Propagation and evolution of rectangular vortex beam array through atmospheric turbulence

Based on the generalized Huygens–Fresnel principle and Rytov approximation, the intensity expression of arbitrary-order rectangular vortex beam array propagating through atmospheric turbulence is derived, and the evolution process is studied in this paper. Vortex beam array will merge into a single vortex beam in atmospheric turbulence, and then degenerate into a Gaussian-like beam. However, vortex beam array with a smaller topological charge will degenerate in a shorter distance. Strong turbulence will lead to a more uniform light field distribution. In weak turbulence, there are lots of spot lattices just like the case in free space. Besides, the studies in this paper found that the outer scale has little influence on the evolution of vortex beam array. The results in this paper can provide a theoretical reference for further applications of vortex beam array in atmospheric turbulence.