Surface effects on bulk plasmons.

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 L−1. The frequencies of low-lying long wavelength modes are given by the dispersion relation of bulk modes, ω = ωp[1 + α(q 2/k2 F )], where the allowed q-values are q(n) = (nπ/L), L ≡ L− 2db, and db is a complex length characteristic of the surface (reminiscent of but different from Feibelman’s d⊥). An explicit expression for db is derived. Resonant excitation by an external field, E0e −iωt, is calculated.