Radially polarized partially coherent beams with prescribed sinh-Gauss non-uniform correlation structure

We introduce a kind of radially polarized partially coherent beam with a prescribed sinh-Gauss non-uniform correlation structure, named a radially polarized sinh-Gauss non-uniformly correlated (RPSNC) beam. Utilizing the ordinary Huygens-Fresnel principle, we derive the analytical formulas for the spectral intensity and the spectral degree of polarization (DOP) in free space and investigate the beam's propagation properties through numerical simulations. The results demonstrate that RPSNC beams exhibit a self-focusing property during propagation, with the focal position adjustable by varying the coherence length. Additionally, the spectral DOP in the central region forms a distinctive single-ring structure as the beam propagates. These unique properties make RPSNC beams promising for applications in free-space optical communications, beam shaping, and optical trapping.