Uniaxial absorbing media: conditions for refraction in the direction of the optical axis

When a plane wave is incident from an isotropic medium into a uniaxial transparent medium so that the ordinary wave propagates in the direction of the optical axis, the extraordinary wave will also propagate in the same direction and with the same refractive index. We will show that this is not the case when the second medium is a uniaxial absorbing material. In this work, we will state a clear and precise interpretation of the meaning of propagation in the direction of the optical axis in the case of uniaxial absorbing media. Assuming that the ordinary wave is refracted in the direction of the optical axis we will analyze the refraction of the extraordinary wave and we will compare it with the case of transparent media. The necessary conditions to have both ordinary and extraordinary waves refracted in the direction of the optical axis will be obtained.