Studying the polarization of paraxial beams propagating through uniaxial anisotropic crystals at an arbitrary angle is a powerful feature to extend the range of utilization of these crystals. In this paper, we derive a general theoretical model, based on the existing theory, to describe the transformations of polarization state in cases of arbitrary beam propagation. Stokes parameters are employed for the determination of polarization state of the light beam. The derived model is applied to a linearly polarized quasi-Gaussian beam propagating through rutile crystal. The dependence of the polarization state of the beam on many parameters such as beam waist, angle of propagation, and thickness of the crystal is investigated. The variation of each of these parameters leads to an extensive and interesting change of the polarization state. Moreover, the results are employed to observe the variations of the spin angular momentum as a function of the above-mentioned parameters. Furthermore, we report on an interesting result regarding the longitudinal component of the propagating field, where we noticed the existence of clearly non negligible values of this component for certain propagation parameters. The results of the current work are promising and can be utilized to obtain the best functioning of the output beam depending on its shape and polarization. In addition, they are promising for other future applications such as designing polarization-based devices which are useful in many fields.

研究以任意角度通过单轴各向异性晶体传播的近轴光束的偏振是扩展这些晶体利用范围的强大功能。在本文中，我们基于现有理论推导出一个通用的理论模型来描述任意光束传播情况下的偏振态变换。斯托克斯参数用于确定光束的偏振状态。导出的模型应用于通过金红石晶体传播的线性偏振准高斯光束。研究了光束偏振态对光束腰、传播角度和晶体厚度等许多参数的依赖性。这些参数中的每一个的变化都会导致偏振态发生广泛而有趣的变化。而且，结果用于观察作为上述参数的函数的自旋角动量的变化。此外，我们报告了一个关于传播场纵向分量的有趣结果，我们注意到对于某些传播参数，该分量存在明显不可忽略的值。当前工作的结果很有希望，可用于根据其形状和偏振来获得输出光束的最佳功能。此外，它们有望用于其他未来应用，例如设计在许多领域有用的基于极化的设备。我们报告了一个关于传播场纵向分量的有趣结果，我们注意到对于某些传播参数，该分量存在明显不可忽略的值。当前工作的结果很有希望，可用于根据其形状和偏振来获得输出光束的最佳功能。此外，它们有望用于其他未来应用，例如设计在许多领域有用的基于极化的设备。我们报告了一个关于传播场纵向分量的有趣结果，我们注意到对于某些传播参数，该分量存在明显不可忽略的值。当前工作的结果很有希望，可用于根据其形状和偏振来获得输出光束的最佳功能。此外，它们有望用于其他未来应用，例如设计在许多领域有用的基于极化的设备。