Abstract
We propose an analytical two-band model for surface plasmon polaritons on corrugated metal surfaces. The generalized eigenvalue equation is derived from Maxwell's equation and matching conditions for electromagnetic fields at the metal surface. Our basic equation is Hermitian for the bands outside of the light cone and perturbation theory is therefore justified. We solve the equation and show the dispersion of the one-dimensional plasmonic crystal, and compare the behaviors of eigenfrequencies with previous works for analytic plasmonic crystals and the band theory for electrons in solids.
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