Channel plasmons

We present a derivation, based on Green's theorem, of the exact dispersion relation for the electrostatic modes guided by a channel of finite width cut into the otherwise planar surface of a solid in contact with vacuum. The solid, which can be either a metal or a polar dielectric medium, is characterized by a real, isotropic, frequency-dependent dielectric constant {ε}({ω}). The results of numerical solutions of this dispersion relation are presented for two forms of the channel cross section.