Geometrical optics response tensors and the transport of the wave energy density

Abstract

Two forms of the transport equation for the wave energy density inherent in two (apparently diverse) formulations of geometrical optics (GO) are discussed on the basis of the relationships among the plane-wave dielectric tensor, the effective dielectric tensor and the effective conductivity tensor. For a generic space-and time-varying medium, a novel relationship between the dielectric tensor and the conductivity tensor is obtained whereupon the equivalence of the two GO formulations is established. The conditions for which either the wave action density or the wave energy density is conserved are discussed.

Axiomatic geometrical optics, Abraham-Minkowski controversy, and photon properties derived classically

“…(The term "optics" here means only that the theory deals with sufficiently large ω and k; i.e., waves need not be electromagnetic.) Although usually defined through rays and wave equations [71][72][73][74][75][76][77][78][79], the most fundamental, axiomatic GO is an abstract field theory that applies to any field having a Lagrangian density of a specific form [Eq. (11); dissipative effects can also be added, Sec.…”

Variational principles for dissipative (sub)systems, with applications to the theory of linear dispersion and geometrical optics

“…(Previously, it has been known that Weyl symbols emerge naturally in wave kinetics [57][58][59].) This can be considered as an invariant definition of ε (ω,k) , as opposed to ad hoc definitions used in literature that have been a source of a continuing debate [60][61][62].…”

On Variational Methods In the Physics of Plasma Waves

“…Equation (67) happens to constitute the essence of the so-called geometrical-optics (GO) approximation and can, in fact, be used as a definition of GO [2], alternative to the standard definition [61][62][63][64][65][66][67][68]. If understood this way, GO becomes a field theory, also broadly known as Whitham's theory.…”