The propagation of electromagnetic waves in magnetoelectric crystals

Abstract

The propagation, of a plane electromagnetic wave in a magnetoelectric crystal is described by an eigenvalue equation in which the eigenvalue is the phase velocity of the wave and the eigenvector is the electric-field. The equation is first solved for the special case in which the dielectric tensor is real and diagonal, the magnetoelectric effect is absent and the magnetic susceptibility is zero. This leads to well-known results (e.g. the existence of double refraction). Perturbation theory is then used to consider the effect of including small additional terms. It is found that the imaginary part of the dielectric tensor leads to optical activity; the real part of the magnetoelectric tensor leads to a new optical effect in which an initially plane polarized wave progressively changes its state of polarization; the imaginary part of the magnetoelectric tensor also leads to optical activity. These results are compared with those of Brown, Shtrikman and Treves who considered wave propagation in a medium in which the dielectric displacement depends on both the electric field and its spatial derivatives.