The Hopfield-Kerr model and analogue black hole radiation in dielectrics

TL;DR

This paper develops a nonlinear, covariant Hopfield model to describe dielectric Kerr perturbations and investigates analogue Hawking radiation and thermal effects in this context.

Contribution

It introduces a nonlinear, relativistically covariant Hopfield model for dielectric Kerr perturbations, extending previous scalar models and analyzing analogue black hole radiation.

Findings

Exact solutions for nonlinear dielectric perturbations

Evidence of analogue Hawking radiation in the model

Discussion of thermal properties confirming previous scalar results

Abstract

In the context of the interaction between the electromagnetic field and a dielectric dispersive lossless medium, we present a non-linear version of the relativistically covariant Hopfield model, which is suitable for the description of a dielectric Kerr perturbation propagating in a dielectric medium. The non-linearity is introduced in the Lagrangian through a self-interacting term proportional to the fourth power of the polarization field. We find an exact solution for the nonlinear equations describing a propagating perturbation in the dielectric medium. Furthermore the presence of an analogue Hawking effect, as well as the thermal properties of the model, are discussed, confirming and improving the results achieved in the scalar case.