Exact results on analogue gravity in optical Plebanski-Tamm media

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.