Probability density performance of Laguerre-Gaussian beams propagating in non-Kolmogorov atmospheric turbulence

Based on the geometrical optics approximation, the analytical expressions of the mode probability density (MPD) and crosstalk probability density (CPD) for a Laguerre-Gaussian (LG) beam propagating through atmospheric turbulence along a horizontal path are derived. Through analytical derivation and numerical simulation, the propagation properties of a single LG beam have been studied in detail. The results of LG beams affected by atmospheric turbulence show that the MPD increases with the smaller topological charge number, lower radial mode number, appropriate waist radius, shorter propagation distance, weaker refractive index structure parameter, and the value much closer to three of non-Kolmogorov turbulence parameter. This investigation is expected to provide useful guidance for study of vortex beams propagating in free-space optical communication.