Electrostatic Edge Modes in a Dielectric Wedge

The dispersion relations are obtained for electrostatic modes localized in the vicinity of the edge of a dielectric wedge formed by the intersection of two semi-infinite planes making an interior angle of $2\alpha$. The dielectric constant of the medium is assumed to be isotropic. The resulting modes can be classifed as even or odd under reflection in the plane bisecting the wedge. Their frequencies are functions of one continuously varying quantum number. The general results obtained are specialized to yield the dispersion relations for edge optical modes and edge plasmons. Properties of dielectric edge modes are compared and contrasted with corresponding properties of surface modes.