Surface plasmons in liquid mercury: Propagation in a nonuniform transition layer

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Abstract
We have examined the propagation of nonradiative surface plasmons in the presence of an inhomogeneous transition zone in the surface region of a conductor. The model we treat in the present paper is the Epstein stratified conductivity profile that has been proposed by Bloch and Rice for liquid mercury. Assuming that photon-plasmon coupling occurs through frustrated total reflection, we evaluate the optical response of mercury to surface-plasmon excitation and find it to be sensitive to the existence of such a zone. Measurements of the dispersion relation should, therefore, provide valuable information regarding the range and degree of such electronic inhomogeneity; preliminary measurements are in good agreement with the theory (Sec. VI). In addition to inhomogeneity in the conductivity of nearly-free electrons in the liquid metal, we have also investigated the effect of the localized resonances near the surface, and we speculate under what conditions the surface-plasmon dispersion relation may exhibit "anomalous dispersion" due to plasmon-localized-state interaction. Finally, the existence of an upper plasmon branch induced by the inhomogeneity is treated. In general, the results of the present investigation suggest that optical surface-plasmon spectroscopy should be a useful technique for the study of nonuniform conducting surfaces.