Massively parallel and universal approximation of nonlinear functions using diffractive processors

• URL: http://arxiv.org/abs/2507.08253v1
• Date: Fri, 11 Jul 2025 01:54:10 GMT
• Title: Massively parallel and universal approximation of nonlinear functions using diffractive processors
• Authors: Md Sadman Sakib Rahman, Yuhang Li, Xilin Yang, Shiqi Chen, Aydogan Ozcan,
• Abstract summary: Large-scale nonlinear computation can be performed using linear optics through optimized diffractive processors composed of passive phase-only surfaces.<n>We numerically demonstrate the parallel computation of one million distinct nonlinear functions, accurately executed at wavelength-scale spatial density.<n>These results establish diffractive optical processors as a scalable platform for massively parallel universal nonlinear function approximation.
• Score: 17.16859564691328
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 multi-variate and complex-valued functions. We also 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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