The electrodynamics of magneto-electric media

Abstract

A general magneto-electric medium is one in which there is a linear, reciprocal relationship between the magnetic field and the electric polarization, and between the electric field and the magnetic polarization, as well as the more familiar linear relationship between the magnetic field and the magnetic polarization and between the electric field and electric polarization. In this paper the relationship between the fields and polarizations is expressed by means of a single tensor equation relating the field and polarization tensors in the medium. The properties of the rank four susceptibility tensor, required to establish this relationship, are investigated. A general tensor wave equation is obtained for a homogeneous anisotropic medium. The equation to the wave vector surface is obtained as a six by six determinant, which must vanish, and which gives well-known results when applied to simple anisotropic dielectric, or magnetic, crystals. When this equation is applied to an ideal magneto-electric medium, in which the magnetic and electric susceptibilities may be neglected, the conclusion is reached that waves of constant amplitude cannot propagate in a magneto-electric medium. If propagation takes place at all the waves will have either positive or negative damping due to an exchange of energy between waves having perpendicular planes of polarization.