Anisotropic dynamics of optical vortex-beam propagating in biaxial crystals: a numerical method based on asymptotic expansion.

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.