One difficulty of angular spectrum representation method in studying optical propagation inside anisotropic crystals is to calculate the double integrals containing highly oscillating functions. In this paper, we introduce an accuracy and numerically cheap method based on asymptotic expansion theory to overcome this difficulty, which therefore allows to compute optical fields with arbitrary incident beam and is not restricted to the paraxial limit. This numerical method is benchmarked against the analytical solutions in uniaxial crystals and excellent agreements between them are obtained. As an application, we adopt it to investigate the propagation of a Gaussian vortex-beam in a biaxial crystal. The general features of anisotropic dynamics and power conversion between field components are revealed. The numerical results is interpreted by making appropriate analytical approximation to the wave equations.

中文翻译：

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双轴晶体中光学涡旋光束传播的各向异性动力学：基于渐近展开的数值方法。

角谱表示法在研究各向异性晶体内部光传播方面的困难之一是计算包含高振荡函数的双积分。在本文中，我们介绍了一种基于渐近展开理论的精度高且价格便宜的方法来克服这一困难，因此可以计算具有任意入射光束的光场，并且不限于近轴极限。该数值方法以单轴晶体中的解析溶液为基准，并获得了它们之间的出色一致性。作为应用，我们采用它来研究高斯涡旋光束在双轴晶体中的传播。揭示了各向异性动力学和场分量之间功率转换的一般特征。