In the edge-enhanced nonlocal metasurface, the co-polarized channel performed real-time edge detection through momentum-space filtering, while the cross-polarized channel simultaneously executed single-layer diffractive classification through PB-phase modulation (He et al., 15 Jun 2026). A plausible implication is that metasurface-based diffractive optical networks increasingly treat optical preprocessing, encoding, and inference as co-designed functions rather than isolated modules.

5. Demonstrated functions and reported performance

Representative demonstrations cover classification, sensing, linear transforms, and inverse-designed optical elements.

System	Function	Reported result
Metasurface smart glass	4-digit and 10-digit coherent object recognition	4-digit: theoretical $100\,\mu$2, experimental $100\,\mu$3 $100\,\mu$4; 10-digit: theoretical $100\,\mu$5, experimental $100\,\mu$6 $100\,\mu$7 (Tsai et al., 2022)
Polarization-multiplexed smart glass	Split-digit recognition; letter + style recognition	Experimental $100\,\mu$8 and $100\,\mu$9 for the two digit groups; $0.8\,\mu$0 $0.8\,\mu$1 letter identity and $0.8\,\mu$2 style (Tsai et al., 2022)
On-chip visible multiplexed DNN	Simultaneous recognition of digital and fashionable items	Simulated accuracy $0.8\,\mu$3 for both channels; experimental on-chip accuracy $0.8\,\mu$4 (Luo et al., 2021)
Arrangeable THz DNN	Layer-reordered multi-task recognition	Simulation: MNIST $0.8\,\mu$5, Fashion-MNIST $0.8\,\mu$6; experiment: MNIST $0.8\,\mu$7, Fashion $0.8\,\mu$8 (Tian et al., 23 Jun 2025)
Bilayer multiplexed metasurface DNN	Dual-task and three-task classification	PM-DNN dual-channel: $0.8\,\mu$9 MNIST and $0.291$0 FMNIST; tri-channel end-to-end joint: $0.291$1 MNIST, $0.291$2 FMNIST, $0.291$3 KMNIST (Behroozinia et al., 2024)
Edge-enhanced spin-multiplexed DNN	Single-layer classification with optical edge preprocessing	MNIST accuracy improved from $0.291$4 to $0.291$5 (He et al., 15 Jun 2026)
Hybrid metasurface-encoded OENN	Wavefront sensing for adaptive optics	At $0.291$6 and $0.291$7 MLP: mean SR $0.291$8 versus $0.291$9 for ANN-only; experiment: median SR $750$00 versus $750$01 (Jimenez et al., 18 Feb 2026)
DON spectropolarimeter	Spectrum and full-Stokes reconstruction	NIR: narrow-band MAE $750$02, broadband MAE $750$03, MRE $750$04, spectral resolution $750$05 nm; chip-integrated visible: narrowband MAE $750$06, broadband MAE $750$07, MRE $750$08, spectral resolution $750$09 nm (Qiu et al., 27 Jul 2025)
DMNN	Super-resolution direction-of-arrival estimation	$750$10 two-source resolution, mean absolute error $750$11 for two incoherent targets within $750$12, AET $750$13 (Yang et al., 7 Sep 2025)
MAODCNN	All-optical convolution plus diffractive decoding	MNIST: $750$14 for $750$15 conv $750$16 $750$17 diffractive, $750$18 for $750$19 conv $750$20 $750$21 diffractive; Fashion-MNIST: $750$22 versus $750$23 for DNN (Liang et al., 5 Dec 2025)

Beyond classification and sensing, diffractive optical networks have been trained as general optical transforms. Permutation networks engineered through deep learning performed arbitrarily selected permutation operations and scaled to a $750$24 permutation, corresponding to $750$25 million interconnects; a three-layer network was experimentally demonstrated at terahertz frequencies (Mengu et al., 2022). The diffractive magic cube network numerically and experimentally validated $750$26-channel holograms, $750$27-channel single-focus/multi-focus patterns, and $750$28-channel OAM beam or comb generation, with mean experimental PCC or CC within $750$29 of simulation (Feng et al., 2024).

Inverse-designed diffractive devices also reveal the continuity between optical neural networks and multifunctional flat optics. Two-layer adaptive deep diffractive neural networks selectively focused radiation over two well-separated spectral bands, achieved peak efficiencies $750$30, surpassed the $750$31 bound of single-layer DOEs, produced Gaussian-shaped bandwidths as narrow as $750$32–$750$33 nm, and generated super-oscillatory focal spots with $750$34 (Chen et al., 2022). This suggests that metasurface-based diffractive optical networks should be understood not only as classifiers but also as a general inverse-design formalism for compact optical operators.

6. Fabrication, integration, applications, and limitations

Fabrication routes are strongly aligned with established nanofabrication workflows. Reported processes include a-Si deposition on SiO$750$35 followed by electron-beam lithography and reactive-ion etching, photolithography plus reactive-ion etching on $750$36 mm Si wafers, TiO$750$37 nanofabrication by EBL, ALD, ion-beam etch, and resist stripping, and 3D printing of THz diffractive layers in UV-curable polymer (Tsai et al., 2022, Tian et al., 23 Jun 2025, Luo et al., 2021, Mengu et al., 2022). CMOS compatibility was emphasized repeatedly, and large-area manufacturing prospects included deep-UV lithography, nanoimprint lithography, and roll-to-roll replication (Tsai et al., 2022). Chip-level integration has already been demonstrated through bonding to commercial CMOS image sensors in both visible classification and spectropolarimetric systems (Luo et al., 2021, Qiu et al., 27 Jul 2025).

The attraction of these systems is their passive optical front end. For the smart-glass classifier, inference was reported as zero power consumption after the light source, with latency determined by light propagation time, approximately $750$38 ps for $750$39 mm, and “physics-guaranteed security” because no electronic read-out or digital image was ever created (Tsai et al., 2022). The terahertz arrangeable DNN similarly reported passive operation, zero additional electrical power beyond the THz source, and total latency below $750$40 ps through both layers and free-space gaps (Tian et al., 23 Jun 2025). In optical convolutional diffractive networks, numerical estimates placed total energy per inference at $750$41 and overall latency near $750$42 ns when detector readout was included (Liang et al., 5 Dec 2025).

Applications follow directly from these properties. Reported scenarios include smart windows or eyewear, contact-lens cameras, embedded IoT sensors, security screening, nondestructive testing, portable biomedical terahertz spectroscopy, free-space optical communications, optical data storage and display, multi-focus microscopy, optical encryption, and onboard remote sensing from raw Sentinel-1 level-0 IQ data (Tsai et al., 2022, Tian et al., 23 Jun 2025, Feng et al., 2024, Liu et al., 10 Mar 2025). The remote-sensing SIM-D$750$43NN reported performance levels around $750$44 directly from real raw IQ data in terms of accuracy, precision, recall, and F1 Score, using four phase-only layers and two output antennas (Liu et al., 10 Mar 2025).

Several limitations recur across the literature. Point-by-point scanning output detectors constrain frame rate in terahertz demonstrations, and integrated focal-plane arrays are identified as necessary for real-time full-field readout (Tian et al., 23 Jun 2025). Fixed phase patterns mean that truly dynamic reprogramming requires active meta-atoms or SLM integration (Tian et al., 23 Jun 2025). Tight alignment tolerances remain important: reported values include feature alignment tolerance $750$45 nm over $750$46m fields, overlay tolerance $750$47 nm in visible on-chip systems, and lateral or axial sensitivity on the order of $750$48m and $750$49m in terahertz reconfigurable networks (Tsai et al., 2022, Luo et al., 2021, Tian et al., 23 Jun 2025). Scalar diffraction approximations can break down when inter-pillar coupling or polarization cross-talk grows, and metasurfaces are often inherently narrowband, while the capacity analysis in coherent diffractive networks assumes monochromatic coherence (Luo et al., 2021, Kulce et al., 2020).

A common misconception is that all metasurface-based diffractive optical networks are fully all-optical from input to decision. Some are: smart-glass classifiers and diffractive permutation networks operate as passive optical transforms whose outputs can be read directly as intensity patterns (Tsai et al., 2022, Mengu et al., 2022). Others are deliberately hybrid. Wavefront sensing used a metasurface encoder followed by a lightweight multilayer perceptron; the spectropolarimeter used a trained CNN decoder; the super-resolution DMNN used a lightweight electronic neural network after optical multiplexing (Jimenez et al., 18 Feb 2026, Qiu et al., 27 Jul 2025, Yang et al., 7 Sep 2025). The distinction is functional rather than conceptual: in all cases, the metasurface stack performs a learned optical encoding that shifts computation into wave propagation, while the electronic back end, when present, decodes a compressed optical representation.