Second-order statistical characteristics of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase in a turbulent atmosphere

Abstract Based on the extended Huygens–Fresnel integral method, we have derived analytical formulae for the cross-spectral density matrix of a radially polarized Gaussian Schell-model beam with elliptical optical vortex phase (i.e., partially coherent radially polarized elliptical vortex (PCRPEV) beam) propagating through atmospheric turbulence, and have investigated the evolution laws of statistical characteristics such as the average intensity, degree of coherence (DOC), and degree of polarization (DOP) of the PCRPEV beam in turbulence. The results indicate that atmospheric turbulence causes the average intensity distribution of the PCRPEV beam to split and rotate during propagation, ultimately degenerating into a Gaussian-like distribution. Moreover, the PCRPEV beam with lower ellipticity, larger coherence length, and higher topological charge degenerates into a Gaussian-like beam at a slower rate in turbulence. Additionally, we also find that DOC distribution is related to topological charge, meaning that it can provide a new way to measure topological charge. In addition, we simulate the propagation of the PCRPEV beam through atmospheric turbulence using the complex screen and the multi-phase screens methods to verify the theoretical results. The research indicates that the simulation results are essentially consistent with the theoretical findings. These outcomes hold significant relevance for the advancement of free-space optical communication and remote sensing technologies.