Bandwidth analysis and improvement of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent algorithm

We present the numerical analysis and improvement of the bandwidth of the beam phasing of fiber amplifiers using the stochastic parallel gradient descent (SPGD) algorithm. Time-varying phase distortions are incorporated into the dynamic simulation. It is shown by numerical calculation that the bandwidth of the standard SPGD algorithm is dependent on the phase distortions and on the number of lasers. The time-averaged cost function will decrease with an increase in the amplitude and frequency of phase distortions, and in the number of lasers. A cross-grouped SPGD algorithm is proposed, which offers attractive performance due to its robustness to various time-varying phase distortions and faster convergence rate for beam phasing of larger number of lasers. Dynamic simulation shows that the control bandwidth can be improved using the cross-grouped SPGD algorithm.