Plasmonic modes at inclined edges of anisotropic two-dimensional materials

Confined modes at the edge arbitrarily inclined with respect to optical axes of nonmagnetic anisotropic 2D materials are considered. By developing the exact Wiener-Hopf and approximated Fetter methods we studied edge modes dispersions, field and charge density distributions. The 2D layer is described by the Lorentz-type conductivities in one or both directions, which is realistic for natural anisotropic 2D materials and resonant hyperbolic metasurfaces. We demonstrate that, due to anisotropy, the edge mode exists only at wave vectors exceeding the nonzero threshold value if the edge is tilted with respect to the direction of the resonant conductivity. The dominating contribution to field and charge density spatial profiles is provided by evanescent 2D waves, which are confined both in space near the 2D layer and along the layer near its edge. The degree of field confinement along the layer is determined by wave vector or frequency mismatch between the edge mode and continuum of freely propagating 2D modes. Our analysis is suitable for various types of polaritons (plasmon, phonon, exciton polaritons, etc.) at large enough wave vectors. Thanks to superior field confinement in all directions perpendicular to the edge these modes look promising for modern plasmonics and sensorics.