Fast Phase Calibration of Reconfigurable MZI Optical Processors via BFGS Quasi-Newton Optimization

Manufacturing errors introduce phase deviations in Mach–Zehnder interferometers (MZIs) that degrade the fidelity of optical processors. To address this issue, we employ a Broyden–Fletcher–Goldfarb–Shanno (BFGS) quasi-Newton method for phase calibration of a 4×4 reconfigurable MZI optical processor based on the Reck architecture. By optimizing the mapping from the target matrix to the optical network, the method determines the optimized phase parameters of 12 phase shifters. Thermo-optic simulations are further used to establish the relationship between the applied bias voltage and the induced phase shift, providing a link between the optimized phase parameters and the electrical driving conditions. Compared with Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Gradient Descent with Momentum (GDM), the BFGS method provides faster convergence and high calibration fidelity. These results demonstrate an efficient approach for phase calibration of programmable MZI optical processors.