We have obtained local impedance boundary conditions for a metal film characterized by an isotropic, frequency-dependent, complex dielectric function ε(ω) that occupies the region ζ(<i>x</i><sub>1</sub>) < <i>x</i><sub>3</sub> < <i>D</i>. The surface-profile function ζ(<i>x</i><sub>1</sub>) is assumed to be a single-valued function of <i>x</i><sub>1</sub> that is differentiable as many times as is necessary. The electromagnetic field in the system is assumed to be <i>p</i> polarized with the plane of incidence, the <i>x</i><sub>1</sub><i>x</i><sub>3</sub> plane. The results are used to study the scattering of <i>p</i>-polarized light from and its transmission through the metal film when the surface-profile function ζ(<i>x</i><sub>1</sub>) in these calculations is assumed to be a stationary, zero-mean, Gaussian random process. These calculations are approximately four times faster than rigorous computer simulations, and their results are qualitatively and quantitatively in good agreement with those of the latter simulations.
© 1999 Optical Society of America
(240.0310) Optics at surfaces : Thin films
(240.4350) Optics at surfaces : Nonlinear optics at surfaces
(240.5770) Optics at surfaces : Roughness
(290.5880) Scattering : Scattering, rough surfaces
Tamara A. Leskova, Alexei A. Maradudin, and Igor V. Novikov, "Impedance Boundary Conditions for a Metal Film with a Rough Surface," Appl. Opt. 38, 1197-1212 (1999)