The scattered light from a two-layer system with a shallow, random, one-dimensional rough surface bounded by semi-infinite dissimilar optical media is calculated. The systems is composed of metallic and weak absorbent dielectric films between glass and vacuum. The dielectric constant and the thickness of the dielectric film are chosen in such a way that in the absence of roughness the system supports eight transverse magnetic (TM) guided modes, whose wave numbers are (λ), or nine transverse electric (TE) guided modes, whose wave numbers are at the wavelength λ. The Rayleigh hypothesis is used to obtain an integral equation relating the amplitudes of the reflected fields to the incident wave. The scattering integral is solved both by perturbation and numerically. Results are obtained by assuming a Gaussian roughness spectrum for the surface, and the formalism is applied to simulate the scattering from the system in the attenuated total reflection configuration, allowing the excitation of guided waves. The angular dependence of the scattering shows four peaks, in addition to the backscattering effect. The angular positions of these peaks are given by with when or when they are also independent of the angle of incidence and are due to single-scattering effects.
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