High-speed phase calibration method for large-scale silicon-based optical phased arrays

A high-speed phase calibration method for large-scale silicon-based optical phased arrays (OPAs) is proposed, integrating the Hadamard parallel gradient descent (HPGD) algorithm and a dedicated hardware architecture. Deterministic, orthogonal Hadamard matrices generate perturbation sequences, enabling efficient optimization. The architecture consists of an FPGA, a DSP, and a high-speed avalanche photodiode (APD), employing the APD to acquire objective functions. Simulations show that, compared with the stochastic parallel gradient descent algorithm, HPGD reduces convergence iterations for a 512-element OPA from 4929 to 2285, and a variant with adaptive gain (adaHPGD) further reduces iterations to 1480 (70.0% reduction). For OPAs with 1024 to 4096 elements, HPGD reduces iterations by 31.8% to 41.3%. Experimentally, on a 512-element OPA, each iteration takes 6.7 ms, with a convergence time of 12.8 s. After calibration, the beam achieves a peak sidelobe ratio of 12.93 dB and a full width at half maximum of 0.110°, matching simulations.