Evolution properties of partially coherent radially polarized Laguerre-Gaussian vortex beams in an anisotropic turbulent atmosphere.

Analytical formulas for the cross-spectral density matrix of a partially coherent radially polarized Laguerre-Gaussian vortex (PCRPLGV) beam in anisotropic atmospheric turbulence are derived based on the extended Huygens-Fresnel principle. The evolution laws of statistical properties of a PCRPLGV beam in turbulence, such as the average intensity, degree of coherence (DOC) and degree of polarization (DOP), are investigated in detail. It is found that the atmospheric turbulence induces degeneration of the intensity distribution of a PCRPLGV beam on propagation, and some new properties, such as self-shaping and self-rotating, will appear on propagation due to vortex phase. In addition, in order to verify our theoretical results, we combined the complex screen method and multi-phase screens method to simulate the propagation of PCRPLGV beam in atmospheric turbulence. And the studies indicate that the simulation results are consistent with the theoretical predictions. Our results will be useful in some potential applications, such lidar detection, remote sensing and free-space optical communications.