Massively parallel and universal approximation of nonlinear functions using diffractive processors
arXiv:2507.08253 · doi:10.1186/s43593-025-00113-w
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.
28 Pages, 7 Figures
References in corpus (14)
- All-Optical Machine Learning Using Diffractive Deep Neural Networks
- Graphene Mode-Locked Ultrafast Laser
- Photonics for artificial intelligence and neuromorphic computing
- 8E-17 fractional laser frequency instability with a long room-temperature cavity
- All-Optical Information Processing Capacity of Diffractive Surfaces
- Misalignment Resilient Diffractive Optical Networks
- Photonics for Neuromorphic Computing: Fundamentals, Devices, and Opportunities
- Nonlinear optical encoding enabled by recurrent linear scattering
- Universal Linear Intensity Transformations Using Spatially-Incoherent Diffractive Processors
- Data class-specific all-optical transformations and encryption
- Sub-hertz frequency stabilization of a commercial diode laser
- Efficient second-harmonic generation of a high-energy, femtosecond laser pulse in a lithium triborate (LBO) crystal
- Broadband nonlinear modulation of incoherent light using a transparent optoelectronic neuron array
- Universal point spread function engineering for 3D optical information processing