We present an analytical solution to the nonparaxial propagation of a Gaussian beam, which is based on the asymptotic expansion of a highly oscillatory integral. The advantage of this method is its application to a highly nonparaxial beam and large transverse radius regime, which are hard to reach by previous approximations. The validity of this analytical expansion is fully investigated, by benchmarking it against the accurate numerical solutions. We extend this method to deduce the analytical expression for a nonparaxial optical field in uniaxial crystals, from which we reveal the vortex generation in each component of the optical field and discuss their evolution dynamics. Moreover, we study the optical power exchange between two circular components of a nonparaxial field. We find that the powers carried by both components undergo a saturation and become equal as the propagating distance increases.

中文翻译：

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单轴晶体中的高度非近轴传播和光功率交换：分析和数值研究

我们提出了高斯光束的非近轴传播的解析解，它基于高度振荡积分的渐近展开。这种方法的优点是它适用于高度非近轴光束和大横向半径区域，这是以前的近似难以达到的。通过将其与准确的数值解进行对比，充分研究了这种分析扩展的有效性。我们扩展了这种方法来推导出单轴晶体中非近轴光场的解析表达式，从中我们揭示了光场中每个分量的涡旋产生并讨论了它们的演化动力学。此外，我们研究了非近轴场的两个圆形分量之间的光功率交换。