Combinatorial study of coherent multi-channel phase-locking based on covariance matrix adaptation evolution strategy

This study explores the performance and channel-scalability of the covariance matrix adaptation evolution strategy (CMA-ES)-based coherent optical phase control algorithm for coherent beam combining (CBC) systems. Leveraging the probabilistic nature of its optimization process, the CMA-ES algorithm emerges as a promising candidate for a next-generation phase control algorithm for CBC systems. To assess its functionality and channel-scalability, we conduct numerical investigations into the CMA-ES-based phase control algorithm applied to both 37- and 61-channel CBC systems with varying its algorithmic parameters. For the 37-channel configuration, consistent results demonstrate an average beam combining efficiency (BCE) exceeding 0.9, with a constrained standard deviation of 0.1 with phase sample numbers surpassing 30. The analysis of the time complexity reveals that the CMA-ES-based algorithm efficiently converges to a BCE value of 0.9 within a 10 MHz bandwidth within a 5 μs atmospheric time scale. In the case of the 61-channel configuration, a majority of phase samples exhibit an average BCE exceeding 0.95, with a small number of trials slightly falling below 0.85 yet still achieving a BCE of approximately 0.8. Similar to the 37-channel case, with the bandwidth < 12 MHz, the CMA-ES-based algorithm can give rise to the BCE level of 0.9 within a 5 μs atmospheric time duration.