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The explosive data growth has resulted in increased computing costs. As Moore&#x2019;s Law is increasingly slowing down, the traditional computing approach based on the von Neumann architecture is gradually becoming unable to fulfill future computing needs. However, optical neural networks have emerged as a potential solution because of their high speed, high bandwidth, and capability to subdue the bottleneck problem of computing power. With the development of optics and nanophotonics, it is possible to implement complex optical neural networks in free-space and nanophotonic platforms. This article reviews the research progress of optical neural networks. Firstly, various methods of implementing optical matrix calculations are described. Secondly, the construction method of optical neural network in free space and nanophotonic platform is introduced respectively. In free space, based on 4f system and diffractive optical elements and in nanophotonic, relied on optical waveguide devices such as microring resonator or Mach-Zehnder Interferometer. Thirdly, we introduce the methods in training and nonlinear activity. Finally, we summarized the current research status and challenges of optical neural networks. In the future, optical neural networks have great application value.

Optical Neural Network in Free-Space and Nanophotonics