Plane Electromagnetic Waves in Isotropic, Homogeneous, Linear Media

Material media typically react to electromagnetic fields by becoming polarized or magnetized, or by developing charge- and current-density distributions within their volumes or on their surfaces. The response of a material medium to the fields could be complicated, as would be the case, for instance, when the relation between induced polarization and the electric field is non-local, non-linear, or history-dependent, or when the induced magnetization is an anisotropic function of the local magnetic and/or electric fields. In many cases of practical interest, however, the media are homogeneous, isotropic, and linear, with the electric dipoles responding only to the local E-field (and magnetic dipoles responding only to the local H-field) in accordance with the Lorentz oscillator model of the preceding chapter. Irrespective of the manner in which the charge-carriers or the dipoles of the medium respond to the fields, there is always an additional complication that the fields are not merely those imposed on the medium from the outside. The motion of the charges and/or the oscillation of the dipoles in response to the fields give rise to new electromagnetic fields, which must then be added to the external fields before the induced charge, current, polarization, or magnetization can be computed. In other words, the entire system of interacting fields and sources, whether originating outside or induced within the media, must be treated self-consistently. This chapter provides a detailed analysis of plane-wave propagation within the simplest kind of material media, namely, those that are homogeneous and isotropic, whose induced electric dipoles are linear functions of the local E-field, and whose induced magnetic dipoles are linear functions of the local H-field.