Lower-depth programmable linear optical processors

Programmable linear optical processors (LOPs) can have widespread applications in computing and information processing due to their capabilities of implementing reconfigurable on-chip linear transformations. A conventional LOP that uses a mesh of Mach-Zehnder interferometers (MZIs) requires 2N + 3 stages of phase shifters for N x N matrices. However, it is beneficial to reduce the number of phase-shifter stages to realize a more compact and lower-loss LOP, especially when long and lossy electro-optic phase shifters are used. In this work, we propose a structure for LOPs that can implement arbitrary matrices as long as they can be realized by previous MZI-based schemes. Through numerical analysis, we further show that the number of phase-shifter stages in the proposed structure can be reduced to N + 2 and N + 3 for a large number of random dense matrices and sparse matrices, respectively. This work contributes to the realization of compact, low-loss, and energy-efficient programmable LOPs.