Numerical simulation of tilt-tip control in coherent beam combining using SPGD algorithm

In coherent beam combining of fiber lasers, the combined beam's quality is strongly affected by not only the piston phase differences between each beamlet, but also the tilt-tip errors of each beamlet. In this paper, we first presented a numerical model of tilt-tip control, then performed the numerical simulation to investigate the tilt-tip wavefront control in coherent beam combining using stochastic parallel gradient descent (SPGD) algorithm. It is demonstrated that the tilt-tip errors can be compensated effectively using SPGD algorithm. Results show that the increase in both the mean square error (MSE) of tilt-tip errors and the number of lasers degrade the control effect. It is difficult to compensate the tilt-tip errors when the MSE is larger than 75% of each beamlet's divergence angle. When the iteration rate of the SPGD algorithm is 100 Hz, the simulated control bandwidth is 16.50 Hz with tilt-tip errors' MSE of 5% of the divergence angle, and 1.90 Hz with MSE of 8% of the divergence angle.

► We present a numerical model of tilt-tip control in coherent beam combining of fiber laser array.
► Simulation of tilt-tip control in coherent combining has been done using SPGD algorithm.
► The system's control effect degrades as the increase of tilt-tip's mean square error and control channel.
► The tilt-tip control bandwidth of different tilt-tip errors has been calculated and analyzed.