Spacetime geometries and light trapping in travelling refractive index perturbations

TL;DR

This paper explores how superluminal refractive index perturbations in Kerr media can be modeled as stationary Gordon-type metrics, revealing phenomena like ergospheres and geodesic behaviors relevant to light trapping.

Contribution

It demonstrates that such perturbations can be described by stationary metrics with ergospheres, extending transformation optics to dynamic, superluminal regimes with numerical analysis.

Findings

Identification of Gordon-type metrics for RIP in Kerr media

Presence of ergospheres in the modeled spacetime

Numerical analysis of geodesic behavior with dispersion

Abstract

In the framework of transformation optics, we show that the propagation of a locally superluminal refractive index perturbation (RIP) in a Kerr medium can be described, in the eikonal approximation, by means of a stationary metric, which we prove to be of Gordon type. Under suitable hypotheses on the RIP, we obtain a stationary but not static metric, which is characterized by an ergosphere and by a peculiar behaviour of the geodesics, which are studied numerically, also accounting for material dispersion. Finally, the equation to be satisfied by an event horizon is also displayed and briefly discussed.