  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.
In this study, we present a novel framework that uses multiple scattering that
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 non-linear optical computing at low power
continuous wave light. Moreover, we empirically found that scaling of this
optical framework follows the power law as in state-of-the-art deep digital
networks.
