Ponderomotive dynamics of waves in quasiperiodically modulated media

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.Comment: 14 pages, 2 figure

Parametric decay of plasma waves near the upper-hybrid resonance

“…[5,6], where field equations are derived by calculating ponderomotive on plasma particles, we propose an arguably more transparent formulation in terms of the plasma linear susceptibility. The fact that ponderomotive forces can be inferred from the linear susceptibility is widely known, for example, as the K-χ theorem [10][11][12][13][14]. We adopt a variational approach to utilize this link efficiently.…”

Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory

“…(Other U may also be justified in some cases, e.g., for dealing with caustics or quasiperiodic media [39], but we shall not consider this possibility in the present work.) The phase θ, which we call the "reference phase", serves as a gauge potential.…”

Quantum dynamics in potentials with fast spatial oscillations

“…We note that a related problem, as a specific case, was studied in Ref. [21], where ponderomotive dynamics was derived as an expansion with respect to the inverse wavenumber k −1 . However, here we are interested in the regime of large oscillation amplitude [in comparison to the particle recoil energy 2 /(2m 2 )].…”