Scaling behavior and surface-plasmon resonances in a model three-dimensional metal-insulator composite

We calculate the ac dielectric function of a model Drude metal-insulator composite, using a three-dimensional (d=3) transfer-matrix algorithm. The real part of the effective conductivity, Re${\mathit{g}}_{\mathit{e}}$(ω), reveals (i) a Drude peak that appears only above the percolation threshold ${\mathit{p}}_{\mathit{c}}$; and (ii) a broad spectrum of surface-plasmon resonances whose lower edge approaches zero frequency at ${\mathit{p}}_{\mathit{c}}$. Sufficiently near ${\mathit{p}}_{\mathit{c}}$, the dielectric function is consistent with an expected scaling form previously verified in d=2. The surface-plasmon spectrum resembles effective-medium predictions except for a weak but persistent peak near 0.4ω/${\mathrm{\omega }}_{\mathit{p}}$.