OPTICAL AND ELECTRICAL-PROPERTIES OF THIN-FILMS

We calculate the de and ac electromagnetic response of thin composite films of dielectric and Drude metal. The composite is modeled as a ran dom impedance network, and the effective impedance is calculated using a transfer matrix algorithm valid in the quasistatic limit. We consid er films of thickness ranging from one to six layers. The resulting ef fective impedances show a clear transition from two-dimensional to thr ee-dimensional behavior as the thickness is increased. The results are very well reproduced by a simple effective-medium approximation for t hin films, which interpolates between two and three dimensions. The th ickness dependences of the percolation threshold and de conductivity a re in qualitative agreement with a scaling theory of Neimark. At thick nesses below a few grains, the effective impedance tenser is anisotrop ic, implying different ac responses for electric field polarized paral lel and perpendicular to the film.