On the propagation of electromagnetic waves in isotropic media that are both electrically and magnetically dispersive

Abstract

The response of a material to an electromagnetic field is governed by the frequency-dependent dielectric and magnetic parameters ϵ and μ. An analysis is presented of the storage and transport of energy in an electromagnetic wave passing through an isotropic non-dissipative dispersive medium. This is achieved by the use of electric circuits as analogues of the actual mechanisms within the medium that account for the dispersive behaviour. These analogue circuits are treated in a general way with the aid of Foster's Reactance Theorem. The energy within a polarized material consists of two parts: the strain energy, made up of the field and elastic energies, and the kinetic energy of the constituent particles. For an electric field e=Ecosωt it is shown that the mean, total, stored energy density is 14ϵ0E2d(ωϵ)/dω, an exact relation involving no approximations. Furthermore, the difference between the mean strain energy and the mean kinetic energy densities is 14ϵ0E2ϵ. Similar results hold in the magnetic case. The early results obtained by Abraham, and by Brillouin, are confirmed and extended. The models proposed for ϵ and μ admit of the possibility that either, or both, of these parameters may become negative at some frequencies. It is shown that the Poynting vector and the propagation vector are always parallel to one another provided that ϵ and μ have the same sign. The speed of energy transmission is calculated and is shown to differ from the group velocity. No support is found for the possibility of negative refraction by materials with negative ϵ and μ, however it is found that such materials would display unusual refractive properties.