Impedance boundary conditions for a metal film with a rough surface

We have obtained local impedance boundary conditions for a metal film chara cterized by an isotropic, frequency-dependent, complex dielectric function epsilon(omega) that occupies the region zeta(x(1)) < x(3) < D. The surface- profile function zeta(x(1)) is assumed to be a single-valued function of x( 1), that is differentiable as many times as is necessary. The electromagnet ic field in the system is assumed to be p polarized with the plane of incid ence, the x(1)x(3) plane. The results are used to study the scattering of p -polarized light from and its transmission through the metal film when the surface-profile function zeta(x(1)) in these calculations is assumed to be a stationary, zero-mean, Gaussian random process. These calculations are ap proximately four times faster than rigorous computer simulations, and their results are qualitatively and quantitatively in good agreement with those of the latter simulations. (C) 1999 Optical Society of America. OCIS codes: 240.0310, 240.4350, 240.5770, 290.5880.