Deep neural networks have achieved remarkable breakthroughs by leveraging multiple layers of data processing to extract hidden representations, albeit at the cost of large electronic computing power. To enhance energy efficiency and speed, the optical implementation of neural networks aims to harness the advantages of optical bandwidth and the energy efficiency of optical interconnections. In the absence of low-power optical nonlinearities, the challenge in the implementation of multilayer optical networks lies in realizing multiple optical layers without resorting to electronic components. Here we present a novel framework that uses multiple scattering, and which is capable of synthesizing programmable linear and nonlinear transformations concurrently at low optical power by leveraging the nonlinear relationship between the scattering potential, represented by data, and the scattered field. Theoretical and experimental investigations show that repeating the data by multiple scattering enables nonlinear optical computing with low-power continuous-wave light. Moreover, we empirically find that scaling of this optical framework follows a power law.

深度神经网络通过利用多层数据处理来提取隐藏的表示，尽管以强大的电子计算能力为代价，但它取得了显著的突破。为了提高能效和速度，神经网络的光学实施旨在利用光带宽的优势和光互连的能源效率。在没有低功耗光非线性的情况下，实现多层光网络的挑战在于在不求助于电子元件的情况下实现多个光层。在这里，我们提出了一个使用多重散射的新框架，它能够通过利用以数据表示的散射电位与散射场之间的非线性关系，以低光功率同时合成可编程线性和非线性变换。理论和实验研究表明，通过多重散射重复数据可以实现低功率连续波光的非线性光学计算。此外，我们凭经验发现，这个光学框架的缩放遵循幂律。