  Surface polaritons in an anisotropic media posses a strong dependence of the
wavevector on the propagation direction, which is called the isofrequency
contour. This can lead to the fact that polariton propagation is possible only
in a limited range of angles in the boundary plane. Notable examples are
Dyakonov surface waves at the boundary of two dielectrics and hyperbolic
plasmons in a hyperbolic metamaterial. Exact closed-form solutions of the
polariton dispersion equation are known only in special cases: in a weakly
anisotropic medium, and in an arbitrary medium for highly symmetric directions
of polariton propagation. This work provides an universal exact solution in
algebraic form for surface polariton at the interface of an arbitrary isotropic
and an uniaxial media for the case of the optic axis parallel to the boundary.
As an example, it is used to analyze the shapes of isofrequency contours of
surface polaritons. The work brings together previously scattered results of
studies on surface polaritons of various types in uniaxial media. In addition
to the cases already considered in the literature, a solution for surface
polaritons at the boundary of a isotropic metal and a Type I hyperbolic medium
is found. The case of "elliptic" polaritons at the boundary of an anisotropic
metal-like medium is apparently analyzed here for the first time.
