Real-Valued Optical Matrix Computing with Simplified MZI Mesh

The Mach-Zehnder interferometer (MZI) mesh, a mainstream structure for optical matrix-vector multiplication (MVM), has been widely employed in recently developed optical neural networks (ONNs) and combination optimization problem solvers. The conventional MZI mesh was designed specifically for complex-valued optical MVM. The network includes 2N2 phase shifters, and coherent detection is indispensable for retrieving the output complex-valued vectors. Nonetheless, the majority of applications, including ONNs, merely require real-valued optical matrices with N2 degrees of freedom (DOFs). The DOF gap between the 2 types of matrices results in a severe redundancy in the number of phase shifters when the conventional MZI mesh is applied to implement real-valued optical MVM. In this study, we propose a simplified MZI mesh for performing real-valued incoherent optical MVM. It has N2 phase shifters and an optical depth of N + 1, and it outperforms the conventional MZI mesh. Furthermore, we constructed an ONN with the proposed MZI mesh and successfully performed the iris classification task via in situ training of particle swarm optimization. More importantly, we introduced a matched on-chip nonlinear activation function, so the proposed MZI mesh can be cascaded onto a single chip. Overall, the proposed real-valued MZI mesh and in situ training method are space efficient, energy efficient, scalable, and robust to fabrication errors. Therefore, they are suitable for large-scale ONNs.