Wavelength dependence of the light scattered from a dielectric film deposited on a metal substrate

We consider a scattering system consisting of a dielectric film deposited on a semi-infinite metal, and focus on the wavelength dependence of the total integrated scattering and angle resolved scattering from such a system. In particular we study theoretically by a large scale rigorous numerical simulation approach the reflectivity, R(λ), as well as the total scattered energy, U(λ), of such systems as functions of the wavelength of the incident light. The scattering system consists of vacuum in the region x3 > d1 + ζ1(x1), a dielectric film in the region, d2 + ζ2(x1) < x3 < d1 + ζ1(x1), and a metal in the region x3 < d2 + ζ2(x1). This system is illuminated from the vacuum side by p-polarized light whose wavelength is allowed to vary from 0.2μm to 1.2μm. The film is assumed to have a dielectric function that is insensitive to the wavelength of the incident light. In obtaining the numerical results reported here the metal substrate is taken to be silver. The dielectric function of silver for a given wavelength is obtained by interpolation from experimental values. The surface profile functions, ζ1,2(x1), are assumed to be either zero or single-valued functions of x1 that are differentiable as many times as is necessary, and to constitute zero-mean, stationary Gaussian random processes. Their surface height auto-correlation function is characterized by a Gaussian power spectrum. We study and discuss the wavelength dependence of R(λ) and U(λ) for several scattering systems obtained by turning on and off the surface profile functions ζ1,2(x1) and/or the correlation between these two surface profile functions