半空间电场型并矢格林函数及其数值计算

从均匀介质中偶极子的辐射场出发,通过谱域展开,推导出半空间的电场型并矢格林函数谱域积分(索末菲尔德积分)形式的完整表达,包括场点与源点处于同侧或异侧时对应的格林函数,重点讨论了场点和源点在垂直方向重合时的结果及其物理解释,排除了一般表达式在场源横向距离为零时会出现奇异性的问题。通过严格的数值积分方法计算半空间分界面的场分布来对公式的正确性进行了检验。

Electric-Field-Type Dyadic Green's Functions for Half-Spaces and It's Evaluation

In this paper, complete spectral integral representations (Sommerfeld integrals) of the electric-field-type dyadic Green's functions for half-space were derived via spectral-domain expansion of the radiation field of dipole located in free space. The Green's functions of reflection or transmission electric field were given, corresponding to the case of source point and observation point located in the same side or the opposite side, respectively. Especially, the results and physical explains were given for source point and observation point overlapping in vertical direction, which eliminate the singularities arising in the general representations. Numerical computation results show the validity of the presented formulas.