On the Eigenfunction Expansions of the Dyadic Green's Functions for Bianisotropic Media

Abstract

This paper presents a novel approach for constructing the complete eigenfunction expansions of electric and magnetic dyadic Green's functions for general linear bianisotropic media. The eigenfunctions are expressed in terms of linear combinations of commonly employed solenoidal and irrotational vector wave functions. Based on the theory of distributions, the source point singularities required for complete expansions of the dyadic Green's functions are derived directly from Maxwell dyadic equations without any integration. Apart from the singularities, the discontinuities associated with the eigenfunction expansions across the source point are also obtained as by-products. These discontinuity relations constitute the fundamental equations from which the eigenfunction expansions outside the source point can be constructed. This approach is parallel to the utilization of Lorentz reciprocity theorem for relating eigenwaves with sources and it is applicable directly to both nonreciprocal as well as reciprocal media. Furthermore, the discontinuity relations also yield directly the jump conditions for electric and magnetic fields across a current sheet.