Flow of Energy from a Localized Source in a Uniform Anisotropic Medium

Show that the flow of electromagnetic energy far from localized, time-dependent sources in a uniform, linear anisotropic dielectric medium is purely radial, despite the complexity of the wavefronts. Thus, the waves are transverse electromagnetic (TEM) in this region, although the electric displacement D has a longitudinal component in general. It suffices to consider sources with time dependence e−iωt near the origin in a medium with unit (relative) permeability and (relative) symmetric dielectric tensor ij that is diagonal with respect to the axes (x, y, z). Then, the electric displacement vector D and electric field vector E are related by Di = iEi, i = x, y, z, (1)