Eigenvalues and eigenvectors of general gyroelectric media

Explicit and relatively simple expressions for eigenvalues and guided (propagating) eigenvectors of a general gyroelectric medium, where the preferred guided wave direction, zˆ, is parallel to the gyrotropic axis and anisotropy is confined to a plane transverse to z, are given. Some special cases of interest, namely, Hermitian, symmetric (biaxial), and uniaxial permittivity tensors, are also considered. The natural, or optic, coordinate basis is used to derive the source-free eigenvectors and to explicitly reveal the polarization states of those eigenvectors. Also under this basis, the evolution of eigenvalues and eigenvectors as off-diagonal terms of the permittivity tensor uniformly vanish, a transition from the biaxial to the uniaxial case, is discussed