We report a theoretical investigation on polarization rotation and singularity evolution of focused fundamental Poincaré beams in free-space propagation and through isotropic and anisotropic Kerr nonlinear media. It is found that the optical nonlinearity enhances the polarization rotation of the focused beams during propagation. Furthermore, the anisotropy of optical nonlinearity causes the symmetry breaking of the polarization distribution. Further studies show that the C-point and L-line singularities of the lemon Poincaré beams do not change while propagating in free space or through the isotropic nonlinear Kerr medium. Interestingly, the anisotropic Kerr nonlinearity evokes the C-point singularity splitting, and the distortion and birth of L-line singularities. However, the total singularity index always remains the conservation within the light field, regardless of the optical nonlinearity.

中文翻译：

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基于各向异性Kerr非线性的基本庞加莱光束的偏振旋转和奇异演化

我们报告了关于聚焦的基本庞加莱光束在自由空间传播以及通过各向同性和各向异性Kerr非线性介质的偏振旋转和奇异演化的理论研究。发现光学非线性增强了传播过程中聚焦光束的偏振旋转。此外，光学非线性的各向异性导致偏振分布的对称破坏。进一步的研究表明，柠檬庞加莱光束的C点和L线奇点在自由空间或各向同性非线性Kerr介质中传播时不会改变。有趣的是，各向异性的Kerr非线性会引起C点奇异性分裂，以及L线奇异性的扭曲和诞生。然而，