Propagation of electromagnetic waves in linear media and pseudo-hermiticity

Abstract

We express the electromagnetic field propagating in an arbitrary time-independent non-dispersive medium in terms of an operator that turns out to be pseudo-Hermitian for Hermitian dielectric and magnetic permeability tensors (epsilon) over left right arrow and (mu) over left right arrow. We exploit this property to determine the propagating field. In particular, we obtain an explicit expression for a planar field in an isotropic medium with (epsilon) over left right arrow = epsilon(1) over left right arrow and mu = mu(1) over left right arrow varying along the direction of the propagation. We also study the scattering of plane waves due to a localized inhomogeneity.