Mode scattering reciprocity relations in waveguides with (bi)anisotropic media

Abstract

In an earlier paper [3] the scattering symmetries of an object imbedded in an infinite plane-stratified (bi)anisotropic (i.e. anisotropic or bianisotropic) medium were considered. The theorem is now extended to the case of a (bi)anisotropic object imbedded in a closed waveguide filled with some other (bi)anisotropic medium. Scattering matrix elements relate amplitudes of scattered waveguide modes a to those of incident modes each mode being associated with a corresponding wavenumber, or If the media of the scattering object and the waveguide are replaced by the corresponding Lorentz-adjoint (complementary) media and all modes are time-reversed, so that an outgoing wave (scattered) mode in the given medium becomes an incoming (incident) mode in the Lorentz-adjoint medium, it is shown that the time-reversed modes are eigenmodes of the Lorentz-adjoint medium, and the corresponding Lorentz-adjoint scattering matrix in this medium, equals the transposed, time-reversed scattering matrix in the original medium.