“…In the past decade, relying on the wide application from material processing and nonlinear optics to free-space optical communication and other fields, the high-power laser beams [1][2][3][4] have increasingly drawn attention, on the other hand, an increase in the laser output power inevitably results in the gain non-uniformity, gain saturation, nonlinear optical effects, and thermal effect further triggering beam distortions on both amplitude and phase which are able to impact the propagation properties of laser beams. [5][6][7][8][9][10][11] Therefore, it is practical important to study the propagation properties of laser beams with beam distortion, including amplitude modulations and phase fluctuations. In order to analyze propagation properties of laser beams with beam distortions theoretically, Manes and Simmons proposed statistical optics model of high-power laser beams for the first time.…”