Anisotropic surface polaritons at isotropic-uniaxial interface: an exact algebraic solution

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.