球坐标下麦克斯韦方程组的解
Solutions to Maxwell's Equations using Spheroidal Coordinates
摘要：
在短波长极限的球坐标系中的波动方程的解析解。径向函数的渐近解被显著简化，允许标量球波函数被定义为一种形式，它直接让人想起光学中傍轴波动方程的拉盖尔-高斯解。标量球波函数的笛卡尔导数的表达式推导，导致一组新的矢量解麦克斯韦方程组。这些结果是计算近轴近似修正的理想出发点。
英文摘要：
Analytical solutions to the wave equation in spheroidal coordinates in the short wavelength limit are considered. The asymptotic solutions for the radial function are significantly simplified, allowing scalar spheroidal wave functions to be defined in a form which is directly reminiscent of the Laguerre-Gaussian solutions to the paraxial wave equation in optics. Expressions for the Cartesian derivatives of the scalar spheroidal wave functions are derived, leading to a new set of vector solutions to Maxwell's equations. The results are an ideal starting point for calculations of corrections to the paraxial approximation.
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