Influence of thermal blooming on the beam quality of an array of Hermite-Gaussian beams propagating in the atmosphere

The influence of thermal blooming on the quality of an array of Hermite-Gaussian (H-G) beams propagating in the atmosphere is studied, where the incoherent combination is considered. An analytical expression of the equivalent distortion parameter of such an array is derived and validated. As the mode order or the inverse radial fill factor of an array of H-G beams increases, the thermal blooming effect weakens, requiring more time to reach steady-state thermal blooming. The focal shift of an array of H-G beams in the atmosphere is also investigated. Owing to the thermal blooming effect in the atmosphere, the actual focus moves away from the geometric focus as the mode order decreases, which is different from the behavior in free space. Additionally, for an array of multimode beams, the actual focus moves away from the target as the weighting factor of increases.