Bisingular surface polaritons

Electromagnetic waves in anisotropic media (e.g., weakly absorbing biaxial dielectric crystals) have a singular profile of the form $\propto (\mathbf{n} \mathbf{r}) \exp(i q \mathbf{n} \mathbf{r})$ along special directions, they are also known as Voigt waves. Therefore, for such directions, the wave polarization depend on the coordinate. A similar singular form is possible for surface waves, but the conditions for its appearance are less strict. The boundary between two, generally different, uniaxial media is considered. Conditions have been determined under which a surface polariton can propagate along the boundary and has a field distribution of singular form in both media. The existence condition of a bisingular surface polariton strongly depends on the angle between the optic axes of the media. It is shown that in simple cases (one the media is almost isotropic, or two identical uniaxial media) a bisingular polariton exists only for a single angle between the optic axes. In general, for two arbitrary media there can be up to five such angles.