A new technique for the derivation of closed-form electromagnetic Green's functions for unbounded planar layered media

Abstract

A closed-form electromagnetic Green's function for unbounded, planar, layered media is derived in terms of a finite sum of Hankel functions. The derivation is based on the direct inverse Hankel transform of a pole-residue representation of the spectral-domain form of the Green's function. Such a pole-residue form is obtained through the solution of the spectral-domain form of the governing Green's function equation numerically, through a finite-difference approximation, rather than analytically. The proposed methodology can handle any number of layers, including the general case where the planar media exhibit arbitrary variation in their electrical properties in the vertical direction. The numerical implementation of the proposed methodology is straightforward and robust, and does not require any preprocessing of the spectrum of the Green's function for the extraction of surface-wave poles or its quasi-static part. The number of terms in the derived closed-form expression is chosen adaptively with the distance between source and observation point as parameter. The development of the closed-form Green's function is presented for both vertical and horizontal dipoles. Its accuracy is verified through a series of numerical examples and comparisons with results from other established methods.