Chip-scale all-optical complex-valued matrix inverter

Matrix inversion is a fundamental and widely utilized linear algebraic operation but computationally expensive in digital-clock-based platforms. Optical computing is a new computing paradigm with high speed and energy efficiency, and the computation can be realized through light propagation. However, there is a scarcity of experimentally implemented matrix inverters that exhibit both high integration density and the capability to perform complex-valued operations in existing optical systems. For the first time, we experimentally demonstrated an iterative all-optical chip-scale processor to perform the computation of complex-valued matrix inversion using the Richardson method. Our chip-scale processor achieves an iteration speed of 10 GHz, which can facilitate ultra-fast matrix inversion with the assistance of high-speed Mach–Zehnder interferometer modulators. The convergence can be attained within 20 iterations, yielding an accuracy of 90%. The proposed chip-scale all-optical complex-valued matrix inverter represents a distinctive innovation in the field of all-optical recursive systems, offering significant potential for solving computationally intensive mathematical problems.