Phase control algorithms for CBC systems based on evolutionary strategy for implementation on FPGA boards

As efforts to increase the number of combining channels in coherent beam combining (CBC) systems have progressed, the limitations of gradient-based phase control algorithms, particularly with respect to the local extremum problem, have become more apparent. Although adaptive phase control techniques can be used in conjunction with them to alleviate the problem, these algorithms remain fundamentally limited. Recent studies have proposed alternatives, including deep learning and statistical algorithms; however, gradient-based methods continue to dominate due to the considerable difficulty of implementing such novel algorithms on field-programmable gate array (FPGA) boards for real-world CBC systems. In this paper, we propose a novel gradient-free statistical phase control algorithm, the correspondence lookup-table adaptation evolution strategy (CLA-ES), which can readily be implemented on FPGA boards. Leveraging CBC system characteristics, the CLA-ES algorithm constructs a correspondence curve to map the relationship between combined beam intensity and phase distribution, which circumvents the otherwise required complex matrix operations and drastically reduces the dimensionality of the problem. Simulations demonstrate that the CLA-ES algorithm achieves convergence performance comparable to the CMA-ES algorithm but with notably greater computational efficiency, achieving over two orders of magnitude improvement in speed for a 127-channel configuration, for example. This result highlights that, in the context of CBC systems, the ultimate design of phase control algorithms should aim to be gradient-free, aligning well with the direction pursued by the CLA-ES algorithm.