Propagation properties of partially coherent array beams with a non-uniform polarization

We study a new class of partially coherent array beams with a non-uniform polarization, named radially polarized Gaussian Schell-model array (RPGSMA) beams and analyze the reliability conditions for the array beams based on the unified theory of coherence and polarization, Moreover, the statistical properties of such beam propagating in free space are investigated in detail. It is found that, the propagation properties of the RPGSMA beams are closely related to initial beam parameters. With an appropriate choice of the beam parameters, the average intensity will evolve into optical lattice patterns, and the degree of coherence (DOC) from the lattice distribution on the original plane evolves into a Gaussian profile in the far field, and the degree of polarization (DOP) appears a periodical grid-like distribution on propagation. These results may be beneficial to particle trapping and free-space optical communications.