Propagation properties of radially polarized hyperbolic sine non-uniform coherent beams in atmospheric turbulence

We investigate the evolution of radially polarized hyperbolic sine non-uniform coherent (RPHSNUC) beams propagating through atmospheric turbulence. Based on the ordinary Huygens–Fresnel principle, we derive the analytical expressions for the spectral intensity and the spectral degree of polarization in atmospheric turbulence. Numerical calculations are conducted to systematically analyze their propagation behaviors. The results reveal that RPHSNUC beams retain their self-focusing property even in turbulent media, while the focal position shifts toward the initial plane compared with the free-space case. Furthermore, RPHSNUC beams with smaller coherence lengths exhibit enhanced robustness against turbulence-induced distortions. These findings provide theoretical insights into the propagation mechanism of structured partially coherent vector beams in complex atmospheric environment, with potential applications for optical communications, optical trapping, and remote sensing.