A chaotic stochastic parallel gradient descent algorithm for fast phase correction of optical phased array

Optical waveguide phased array can realize high-speed beam scanning without mechanical deflection, which is a research hotspot of new system LiDAR. Limited by the manufacturing error of the device, the theoretical value of the modulation phase cannot achieve precise beam steering. The most commonly used SPGD algorithm achieves accurate beam deflection without pre-wavefront phase detection by optimizing the phase modulation voltages of the array elements, avoiding cumbersome parameter error calibration. However, in some cases, the SPGD algorithm converges slowly and is prone to local extremum. To achieve fast adaptive phase correction, a chaotic stochastic parallel gradient descent (CSPGD) algorithm combining chaos theory and SPGD is proposed in this paper. The neighborhood chaotic search is centered on the wave control voltages obtained by SPGD optimization. The ergodicity of chaotic sequences is employed to improve the fine search performance of the algorithm, thereby speeding up the correction and improving the correction accuracy. Plus, a phase-correcting optical system is built using a one-dimentional eight-element (1x8) lithium niobate (LiNbO3) optical waveguide phased array to verify the convergence performance of the new algorithm. The random phase modulation OPA is used to simulate a large phase error scenario. Simulation and experimental results show that the CSPGD phase correction algorithm can deflect the beam to the target direction more quickly and improve the beam quality effectively within the same iteration scale, compared with the classical SPGD algorithm.