Theory of the optical and microwave properties of metal-dielectric films

We present a detailed theoretical study of the high frequency response (optical, infrared, and microwave) of thin, metal-dielectric inhomogeneous films. Semicontinuous metal films are normally prepared by thermal evaporation or sputtering of the metal on an insulating substrate. The optical properties of such films show anomalous phenomena, which are absent in both the bulk metal and the bulk insulator. Our approach is based upon a direct solution of Maxwell’s equations, without having to invoke the quasi-static approximation. Electric and magnetic fields outside the film are related to the currents inside the film. The electromagnetic properties of semicontinuous films are described by two Ohmic parameters, in contrast with the usual description by a single complex conductivity. Our theory reproduces most of the known experimental data. For example, we are able to explain a prominent absorption band near the percolation threshold, which was observed previously in such systems, as well as some other peculiar features of the reflectance and transmittance. We find that metal-dieletric films can exhibit very interesting properties when there is a strong skin effect in the metal grains. The surface conductivity has a universal value c/(2π) at the percolation threshold. We predict that under such conditions the absorptance A, as a funciton of the metal concentration, is dome shaped with sharp edges. It has a maximum at the percolation threshold and its value at this point is universal, namely A=0.5, while the reflectance R and transmittance T have the equal universal value R=T=0.25. This approach can be extended to semicontinuous superconducting films. Such films are also expected to have a well defined absorption band near the percolation threshold. We believe that such a threshold can be approached not only by decreasing the superconductor concentration but also by increasing the temperature towards and above the critical temperature ${\mathit{T}}_{\mathit{c}}$. Thus we can expect that measurements of infrared and microwave properties of thin high ${\mathit{T}}_{\mathit{c}}$ films near ${\mathit{T}}_{\mathit{c}}$ will lead to an insight regarding the nature of their microstructure.