Statistical properties of a partially coherent radially polarized vortex beam propagating in a uniaxial crystal.

Free-space propagation and experimental generation of a partially coherent radially polarized (PCRP) vortex beam were studied recently [Opt. Express24, 13714 (2016)OPEXFF1094-408710.1364/OE.24.013714]. In this work, we explore the statistical properties of such a PCRP vortex beam propagating in a uniaxial crystal. We show that the anisotropy of the refractive index of the uniaxial crystal induces the asymmetrical distribution of the intensity, the degree and the state of polarization, as well as the degree of coherence of the beam during propagation. Further, by comparing the asymmetrical distribution of the statistical properties of the PRCP vortex beam with those of a PRCP beam without a vortex phase, we find that the asymmetrical features can be used for determining whether a PCRP beam carries the vortex phase. Further, we show that from the far-field distribution of the degree of coherence, we could quantify the topological charge and distinguish the handedness of the vortex phase. Our findings provide a novel approach for measuring the phase information of the partially coherent vortex beams.