  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.
