索末菲型积分精确球面波函数展开方法的构成与应用

项目名称： 索末菲型积分精确球面波函数展开方法的构成与应用

项目编号： No.60871035

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 江滨浩

作者单位： 哈尔滨工业大学

项目金额： 27万元

中文摘要： 索末菲型积分是平面层状介质中格林函数的连续谱圆柱波函数的广义积分表达式。研究索末菲型积分的形成演化和有效计算方法是有助于提升诸多学科研究水平和内涵的基础性课题，近百年来它已受到众多学者的持续关注。 基于球坐标系统中本征波函数的离散谱性质和圆柱波函数与球面波函数的转换关系，本项目拟探索索末菲型积分的全新精确解析方法-球面波函数展开法。研究索末菲型积分结构和被积函数在复平面的分布特征，阐明各类波模式与奇点的关联关系和分解方法，利用积分变换和球波函数坐标变换等方法，分别推导索末菲型积分的精确球面波函数展开式和平面层状介质中反射问题的矢量球面波函数展开式，分析两种展开式的数学物理属性。 应用展开式，揭示平面层状中电磁波的传播规律，研究辐射和散射问题中并矢格林函数的优化使用，提出研究瞬态电磁场和（双）各向（异）同性介质的性质等复杂问题的新思路，为深入系统地研究相关问题奠定了坚实的理论基础。

中文关键词： 电磁场理论；平面层状介质；索末菲型积分；球面波函数展开

英文摘要： The general integral expressions of cylindrical wave functions in continuous spectrum for the Green's function in the planar stratified media are called as Sommerfeld type integrals. The derivation and the accurate efficient evaluation for the Sommerfeld type integrals serve as the foundation for promoting the level and connotation in many related fields and have drawn the persistent attention of many researchers in near 100 years. Based on the discrete spectrum expressions for eigenfunctions in a spherical coordinate system and with the help of the expansion of spherical wave functions for a cylindrical wave function, a novel and analytical approach, namely, the method of spherical wave functions expansion，is described for the evaluation of the Sommerfeld type integrals in this project. The structure of Sommerfeld integrals and the behavior of the integrand in the complex plane are investigated, and the relationship between the wave mode and the singularity of the integrand are illuminated. By using the transformation of the integration and spherical wave functions，the accurate expansion of the scalar and vector spherical wave functions are derived for the Sommerfeld type integrals and the Sommerfeld reflecting half-space problems，respectively; and the mathematical and physical properties of series expressions are analyzed. The expansion obtained are employed to analyze the radio waves propagation in the planar stratified and to optimize the dyadic Green's function in the planar stratified media for electromagnetic waves radiation and scattering; and the accurate and analytical expressions obtained can provide a good framework for understanding or explaining the physical concepts of the description of the time-varying electromagnetic fields and the character of bi-anisotropic media, and thus can give a good service to related investigations in theory and applications.

英文关键词： electromagnetic theory; stratified media；Sommerfeld type integral; expansion of spherical wave functions