Green’s tensors and associated potentials for electromagnetic waves in inhomogeneous material media

Abstract

The explicit form of the Green’s tensor in unbounded inhomogeneous dielectric, magnetic and partly conducting material is obtained. The tensor is given explicitly in terms of two scalar Green’s function potentials, each of which obeys its own wave equation. It is found that the gradients of the constitutive parameters at the source of the radiating currents may have a strong effect on the multipolar field. For example, an electric dipole embedded in a uniaxially inhomogeneous source-zone is found to produce additional fields with the characteristics of electric quadrupole (l = 2, m = ± 1) and a magnetic dipole (l = 1, m = ± 1). I present a mathematical formulation of Huygens’ principle for inhomogeneous media in terms of the Green’s tensor and its associated tensor potentials, thus extending the use of the Green’s tensor to scattering problems in inhomogeneous finite domains.