Multilayered media green's functions for MPIE with general electric and magnetic sources by the hertz potential approach

Abstract

A complete set of three dimensional multilayered media Green's functions is presentedfor general electric andmagnetic sources. The Green's functions are derived in the mixed potential form, which is identical with the Michalski-Zheng C-formulation. The approach appliedin this paper is basedon the classical Hertz potential representation. A special emphasis is on the formulation of the dyadic Green's functions ḠHJ and ḠEM. In these functions the derivatives due to the curl operator are taken in the spectral domain. This avoids the needof the numerical differentiation. Furthermore, it is foundthat the Hertzian potentials satisfy several useful duality and reciprocity relations. By these relations the computational efficiency of the Hertz potential approach can be significantly improvedandthe number of requiredSommerfeldintegrals can be essentially reuced. We show that all spectral domain Green's functions can be obtained from only two spectral domain Hertzian potentials, which correspond to the TE component of a vertical magnetic dipole and the TM component of a vertical electric dipole. The derived formulas are verified by numerical examples.