Deep learning enabled design of complex transmission matrices for universal optical components

Recent breakthroughs in photonics-based quantum, neuromorphic and analogue processing have pointed out the need for new schemes for fully programmable nanophotonic devices. Universal optical elements based on interferometer meshes are underpinning many of these new technologies, however this is achieved at the cost of an overall footprint that is very large compared to the limited chip real estate, restricting the scalability of this approach. Here, we consider an ultracompact platform for low-loss programmable elements using the complex transmission matrix of a multi-port multimode waveguide. We propose a deep learning inverse network approach to design arbitrary transmission matrices using patterns of weakly scattering perturbations. The demonstrated technique allows control over both the intensity and phase in a multiport device at a four orders reduced device footprint compared to conventional technologies, thus opening the door for large-scale integrated universal networks.