Diffractive Neural Networks

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Aug 5, 2026

Universal Function Approximation via Diffractive Optical Processors: Physical Limits, Error Bounds, and Learnability

We present a unified theoretical framework connecting classical universal approximation theory, Fourier-feature approximation, and diffractive optical processors. We show that phase-encoded diffractive processors implement finite Fourier-feature expansions whose mathematical completeness follows from Fourier/Stone-Weierstrass arguments, while their physical realizability is governed by finite coefficient synthesis through optimized spatially varying coherent point-spread functions (PSFs). Our analyses derive approximation-error bounds that separate Fourier truncation, PSF-synthesis, input phase error, optical hardware, readout, and noise contributions; establish scaling relationships linking approximation complexity to optical degrees of freedom and input/output space-bandwidth products; derive photon-budget and throughput limits imposed by photon statistics; formulate finite-class statistical learnability bounds for phase-quantized diffractive function approximators; and analyze the impact of spatially incoherent illumination. We further analyze coherent optical cascadability and show that quadratic feature expansion through coherent mixing and optical readout provides a mechanism for enhanced representation while remaining fundamentally distinct from the depth-separation results established for digital neural networks. Our analyses provide a rigorous theoretical foundation for diffractive nonlinear function approximation and establish quantitative relationships among mathematical expressivity, optical hardware resources, statistical learning, and physical performance limits, thereby offering general design principles for large-scale analog optical computing systems.

Md Sadman Sakib Rahman, Che-Yung Shen, Aydogan Ozcan

Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA · Bioengineering Department, University of California, Los Angeles, CA, 90095, USA · California NanoSystems Institute (CNSI), University of California, Los Angeles, CA, 90095, USA

Diffractive Neural NetworksUniversal ApproximationPhotonic Computing
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Jun 15, 2026

HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting

Simple linear and frequency-domain models remain surprisingly competitive in long-horizon time-series forecasting, and recent mechanistic evidence suggests that standard forecasting benchmarks may not require the dense superposed representations that make transformers powerful in other domains. This raises a substrate-level question: if the core forecasting operator is often low-complexity and approximately linear, does it need to be implemented as learned digital temporal mixing? We introduce HAMON, a passive diffractive optical forecasting core in which historical values are encoded onto an optical aperture, future positions are left dark, and cascaded trainable phase masks with free-space diffraction shape the forecast directly in the output field. At inference, prediction is performed by a single passive optical propagation pass with no trainable digital sequence-mixing layer. Across standard benchmarks, HAMON outperforms the strongest digital baselines considered on ETTm2 at all horizons and on ETTh2 at all but the longest horizon, improving MSE by up to 14% and doing so consistently across horizons rather than at isolated points. It is competitive on Weather and trails the strongest baselines on the remaining ETT settings and on the high-channel-count Traffic and Electricity datasets. Phase encoding, intensity-compatible readout, and phase-scrambling ablations, together with a TorchOptics cross-simulator check, indicate that the forecasts arise from the data-bearing optical field rather than from a digital forecasting head. Because the passive core uses standard Fourier optics, HAMON defines a concrete target for optical hardware and for passive physical sequence mixing.

Alper Yıldırım

Long-Term Time Series ForecastingDiffractive Neural NetworksTime Series ForecastingPhotonic Computing
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Jun 15, 2026

Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network

We introduce a wavelength-addressable diffractive optical network that transforms illumination wavelength into a high-dimensional control parameter for arbitrarily programmable 2D beam steering. The proposed passive architecture comprises cascaded spatially optimized diffractive layers, jointly designed using deep learning, to rapidly map distinct wavelengths to predefined/desired output angles. Unlike conventional single-layer dispersive optical elements, which are physically restricted to 1D linear mapping, this framework harnesses complex wavefront transformations to utilize the illumination wavelength as an intrinsic addressing key for arbitrary 2D beam steering, eliminating the need for mechanical scanning or electronic phase control. We numerically demonstrate wavelength-controlled beam steering across 625 wavelength channels spanning 400-750 nm, realizing a 25 x 25 array of independently addressable beam positions with subwavelength positioning accuracy and high channel fidelity. Unlike conventional gratings, which constrain wavelength routing to a linear trajectory, the proposed diffractive network performs nonlocal wavefront transformations, enabling arbitrary wavelength-to-angle mappings across a 2D field of view. We further validate the proposed framework experimentally in both the terahertz and visible spectral regimes, demonstrating wavelength-multiplexed beam steering using 3D fabricated passive diffractive layers at terahertz frequencies and phase-only spatial light modulators in the visible spectrum. This wavelength-addressable diffractive architecture establishes a compact and scalable paradigm for high-speed programmable beam steering, with potential applications in optical communications, routing, imaging, sensing, and emerging photonic information-processing systems.

Che-Yung Shen, Yuhang Li, Cagatay Isil +3

1Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA · 2Bioengineering Department, University of California, Los Angeles, CA, 90095, USA · 3California NanoSystems Institute (CNSI), University of California, Los Angeles, CA, 90095, USA

Diffractive Neural Networks
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Jun 5, 2026

Beyond the Thin-Layer Limit: Differentiable Volumetric Training for Visible-Range Diffractive Neural Networks

Diffractive deep neural networks (D2NNs) promise miniaturized, power-efficient, light-speed optical front-ends for machine vision, yet the most mature demonstrations remain in the terahertz regime, built from readily fabricated millimeter-scale neurons. Translating D2NNs to the visible range, where nearly all vision pipelines operate, was long blamed on the difficulty of fabricating nanoscale neurons; but even after recent advances removed that barrier, visible-range D2NNs matching their terahertz counterparts remain out of reach. We identify the true obstacle as the thin-layer approximation underlying nearly all D2NN training, which treats each diffractive layer as an infinitely thin mask. It fails not because of the short wavelength, as is commonly assumed, but because the low-refractive-index materials (n approximately 1.3-1.5) used at visible wavelengths require relief structures thick enough that intra-layer diffraction and phase accumulation become significant. To overcome this, we introduce a differentiable beam-propagation (∂\partialBPM) layer that models each element as a finite-thickness volume and propagates light through it during training, keeping the fabrication-compatible height map end-to-end trainable without full-wave simulation in the loop. Across MNIST, Fashion-MNIST, and CIFAR-100 classification and imaging, ∂\partialBPM training substantially reduces the design-to-device mismatch, and full-wave FDTD validation raises classification accuracy from 50% to 90% without re-optimization. The ∂\partialBPM layer thus offers a scalable, physics-aware bridge between efficient optical neural-network optimization and fabrication-consistent diffractive design.

Dineth Jayakody, Dushan N. Wadduwage

Department of Computer Science, Old Dominion University, Norfolk, VA 23529, USA · School of Data Science, Old Dominion University, Norfolk, VA 23529, USA · Department of Physics, Old Dominion University, Norfolk, VA 23529, USA

Diffractive Neural NetworksDifferentiable PhysicsDifferentiable Optimization
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May 31, 2026

Breaking the Cascade: Compact Nonlinear Optical Computing with Single-Layer Encoder-Decoder Co-Localization

We demonstrate that nonlinear computing can be achieved with a single linear diffractive surface under coherent illumination. We introduce a compact encoder-decoder co-localization (E+D) architecture in which an input-dependent dynamic encoder and a static optimized decoder are integrated within the same phase-only diffractive plane. Following free-space propagation, coherent interference between the encoder and decoder fields, combined with intensity detection, generates programmable nonlinear input-output mappings without requiring nonlinear optical materials or multiple diffractive layers. We prove that the proposed E+D optical processor is a universal approximator for arbitrary real-valued band-limited nonlinear functions and identify the physical factors governing its approximation fidelity, including the decoder degrees-of-freedom, detector aperture, and axial propagation distance. Crucially, we demonstrate that introducing a trained, frozen phase bias to the encoder region systematically enhances functional expressivity, providing robustness against coarse phase quantization on spatial light modulators. Using this framework, we accurately synthesize diverse nonlinear functions, including commonly used neural network activation functions and complex-valued nonlinear functions. Finally, we experimentally validate the proposed approach using a visible-light optical set-up trained through in situ learning, demonstrating the parallel approximation of 9 nonlinear functions in a single optical forward pass. By collapsing nonlinear optical computation into a single diffractive surface, the E+D architecture substantially reduces hardware and alignment complexity while preserving powerful function-approximation capabilities, providing a compact and scalable framework for analog information processing.

Yuntian Wang, Alexander Chen, Md Sadman Sakib Rahman +1

1Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA

Diffractive Neural NetworksPhotonic Computing
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May 8, 2026

Pre-training Enables Extraordinary All-optical Image Denoising

Optical neural networks are emerging as powerful machine learning and information processing tools because of their potential advantages in speed and energy efficiency. The training methods of these physical models, however, remain underexplored compared to their digital counterparts and are leading to suboptimal performance. This paper reports a pre-training-driven approach that leads to snapshot image denoising with substantially improved quality. We demonstrated effective free-space optical denoising by a diffractive network optimized by a two-step process including (1) pre-training using a massive dataset of 3.45 million diverse but simple images and (2) fine-tuning with the corresponding task-specific datasets. Compared to conventional Fourier-domain filtering and directly trained diffractive networks, such a transfer learning process exhibited prominent advantages for denoising images degraded by severe noise, peak signal-to-noise ratio (PSNR) below 8 dB, while preserving fine image features and improving the PSNR to above 18 dB. Importantly, the same pre-trained optical network could be consistently fine-tuned to process degraded images from highly diverse styles ranging from handwritten digits (MNIST) and chest X-rays (ChestMNIST) to CIFAR-10 images and human faces (CelebA). We further demonstrated the critical role of our optical denoisers in vision-based applications, including face detection, plate recognition, and localization of UAVs in noisy conditions.

Xudong Lv, Yuxiang Sun, Shuo Wang +3

Ministry of Industry and Information Technology Key Lab of Micro-Nano Optoelectronic Information System, Guangdong Provincial Key Laboratory of Semiconductor Optoelectronic Materials and Intelligent Photonic System, Harbin Institute of Technology, Shenzhen, 518055, Guangdong, China. · School of Electronics and Information Engineering, Zhejiang Provincial Key Laboratory of Intelligent Vehicle Electronics Research, Hangzhou Dianzi University, Hangzhou, 310018, Zhejiang, China. · School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen), Shenzhen, 518172, Guangdong, China. +2

Diffractive Neural NetworksImage Denoising
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Apr 14, 2026

Photonic AI: A Hybrid Diffractive Holographic Neural System for Passive Optical Real-Time Image Classification

Edge intelligence is constrained by the energy and latency costs of shuttling data through electronic memory hierarchies. Optical systems offer a fundamentally different computational regime: once an input wavefront is launched into a structured medium, propagation, diffraction, and interference jointly enact a linear transformation whose cost is determined by wave physics rather than by clocked arithmetic. This paper develops a rigorous systems-level treatment of that regime and introduces a hybrid diffractive holographic architecture for image classification. The proposed model couples a Diffractive Optical Neural Network (DONN) with a Holographic Interference-Based Learning (HIBL) operator a formal map from digitally optimized phase distributions to physically realizable, fabrication-compatible interference patterns embeddable in passive optical elements. We express the full inference pipeline as a composition of encoding, phase modulation, free-space propagation, and intensity measurement operators, making explicit which quantities are learned, which are fixed by design, and where nonlinearity enters through photodetection. This operator-theoretic view resolves a persistent gap in the optical-ML literature between learning a transformation and physically realizing it. In physics-informed simulation on MNIST, a three-layer system with approximately 25,000 phase elements achieves 91.2% test accuracy with propagation-limited nanosecond-scale latency. The primary contribution is not a performance claim but a precise computational framework: learned representations can be physically embedded into structured optical media so that inference is executed by wavefront transformation through a passive, fabricated object rather than by sequential electronic multiply accumulate operations.

Prakul Sunil Hiremath

Department of Computer Science and Engineering, Visvesvaraya Technological University (VTU), Belagavi, India · Aliens on Earth (AoE) Autonomous Research Group, Belagavi, India

Diffractive Neural NetworksPhotonic ComputingImage Classification
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Apr 8, 2026

TurPy: a physics-based and differentiable optical turbulence simulator for algorithmic development and system optimization

Developing optical systems for free-space applications requires simulation tools that accurately capture turbulence-induced wavefront distortions and support gradient-based optimization. Here we introduce TurPy, a GPU-accelerated, fully differentiable wave optics turbulence simulator to bridge high fidelity simulation with end-to-end optical system design. TurPy incorporates subharmonic phase screen generation, autoregressive temporal evolution, and an automated screen placement routine balancing Fourier aliasing constraints and weak-turbulence approximations into a unified, user-ready framework. Because TurPy's phase screen generation is parameterized through a media-specific power spectral density, the framework extends to atmospheric, oceanic, and biological propagation environments with minimal modification. We validate TurPy against established atmospheric turbulence theory by matching 2nd order Gaussian beam broadening and 4th order plane wave scintillation to closed-form models with 98% accuracy across weak to strong turbulence regimes, requiring only the medium's refractive index structure constant and power spectral density as inputs. To demonstrate TurPy as a gradient-based training platform, we optimize a dual-domain diffractive deep neural network (D2NN) in a two-mask dual-domain architecture to recover a Gaussian beam from a weakly turbulent path and achieving over 58% reduction in scintillation relative to an uncompensated receiver in simulation. TurPy is released as an open-source package to support synthetic data generation, turbulence-informed algorithm development, and the end-to-end design of optical platforms operating in turbulent environments.

Joseph L. Greene, Alfred Moore, Iris Ochoa +3

Georgia Tech Research Institute, Atlanta, GA, 30318, USA

Diffractive Neural NetworksPhysics-Based Simulation
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Mar 1, 2026

3D aperture-engineered diffractive neural networks for super-resolution electromagnetic wave computing

The rapid progress in 6G communication and high-bandwidth radar has driven an unprecedented surge in the spatial density of signal sources, resulting in an increasingly congested electromagnetic (EM) environment. When resolving closely spaced signals and interference, existing architectures are strictly bounded by the inherent diffraction limits of two-dimensional (2D) physical apertures, hindering super-resolution sensing and multi-interference mitigation in complex scenarios. Here, we present a 3D aperture-engineered diffractive neural network (AE-DNN) that achieves super-resolution sensing and computing by extending the traditional 2D aperture into 3D. The 3D aperture engineering framework is realized by constructing deep cascaded metasurface layers so that the diffractive propagation from oblique incident fields can be layer-wise modulated and piecewise encoded for perceiving EM fields far exceeding physical aperture limits. The N-layer AE-DNN has the capability to achieve ~N times higher angular resolution than the 2D aperture diffraction limit. The multi-dimensional synthetic aperture (MSA) training is developed to achieve speed-of-light coherent synthesis of the 3D aperture and integrate neural network-based modeling of multi-dimensional metasurface modulation. By orthogonalizing array response vectors in the analog domain, AE-DNN performs parallel super-resolution angle estimation, source number estimation, and source separation for up to 10 independent coherent or incoherent sources. Experimental results across the 36-41 GHz band demonstrate that AE-DNN resolves and suppresses closely spaced multi-interference by ~20 dB, enhances communication capacity by 13.5X, and reduces latency by three orders of magnitude. AE-DNN heralds a paradigm shift in signal processing for advanced radar and 6G communications.

Sheng Gao, Songtao Yang, Haiou Zhang +2

Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China. · Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing, 100084, China.

Diffractive Neural NetworksDirection-of-Arrival EstimationIntegrated Sensing and CommunicationMillimeter-Wave Radar
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Feb 27, 2026

ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity

Diffractive optical neural networks (DONNs) have demonstrated unparalleled energy efficiency and parallelism by processing information directly in the optical domain. However, their computational expressivity is constrained by static, passive diffractive phase masks that lack efficient nonlinear responses and reprogrammability. To address these limitations, we introduce the Recurrent Diffractive Optical Neural Processor (ReDON), a novel architecture featuring reconfigurable, recurrent self-modulated nonlinearity. This mechanism enables dynamic, input-dependent optical transmission through in-situ electro-optic self-modulation, providing a highly efficient and reprogrammable approach to optical computation. Inspired by the gated linear unit (GLU) used in large language models, ReDON senses a fraction of the propagating optical field and modulates its phase or intensity via a lightweight parametric function, enabling effective nonlinearity with minimal inference overhead. As a non-von Neumann architecture in which the primary weighting elements (metasurfaces) remain fixed, ReDON substantially extends the nonlinear representational capacity and task adaptability of conventional DONNs through recurrent optical hardware reuse and dynamically tunable nonlinearity. We systematically investigate various self-modulation configurations to characterize the trade-offs between hardware efficiency and computational expressivity. On image recognition and segmentation benchmarks, ReDON improves test accuracy and mean intersection-over-union (mIoU) by up to 20% compared with prior DONNs employing either optical or digital nonlinearities at comparable model complexity and negligible additional power consumption. This work establishes a new paradigm for reconfigurable nonlinear optical computing, uniting recurrence and self-modulation within non-von Neumann analog processors.

Ziang Yin, Qi Jing, Raktim Sarma +3

Arizona State University, Tempe, AZ, USA · Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, USA · Rensselaer Polytechnic Institute, Troy, NY, USA

Diffractive Neural NetworksPhotonic ComputingNeural Network ExpressivityDynamic Neural NetworksRecurrent Neural Networks
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