Generalization of an Eigemnode Scattering Theorem

Abstract

A (bi)anisotropic scattering object is imbedded in a plane-stratified anisotropic or bianisotropic medium. Scattering matrix elements Sαβ(k_t, k_t) relate amplitudes of outgoing eigenmodes α of the host medium to incoming eigenmodes β, and are defined in terms of the projections of the incident and scattered wave vectors, k and k', , on the stratification plane. If the media of the scattering object and its environment are replaced by the Lorentz-adjoint media, and all modes are time-reversed, so that an outgoing wave in the given medium becomes an incoming wave in the the adjoint medium, it is found that the time-reversed modes are eigenmodes of the Lorentz-adjoint medium. Furthermore, the scattering matrix S^(L)(-k_t, -k_t') in this medium equals the transposed scattering matrix S^T (k_t', k_t) in the given medium. In the limiting case where the (bi)anisotropic medium becomes homogeneous this yields a straightforward eigenmode generalization of a scattering theorem due to Kerns.