Massively parallel and universal approximation of nonlinear functions using diffractive processors

TL;DR

This paper introduces a novel optical computing approach that uses passive diffractive processors to perform massively parallel nonlinear function approximation without relying on nonlinear optical materials, enabling ultrafast and scalable analog computation.

Contribution

The authors demonstrate that linear diffractive optical processors can serve as universal approximators for nonlinear functions, achieving high-density parallel computation both numerically and experimentally.

Findings

Numerically approximated one million nonlinear functions in parallel.

Experimentally validated 35 nonlinear functions with a compact setup.

Established diffractive processors as scalable platforms for nonlinear function approximation.

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.