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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.
Alan J. Bennett (Thu,) studied this question.