Phase-shift determination for a 4 × 4 intelligent photonic neural network with compatible learning.

Intelligent photonic circuits (IPCs) tuned with an appropriate phase-shift vector could enable a photonic intelligent matrix possibly implemented in multiple neural layers for a task-oriented topologies. A photonic Mach-Zehnder Interferometer (MZI) is a fundamental photonic component in IPCs, whose matrix representation could be broadcasted into an arbitrary matrix that is equipped with an optimized phase-shift vector. The initialized MZIs' phases are tentatively probed between analytical elements and a digital weight matrix that is learned from samples with efficient compatible learning for complex-valued neural networks. Nonlinear least squares is utilized to formulate a phase determination system to refine the optimal phase-shift solutions. The robustness of phase determination system for photonic neural networks is discussed in detail. For a preliminary implementation, a basic 4×4 intelligent photonic neural network is utilized to verify the proof of concept on phase-shift determination in IPC through numerical experiments.