ELECTROSTATIC SURFACE SHAPE RESONANCES OF A FINITE NUMBER OF RIDGES

The resonance properties of localized electrostatic surface modes asso ciated with a finite number of ridges on an otherwise planar surface a re investigated. Numerical solutions of the homogeneous integral equat ions that describe the electromagnetic fields in the vicinity of the r idges are used to obtain the dispersion relation of surface plasmons. The frequencies of the electrostatic surface shape resonances are calc ulated for ridges with Gaussian, Lorentzian, sinusoidal, exponential, and triangular profiles. We show the existence of splittings of the pl asmon frequencies, which depends on the surface profile function and o n the distance between the ridges. Considering the ridge with a sinuso idal profile, we obtain the limit on the number of ridges which genera tes a frequency splitting of the electrostatic surface shape resonance s, whose frequency values converge to those of the dispersion relation of surface plasmons on one-dimensional sinusoidal grating.