Massively parallel and universal approximation of nonlinear functions using diffractive processors

Md Sadman Sakib Rahman; Yuhang Li; Xilin Yang; Shiqi Chen; Aydogan Ozcan

doi:10.1186/s43593-025-00113-w

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Massively parallel and universal approximation of nonlinear functions using diffractive processors

eLight Vol. 5, (2025)

Research Article | Updated：2025-12-01

- Massively parallel and universal approximation of nonlinear functions using diffractive processors
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- DOI：10.1186/s43593-025-00113-w
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- Received：21 September 2025，
  
  Revised：2025-10-16，
  
  Accepted：24 October 2025，
  
  Published Online：06 November 2025，
  
  Published：2025-12
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Md Sadman Sakib Rahman, Yuhang Li, Xilin Yang, et al. Massively parallel and universal approximation of nonlinear functions using diffractive processors[J]. eLight, 2025, 5.
DOI：

Md Sadman Sakib Rahman, Yuhang Li, Xilin Yang, et al. Massively parallel and universal approximation of nonlinear functions using diffractive processors[J]. eLight, 2025, 5. DOI： 10.1186/s43593-025-00113-w.

摘要

Abstract

Nonlinear computation is essential for a wide range of information processing tasks

yet implementing nonlinear functions using optical systems remains a challenge due to the weak and power-intensive nature of optical nonlinearities. Overcoming this limitation without relying on nonlinear optical materials could unlock unprecedented opportunities for ultrafast and parallel optical computing systems. Here

we demonstrate that large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces. In this framework

the input variables of nonlinear functions are encoded into the phase of an optical wavefront—e.g.

via a spatial light modulator (SLM)—and transformed by an optimized diffractive structure with spatially varying point-spread functions to yield output intensities that approximate a large set of unique nonlinear functions–all in parallel. We provide proof establishing that this architecture serves as a universal function approximator for an arbitrary set of bandlimited nonlinear functions

also covering wavelength-multiplexed nonlinear functions as well as multi-variate and complex-valued functions that are all-optically cascadable. Our analysis also indicates the successful approximation of typical nonlinear activation functions commonly used in neural networks

including the sigmoid

tanh

ReLU (rectified linear unit)

and softplus. We numerically demonstrate the parallel computation of one million distinct nonlinear functions

accurately executed at wavelength-scale spatial density at the output of a diffractive optical processor. Furthermore

we experimentally validated this framework using in situ optical learning and approximated 35 unique nonlinear functions in a single shot using a compact setup consisting of an SLM and an image sensor. These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation

paving the way for new capabilities in analog optical computing based on linear materials.

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Keywords

references

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