Bandwidth and stability of the stochastic parallel gradient descent algorithm for phase control in coherent beam combination

The bandwidth and stability limits of the stochastic parallel gradient descent (SPGD) algorithm used for coherent beam combination is investigated by deriving an analytical model for the phase control loop. The analytical model is compared to experiments and numerical simulations using a laboratory tiled coherent beam combination setup. The setup consisted of four sub-beams from fiber-optic collimators and used a backreflected signal as feedback. A rotating phase plate was used to induce phase disturbances into the system. The analytical model compared favorably to numerical simulations and experiments as well as to other studies found in the literature. The results can be used to provide an estimate of the achievable phase control bandwidth of coherent beam combination systems using SPGD as a control algorithm.