Theory of AdmSPGD algorithm in fiber laser coherent synthesis

The stochastic parallel gradient descent (SPGD) algorithm is one of the promising approaches for performing an efficient coherent beam combining (CBC) for power-scaling of the fiber lasers. However, this algorithm likewise suffers from certain shortcomings, including slow convergence speed and ease catching into local extremes. This paper proposes an AdmSPGD algorithm that modifies the conventional one with adaptive gain and momentum. Notably, the adaptive gain coefficient improves convergence speed by adjusting such gain coefficient in realtime, while the momentum factor suppresses high-frequency interference by adjusting update direction. The proposed algorithm is testified through relevant simulations and experiments, whose results depict that the proposed algorithm can significantly increase convergence speed, robustness and effective bandwidth in the fiber laser beam combining system.