Propagation of radially polarized beams with a Hermite non-uniformly correlated array in free space and turbulent atmosphere.

We introduce what we believe to be a novel class of radially polarized partially coherent beams in which the correlation function possesses a Hermite non-uniformly correlated array. The source parameter conditions required to generate a physical beam are derived. The statistical properties of such beam propagating in free space and turbulent atmosphere are thoroughly examined using the extended Huygens-Fresnel principle. It is shown that the intensity profile of such beams presents a controllable periodic grid distribution due to its multi-self-focusing propagation property and can keep the shape in free space while propagating in turbulent atmosphere, it exhibits self-combining properties over a long-ranges. Owing to the interaction between the non-uniform correlation structure and the non-uniform polarization, this beam can locally self-recover the polarization state after propagating a long distance in a turbulent atmosphere. Furthermore, the source parameters play essential roles in determining the distribution of spectral intensity, the state of polarization, and the degree of polarization of the RPHNUCA beam. Our results may benefit multi-particle manipulation and free-space optical communication applications.