Derivation of Hawking radiation in dispersive dielectric media

TL;DR

This paper provides a relativistic microscopic derivation of Hawking radiation analog in a nonlinear dielectric medium, revealing a frequency-dependent spectrum and confirming the temperature's relation to surface gravity.

Contribution

It offers the first analytic derivation of Hawking radiation in a dielectric medium using the Hopfield model, including the gray-body factor and nonthermal spectrum.

Findings

Hawking temperature matches surface gravity analog

Discovery of a frequency-dependent gray-body factor

Nonthermal spectrum at infinity

Abstract

Motivated by recent experimental efforts, we study a black hole analog induced by the propagation of a strong laser pulse in a nonlinear dielectric medium. Based on the Hopfield model (one pair of Sellmeier coefficients), we perform an analytic and fully relativistic microscopic derivation of the analog of Hawking radiation in this setup. The Hawking temperature is determined by the analog of the surface gravity (as expected), but we also find a frequency-dependent gray-body factor (i.e., a nonthermal spectrum at infinity) due to the breaking of conformal invariance in this setup.