Surface Plasmons in Thin Films

Abstract

The dispersion relations for surface plasma oscillations in normal metals are investigated for single- and multiple-film systems taking retardation effects into account. The simple dielectric function $\epsilon \left(\omega \right)=1-\frac{{{\omega }_p}^2}{{\omega }^2}$ is found to be adequate for the high-frequency region in which oscillations remain undamped. Two types of possible modes of oscillation are found. One type corresponds to dispersion relations which behave linearly for not-so-high frequency, with a phase velocity always smaller than the velocity of light in the dielectric, but at least ten times larger than the Fermi velocity, while the other type consists of high-frequency modes ($\omega \sim {\omega }_p$). The role of these oscillations in the problem of transition radiation is reexamined. In the case of a thin metal film, a new interpretation is proposed for the peak observed in the transition radiation spectrum. Finally, the work is extended to superconducting metals where, in the frequency range $\hslash \omega <2\mathrm{}\Delta$ ($2\Delta$ is the superconducting energy gap), we have justified the use of a dielectric function of the same functional form as given above but with ${{\omega }_p}^2$ replaced by an almost frequency-independent quantity ${{\omega }_{\mathrm{ps}}}^2$, where ${\omega }_{\mathrm{ps}}=\frac{c}{{\lambda }_{\mathrm{ps}}}$ and ${\lambda }_{\mathrm{ps}}$ is the actual penetration depth. In this frequency range, the oscillations are essentially undamped and play an important role in the electromagnetic properties of the multiple-film systems, and particularly when the systems exhibit the ac Josephson effect.