Diffractive Neural Networks

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Universal Function Approximation via Diffractive Optical Processors: Physical Limits, Error Bounds, and Learnability
Aug 5, 2026Md Sadman Sakib Rahman, Che-Yung Shen, Aydogan OzcanDiffractive Neural Networks Universal Approximation
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
HAMON: Passive Optical Sequence Mixing for Long-Horizon Forecasting
Jun 15, 2026Alper YıldırımLong-Term Time Series Forecasting Diffractive Neural Networks
Wavelength-Multiplexed 2D Beam Steering via a Passive Diffractive Network
Jun 15, 2026Che-Yung Shen, Yuhang Li, Cagatay Isil +3Diffractive Neural Networks
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
Beyond the Thin-Layer Limit: Differentiable Volumetric Training for Visible-Range Diffractive Neural Networks
Jun 5, 2026Dineth Jayakody, Dushan N. WadduwageDiffractive Neural Networks Differentiable Physics
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
Breaking the Cascade: Compact Nonlinear Optical Computing with Single-Layer Encoder-Decoder Co-Localization
May 31, 2026Yuntian Wang, Alexander Chen, Md Sadman Sakib Rahman +1Diffractive Neural Networks Photonic Computing
1Electrical and Computer Engineering Department, University of California, Los Angeles, CA, 90095, USA
Pre-training Enables Extraordinary All-optical Image Denoising
May 8, 2026Xudong Lv, Yuxiang Sun, Shuo Wang +3Diffractive Neural Networks Image Denoising
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
Photonic AI: A Hybrid Diffractive Holographic Neural System for Passive Optical Real-Time Image Classification
Apr 14, 2026Prakul Sunil HiremathDiffractive Neural Networks Photonic Computing
Department of Computer Science and Engineering, Visvesvaraya Technological University (VTU), Belagavi, India · Aliens on Earth (AoE) Autonomous Research Group, Belagavi, India
TurPy: a physics-based and differentiable optical turbulence simulator for algorithmic development and system optimization
Apr 8, 2026Joseph L. Greene, Alfred Moore, Iris Ochoa +3Diffractive Neural Networks Physics-Based Simulation
Georgia Tech Research Institute, Atlanta, GA, 30318, USA
3D aperture-engineered diffractive neural networks for super-resolution electromagnetic wave computing
Mar 1, 2026Sheng Gao, Songtao Yang, Haiou Zhang +2Diffractive Neural Networks Direction-of-Arrival Estimation
Department of Electronic Engineering, Tsinghua University, Beijing, 100084, China. · Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing, 100084, China.
ReDON: Recurrent Diffractive Optical Neural Processor with Reconfigurable Self-Modulated Nonlinearity
Feb 27, 2026Ziang Yin, Qi Jing, Raktim Sarma +3Diffractive Neural Networks Photonic Computing
Arizona State University, Tempe, AZ, USA · Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM, USA · Rensselaer Polytechnic Institute, Troy, NY, USA

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

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 Networks Universal Approximation Photonic Computing

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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.