OPTICAL-PROPERTIES OF THIN-FILMS UP TO 2ND-ORDER IN THE THICKNESS

In this paper we give expressions for the reflection and transmission amplitudes of isotropic non-magnetic films for which the average thickness and the correlation length, which describe the film structure, are small in comparison with the wavelength of the incident light. It is shown that these expressions can be expressed consistently up to second order in the ratio of the thickness to the wavelength in four universal constitutive coefficients. These four coefficients are found to be related to the density of the static dipole and quadrupole polarizabilities in the film. For island films on a plane substrate and for stratified media, we give explicit expressions for these coefficients and discuss our results by comparing with experimental results and with other theoretical approaches. As an example we calculate numerically the optical properties of gold spheres on a sapphire substrate as a function of the coverage and the frequency. A quadrupole approximation is introduced, which is found to be accurate within a few percent up to coverages of about 50% compared with exact numerical results which use multipoles to arbitrary order.