Symmetries and scattering relations in plane-stratified anisotropic, gyrotropic, and bianisotropic media

Abstract

We consider plane-wave propagation in uniaxial anisotropic, gyrotropic or bianisotropic plane-stratified media, characterized by 6×6 constitutive tensors$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K}$ which relate the wave fieldsD andB toE andH. Biorthogonality of the given and adjoint eigenmodes is derived for all media. Seven different 6×6 diagonal matrices$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P}$ are considered, which either transform$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K}$ into its transpose (

), or leave it unchanged, each transformation being applicible to at least one of the media discussed. By applying the transformation to the corresponding adjoint propagation equations, it is shown that the solution of a given propagation problem leads to the formulation and solution of a “conjugate” problem, in which either, or both, of the tangential components of the propagation vector are reversed in sign. Some of the transformations converting$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K}$ to

lead to a reciprocity-type scattering relation, with positive-going waves in the given problem being related to negative-going waves in the conjugate problem. Some of the transformations leaving$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K}$ unchanged ($\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K} \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{P} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{K}$) lead to an equivalence relationship between scattering matrices in the two problem.

Interesting consequences with regard to the formulation of Lorentz-type reciprocity relations between currents and fields are envisaged.