We discuss the effects of surfaces on bulk plasma oscillations in a metallic film of thickness L. The leading corrections to the plasma frequencies due to the surfaces are proportional to ${\mathit{L}}^{\mathrm{-}1}$. The frequencies of low-lying long-wavelength modes are given by the dispersion relation of bulk modes, ω=${\mathrm{\omega }}_{\mathit{p}}$[1+α(${\mathit{q}}^2$/${\mathit{k}}_{\mathit{F}}^2$)], where the allowed q values are ${\mathit{q}}^{\left(\mathit{n}\right)}$=(nπ/L¯), L¯≡L-2${\mathit{d}}_{\mathit{b}}$, and ${\mathit{d}}_{\mathit{b}}$ is a complex length characteristic of the surface (reminiscent of, but different from, Feibelman’s ${\mathit{d}}_{\mathrm{\perp }}$). An explicit expression for ${\mathit{d}}_{\mathit{b}}$ is derived. Resonant excitation by an external field ${\mathit{E}}_0$${\mathit{e}}^{\mathrm{-}\mathit{i}\mathrm{\omega }\mathit{t}}$ is calculated.

• Received 2 July 1993

DOI:https://doi.org/10.1103/PhysRevB.48.12240