Hermitian Formulation of a Plasmonic Band Theory for One-dimensional Plasmonic Crystals

Abstract

An analytic theory for the band structure of surface plasmon polaritons in a one-dimensional corrugated metal surface is constructed. We construct a perturbation theory by regarding the surface corrugation as a perturbation. A hermitian eigenvalue equation is obtained from the matching conditions of electromagnetic fields. Hermiticity of the eigenvalue equation determines the condition for radiation of surface plasmon polaritons. Solutions of the equation are derived, and dependences on the perturbation coincide with those in the electronic band theory in solids.