Hybrid CMA-ES/SPGD Algorithm for Phase Control of a Coherent Beam Combining System and its Performance Analysis by Numerical Simulations

In this study, we propose a hybrid phase-control algorithm for multi-channel coherent beam combining (CBC) system by combining the covariant matrix adaption evolution strategy (CMA-ES) and stochastic parallel gradient descent (SPGD) algorithms and analyze its operational performance. The proposed hybrid CMA-ES/SPGD algorithm is a sequential process which initially runs the CMA-ES algorithm until the combined final output intensity reaches a preset interim value, and then switches to running the SPGD algorithm to the end of the whole process. For ideal 7-channel and 19-channel all-fiber-based CBC systems, we have found that the mean convergence time can be reduced by about 10% in comparison with the case when the SPGD algorithm is implemented alone. Furthermore, we analyzed a more realistic situation in which some additional phase noise was introduced in the same CBC system. As a result, it is shown that the proposed algorithm reduces the mean convergence time by about 17% for a 7-channel CBC system and 16-27% for a 19-channel system compared to the existing SPGD alone algorithm. We expect that for implementing a CBC system in a real outdoor environment where phase noise cannot be ignored, the hybrid CMA-ES/SPGD algorithm proposed in this study will be exploited very usefully.