球形分层媒质中并矢格林函数的求解Ⅰ:并矢格林函数的推导

Solving Dyadic Green's Functions for Spherically Multilayered Media Ⅰ:Introduction of Dyadic Green's Functions

首先,在球坐标系下,通过德拜位函数得到均匀各向同性介质中矢量波动方程的解。然后,分析了内、外向波的单界面和多层界面的反射和透射,得到了相应的反射系数和透射系数以及广义反射系数和透射系数。接着,推导了δ源在球形分层介质中的不同位置产生的德拜位。最后,根据得到的德拜位,用球坐标系下的矢量波函数表达出场点在不同位置时的电并矢格林函数和磁并矢格林函数。

Firstly, the solutions of vector wave equation in isotropic medium are obtained by the Debye potential func- tions under the spherical coordinates. Then, the reflection and transmission process of in-coming and out-going waves in sin- gle layer and in spherically multilayered media are analyzed, and the corresponding reflection coefficients, transmission coef- ficients, the generalized reflection coefficients and generalized transmission coefficients are gained. Next, the Debye func- tions produced by 8 source at different places in spherically muhilayered media are achieved. Finally, the electric type of dy- adic Green＇ s functions and the magnetic type of dyadic Green＇ s functions are expressed by the vector wave functions under the spherical coordinates based on the Debye potential functions obtained.