Dispersive dielectrics and time reversal: Free energies, orthogonal spectra, and parity in dissipative media

Abstract

Free energies of dissipative media are reviewed. Then we use free-energy-optimal excitation and de-excitation fields to generate a dielectric's time-reversal spectrum, with several properties: a) The spectrum generalizes the time-reversal parity from "even" and "odd" of conservative systems to an interval [-1,+1] of "time-reversal eigenvalues" λ in dissipative media. b) It yields eigenmodes that are complete: any state of the medium is optimally excitable or de-excitable by them. c) These excitations are orthogonal with respect to the work function of the medium and, so, d) characterize field excitations for the given medium that, when superimposed, only do work on the medium, not on each other via the medium-field interaction mechanism. Notions of en masse potential and kinetic energy in the dissipative medium arise through even (λ=+1) and odd (λ=-1) parity, but also other energy notions via alternative parity (|λ|<1) under time reversal.