Free-space propagation and experimental generation of a partially coherent radially polarized (PCRP) vortex beam were studied recently [Opt. Express 24, 13714 (2016) [CrossRef] ]. 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.

中文翻译：

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在单轴晶体中传播的部分相干径向偏振涡旋光束的统计特性

最近研究了部分相干径向偏振（PCRP）涡旋光束的自由空间传播和实验生成[Opt。快递24，13714（2016）[交叉引用] ]。在这项工作中，我们探索了这种在单轴晶体中传播的PCRP涡旋光束的统计特性。我们表明，单轴晶体折射率的各向异性会引起强度，偏振度和偏振态以及光束在传播过程中的相干度的不对称分布。此外，通过比较PRCP涡旋光束的统计特性与不具有涡旋相位的PRCP光束的统计特性的不对称分布，我们发现该不对称特征可用于确定PCRP光束是否带有涡旋相位。此外，我们表明，从相干程度的远场分布中，我们可以量化拓扑电荷并区分旋涡相的顺手性。