Conditions for the concurrent refraction of the ordinary and extraordinary rays along the optical axis in absorbing uniaxial media

When a plane wave propagating in an isotropic medium is refracted in the interface with a uniaxial transparent medium in such a way that the ordinary ray propagates along the optical axis, then the extraordinary ray necessarily propagates along the optical axis too. In this situation the medium behaves as an isotropic medium with refractive index nω. In general this is not the case with absorbing uniaxial media unless some conditions are also fulfilled. In this work we obtain the necessary conditions that must be accomplished in order to have both the refracted ordinary and extraordinary rays propagating along the optical axis so that the uniaxial absorbing medium behaves like an isotropic one.