Ponderomotive dynamics of waves in quasiperiodically modulated media

TL;DR

This paper develops a covariant variational theory describing how linear waves in nondissipative media are affected by high-frequency modulations, unifying classical and quantum wave dynamics.

Contribution

It introduces a novel theoretical framework for ponderomotive effects on waves, applicable to a broad class of media and including quantum particles and photons.

Findings

Derivation of a covariant variational theory for wave ponderomotive effects

Demonstration that waves act as polarizable entities influencing the dielectric tensor

Calculation of ponderomotive Hamiltonians for quantum particles and photons

Abstract

Similarly to how charged particles experience time-averaged ponderomotive forces in high-frequency fields, linear waves also experience time-averaged refraction in modulated media. Here we propose a covariant variational theory of this "ponderomotive effect on waves" for a general nondissipative linear medium. Using the Weyl calculus, our formulation accommodates waves with temporal and spatial period comparable to that of the modulation (provided that parametric resonances are avoided). Our theory also shows that any wave is, in fact, a polarizable object that contributes to the linear dielectric tensor of the ambient medium. The dynamics of quantum particles is subsumed as a special case. As an illustration, ponderomotive Hamiltonians of quantum particles and photons are calculated within a number of models. We also explain a fundamental connection between these results and the commonly known expression for the electrostatic dielectric tensor of quantum plasmas.