Influence of the Electron Charge Distribution on Surface-Plasmon Dispersion

The effects of the spatial variation of the electron density on the surface-plasmon dispersion relation are investigated. We show that measurements of that relation are a useful probe of the electron density in the surface region. Previous calculations on homogeneous materials have predicted a linear or quadratic dependence of the frequency on momentum parallel to the surface. We find that the usual surface-plasmon resonance frequency at first decreases with increasing momentum and then increases with further increases in momentum. This behavior agrees with the experimentally observed dispersion. Additional higher-frequency surface modes, similar to those observed in laboratory plasmas, are identified.