Propagation properties of partially coherent vortex cosine-hyperbolic-Gaussian beams in uniaxial crystal orthogonal to the optical axis

The analytical propagation functions for partially coherent vortex cosine-hyperbolic-Gaussian beams (PCvChGB) propagating through uniaxial crystal orthogonal to the optical axis are derived, and numerical examples analyze their spreading properties. It's shown that the intensity distribution of the PCvChGB is astigmatic and related to the initial beam parameters, namely the decentered parameter b and topological charge M, the coherence length σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sigma_{0}$$\end{document}, and the ratio of refractive index nenen0n0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{n_{e} } \mathord{\left/ {\vphantom {{n_{e} } {n_{0} }}} \right. \kern-0pt} {n_{0} }}$$\end{document}. The obtained results could be beneficial for application of partially coherent beam in anisotropic medium.