Electrostatic surface shape resonances of a finite number of ridges

Abstract

The resonance properties of localized electrostatic surface modes associated with a finite number of ridges on an otherwise planar surface are investigated. Numerical solutions of the homogeneous integral equations that describe the electromagnetic fields in the vicinity of the ridges are used to obtain the dispersion relation of surface plasmons. The frequencies of the electrostatic surface shape resonances are calculated for ridges with Gaussian, Lorentzian, sinusoidal, exponential, and triangular profiles. We show the existence of splittings of the plasmon frequencies, which depends on the surface profile function and on the distance between the ridges. Considering the ridge with a sinusoidal profile, we obtain the limit on the number of ridges which generates a frequency splitting of the electrostatic surface shape resonances, whose frequency values converge to those of the dispersion relation of surface plasmons on one-dimensional sinusoidal grating.