Scaling behavior and surface-plasmon modes in metal-insulator composites

The ac dielectric response of metal-insulator composites is studied numerically, using the transfer-matrix algorithm of Derrida and Vannimenus. For two-dimensional random composites with site percolation, we verify numerically that the effective dielectric function can be written numerically in the form εₑ/ε₁=ξ^-t/ν{G}_{±{}}$((${{{ε}}}₂$/${{{ε}}}₁$)${{ξ}}^{(t+s)/{ν}}ξ/L, where{{ε}}₁$ and ${{ε}}₂are the dielectric functions, ξ is the correlation length, L is the system size (or wavelength of the electric field),{G}₊$ and ${G}_{{{-}}}$ are universal functions above and below percolation, and t, s, and {ν} are standard percolation exponents. A similar form has been previously verified for bond percolation by Bug et al. We also study surface-plasmon resonances in a two-dimensional lattice model of a composite of Drude metal and insulator. The effective conductivity of the composite in this case is found to consist of a Drude peak which disappears below the metal percolation threshold, plus a band of surface-plasmon states separated from zero frequency by a gap which appears to vanish near the percolation threshold. The results in this case agree qualitatively with effective-medium predictions. The potential relation of these results to experiment, and the possibility of a Lifshitz tail in the surface-plasmon density of states, are briefly discussed.