Phase correction for a distorted orbital angular momentum beam using a Zernike polynomials-based stochastic-parallel-gradient-descent algorithm.

A stochastic-parallel-gradient-descent algorithm (SPGD) based on Zernike polynomials is proposed to generate the phase correction pattern for a distorted orbital angular momentum (OAM) beam. The Zernike-polynomial coefficients for the correction pattern are obtained by monitoring the intensity profile of the distorted OAM beam through an iteration-based feedback loop. We implement this scheme and experimentally show that the proposed approach improves the quality of the turbulence-distorted OAM beam. Moreover, we apply phase correction patterns derived from a probe OAM beam through emulated turbulence to correct other OAM beams transmitted through the same turbulence. Our experimental results show that the patterns derived this way simultaneously correct multiple OAM beams propagating through the same turbulence, and the crosstalk among these modes is reduced by more than 5 dB.