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Abstract Free‐space optical systems are emerging as a hardware platform for high‐throughput and energy‐efficient computing. In this review, the pioneering works are first introduced to lay the foundation for the principles and architectures of systems. The modern hardware implementations of two types of optical computing systems, matrix, and vector multiplication systems and diffractive optical neural network systems, are covered from material, device, and system perspectives. Further, the system deployment to various applications is also discussed. This review serves as an introduction and guideline to the current progress of developing and utilizing free‐space optical computing systems in various domains. 

Abstract Solving partial differential equations (PDEs) is the cornerstone of scientific research and development. Data-driven machine learning (ML) approaches are emerging to accelerate time-consuming and computation-intensive numerical simulations of PDEs. Although optical systems offer high-throughput and energy-efficient ML hardware, their demonstration for solving PDEs is limited. Here, we present an optical neural engine (ONE) architecture combining diffractive optical neural networks for Fourier space processing and optical crossbar structures for real space processing to solve time-dependent and time-independent PDEs in diverse disciplines, including Darcy flow equation, the magnetostatic Poisson’s equation in demagnetization, the Navier-Stokes equation in incompressible fluid, Maxwell’s equations in nanophotonic metasurfaces, and coupled PDEs in a multiphysics system. We numerically and experimentally demonstrate the capability of the ONE architecture, which not only leverages the advantages of high-performance dual-space processing for outperforming traditional PDE solvers and being comparable with state-of-the-art ML models but also can be implemented using optical computing hardware with unique features of low-energy and highly parallel constant-time processing irrespective of model scales and real-time reconfigurability for tackling multiple tasks with the same architecture. The demonstrated architecture offers a versatile and powerful platform for large-scale scientific and engineering computations. 

All‐optical and fully reconfigurable transmissive diffractive optical neural network (DONN) architectures emerge as high‐throughput and energy‐efficient machine learning (ML) hardware accelerators in broad applications. However, current device and system implementations have limited performance. In this work, a novel transmissive diffractive device architecture, a digitized phase‐change material (PCM) heterostack, which consists of multiple nonvolatile PCM layers with different thicknesses, is demonstrated. Through this architecture, the advantages of PCM electrical and optical properties can be leveraged and challenges associated with multilevel operations in a single PCM layer can be mitigated. Through proof‐of‐concept experiments, the electrical tuning of one PCM layer is demonstrated in a transmissive spatial light modulation device, and thermal analysis guides the design of multilayer devices and DONN systems to avoid thermal cross talk if individual heterostacks are assembled into an array. Further, a heterostack containing three PCM layers is designed based on experimental results to produce a large‐phase modulation range and uniform coverage, and the ML performance of DONN systems with the designed heterostack is evaluated. The developed device architecture is practically feasible and scalable for future energy‐efficient, fast‐reconfigured, and compact transmissive DONN systems.