Based on the plane-wave angular spectrum representation, we derive a formal expression for any light fields propagating in biaxial crystals, and particularly, present an effective numerical method to investigate the propagation behavior for a Gaussian light beam. Unlike uniaxial crystals, we observe the intriguing formation, repulsion and disappearance of vortex pairs, as the refractive indices deviate slightly and gradually from the uniaxial limit. In the Minkowski angular momentum picture, we also investigate the orbital angular momentum dynamics for both left- and right-handed circularly polarized components. Of further interest is the revelation of nonconservation of the angular momentum within the light field during the spin-orbit interactions, and the optical torque per photon that the light exerts on the biaxial crystal is quantified. We interpret these interesting phenomena by the weakly broken rotational invariance of biaxial crystals. The self-consistency of our theory is confirmed by the balance equation describing the conservation law of total angular momentum of filed and crystal in the Minkowski picture.

中文翻译：

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在双轴晶体中传播的高斯光的自旋轨道相互作用。

基于平面波角谱表示，我们导出了在双轴晶体中传播的任何光场的形式表达式，尤其是，提出了一种有效的数值方法来研究高斯光束的传播行为。与单轴晶体不同，我们观察到涡流对的形成，排斥和消失，这是因为折射率从单轴极限轻微地逐渐偏离。在Minkowski角动量图中，我们还研究了左旋和右旋圆极化分量的轨道角动量动力学。进一步令人感兴趣的是在自旋轨道相互作用期间光场内角动量不守恒的揭示，并且量化了光施加在双轴晶体上的每个光子的光学转矩。我们通过弱断裂双轴晶体的旋转不变性来解释这些有趣的现象。我们的理论的自洽性由描述Minkowski图像中场和晶体的总角动量守恒律的平衡方程所证实。