In this paper, we discuss, both analytically and numerically, the paraxial propagation of the radially polarized Laguerre-Gaussian-correlated Schell-model (LGCSM) beams orthogonal to the optical axis in uniaxial crystals. The analytical expression for the cross-spectral density function and the second-order moments of the radially polarized LGCSM beams are derived, and the evolution properties of the normalized intensity distribution, the spectral degree of the coherence (SDOC), and the spectral degree of the polarization (SDOP) in uniaxial crystals are elucidated by numerical examples. It is found that the intensity distribution of the radially polarized LGCSM beams evolves from a doughnut shape into a solid shape and finally converts into an elliptical symmetric hollow-ring profile in uniaxial crystals due to the combined effect of special correlation functions and the anisotropy effect of the uniaxial crystals. The evolution of the SDOC and SDOP for the radially polarized LGCSM beams is quite different from that of the radially polarized Gaussian-Schell-model beams. In addition, the propagation properties of the radially polarized LGCSM beams are closely related to the spatial coherence length, the mode order, and the ratio of extraordinary and ordinary reflective indices. The results show that the uniaxial crystals could modulate the evolution properties of the radially polarized LGCSM beams.

中文翻译：

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在单轴晶体中传播的径向偏振Laguerre-Gaussian相关Schell模型光束的演化特性。

在本文中，我们在分析和数值上都讨论了单轴晶体中与光轴正交的径向偏振Laguerre-Gaussian相关Schell模型（LGCSM）光束的近轴传播。推导了径向偏振LGCSM光束的跨谱密度函数和二阶矩的解析表达式，并归一化了强度分布，相干光谱度（SDOC）和光谱度的演化特性。数值例子说明了单轴晶体的极化（SDOP）。研究发现，由于特殊的相关函数和各向异性效应的共同作用，径向偏振的LGCSM光束的强度分布从甜甜圈形演化为固态，最后转变为单轴晶体的椭圆对称空心环轮廓。单轴晶体。径向偏振的LGCSM光束的SDOC和SDOP的演变与径向偏振的高斯-谢尔模型光束的演变完全不同。另外，径向偏振的LGCSM光束的传播特性与空间相干长度，模式阶数以及非常规和常规反射率之比密切相关。结果表明，单轴晶体可以调节径向偏振LGCSM光束的演化特性。