Eigenfunctional representation of dyadic Green's functions in multilayered gyrotropic chiral media

Abstract

Studying electromagnetic waves in complex media has been an important research topic due to its useful applications and scientific significance of its physical performance. Dyadic Green's functions (DGFs), as a mathematical kernel or a dielectric medium response, have long been a valuable tool in solving both source-free and source-incorporated electromagnetic boundary value problems for electromagnetic scattering, radiation and propagation phenomena. A complete eigenfunctional expansion of the dyadic Green's functions for an unbounded and a planar, arbitrary multilayered gyrotropic chiral media is formulated in terms of the vector wavefunctions. After a general representation of Green's dyadics is obtained, the scattering coefficients of Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of Green's dyadics and their scattering coefficients, three cases are considered, i.e. the current source is immersed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for an unbounded gyroelectric medium has been reported in the literature, we here present not only unbounded but also multilayered DGFs for the gyrotropic chiral media. The explicit representation of the DGFs after reduction to the gyroelectric or isotropic case agrees well with those existing corresponding results.