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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.
Spherical wave function expansion of incident plane electromagnetic wave is an important tool to solve the problem of plane wave scattering of different spherical structures. Relevant documents use the coordinate decomposition of the field and the vector potential method respectively to obtain two different forms of expansion of the spherical wave function of the incident plane wave By using the existence and uniqueness theorem of the solution to the boundary value problems of partial differential equations, a concise analytical proof of equivalence of the two expansions is given and the numerical verification is carried out.