Comparative analysis of two formulations of geometrical optics. The effective dielectric tensor

Abstract

Two apparently diverse formulations of geometrical optics relevant to space- and time-varying dispersive, anisotropic media are shown to be equivalent by virtue of the relationship between the effective dielectric tensor and the plane-wave dielectric tensor. As a counterpart of the wave kinetic equation governing the wave-action density in phase space, the equation for the transport of action density in physical configuration space is obtained, which entails, in particular, a wavepacket adiabatic invariant in the limit of which the effect of both dissipation and (internal and/or external) current-sources is negligible.