入射平面电磁波两类球面波函数展开式的等价性证明

入射平面电磁波的球面波函数展开是求解不同圆球结构的平面波散射问题的重要工具,相关文献分别利用场的坐标分解和矢量势法得到了入射平面波的球面波函数的两种不同形式的展开式.利用偏微分方程边值问题解的存在唯一性定理,给出了这两种展开式的等价性的一个简洁的解析证明,并进行了数值验证.

Proof of the Equivalence Between Two Expansions of a Plane Wave Into Spherical Wave Functions

Expanding the incident plane wave with spherical wave functions is an important tool to solve scatter problems of a plane wave from different spherical structures.Two different kind of expansions can be obtained by the method of wave transformations and vector potential functions respectively in1].Especially,it points out that the equivalence between these two expansions is very difficult to be proved by the analytical method.In this paper,the equivalence is proved by the theorem on the existence and uniqueness of solutions of a partial differential equation with the boundary value problem.Moreover,the equivalence is shown by numerical simulations.