Optical and electrical properties of thin films

We calculate the dc and ac electromagnetic response of thin composite films of dielectric and Drude metal. The composite is modeled as a random impedance network, and the effective impedance is calculated using a transfer matrix algorithm valid in the quasistatic limit. We consider films of thickness ranging from one to six layers. The resulting effective impedances show a clear transition from two-dimensional to three-dimensional behavior as the thickness is increased. The results are very well reproduced by a simple effective-medium approximation for thin films, which interpolates between two and three dimensions. The thickness dependences of the percolation threshold and dc conductivity are in qualitative agreement with a scaling theory of Neimark. At thicknesses below a few grains, the effective impedance tensor is anisotropic, implying different ac responses for electric field polarized parallel and perpendicular to the film.