Far-infrared studies of two-dimensional random metal-insulator composites

Samples consisting of 10-μm squares of gold film (500 Å thick) are deposited as random two-dimensional (2D) arrays on sapphire substrates by using microfabrication techniques. The arrays represent a square lattice of the 2D site-percolation problem with a lattice constant of 10 μm. Far-infrared transmission and reflection spectra are measured between 8 and 92 ${\mathrm{cm}}^{\mathrm{-}1}$. A smooth change, rather than a sharp transition near the percolation threshold, is observed in the measured spectra. The experimental effective conductivity which is derived under the assumption that our sample looks homogeneous in the long-wavelength limit is shown to be different from the effective-medium-approximation prediction by several orders of magnitude. A scaling theory, based on the conductivity fluctuation near the percolation threshold, is found to give better description. However, there still exists a significant discrepancy between its prediction and the absorption spectra of our measurement, which we suggest is due to magnetic-dipole absorption.