Exact results on analogue gravity in optical Plebanski-Tamm media

TL;DR

This paper derives exact Hamiltonian equations for ray tracing in Plebanski-Tamm optical media, demonstrating their application by modeling light trajectories in an analogue of G"odel's universe.

Contribution

It provides explicit Hamiltonian equations for electromagnetic wave propagation in Plebanski-Tamm media, advancing the understanding of optical analogues of curved spacetime.

Findings

Derived explicit Hamilton equations for ray tracing in Plebanski-Tamm media.

Applied the equations to model light trajectories in a G"odel universe analogue.

Demonstrated the feasibility of simulating complex spacetime geometries using optical media.

Abstract

Exact results concerning ray-tracing methods in Plebanski-Tamm media are derived. In particular, Hamilton equations describing the propagation of quasi-plane wave electromagnetic fields in the geometrical optics regime are explicitly written down in terms of the 3-metric representing the properties of the optical analogue, anisotropic medium. We exemplify our results by obtaining the trajectories of light in the resulting analogue medium recreating G\"odel's universe.