Bisingular surface polaritons at the interface of two uniaxial media

In some anisotropic bulk media (for example, biaxial weakly absorbing crystals) there are special directions along which the plane wave field distribution has a singular profile of the form $\propto (\mathbf{n} \mathbf{r}) \exp(i q \mathbf{n} \mathbf{r})$. They are also known as Voigt waves. Similar singular profiles also arise in the theory of surface electromagnetic waves in anisotropic media. In this work we have considered surface polaritons at the interface of two, generally different, uniaxial media. Optic axis of both media is parallel to the interface. One of the specific solutions, called bisingular, greatly simplifies the dispersion equation for surface polaritons. In this case the analytical solution in closed form is found and existence conditions have been determined. It is shown that bisingular surface polariton exists only for certain angles between the optic axes, which are found from two cubic equations. All parameters of the bisingular surface polariton depend only on permittivities and this angle. If one medium is weakly anisotropic, or both media are almost the same then two angles exist. In the general case of two arbitrary media there can be from two to six such angles.