Scattering of light from a two-layer system with a rough surface

The scattered light from a two-layer system with a shallow, random, one-dim ensional rough surface bounded by semi-infinite dissimilar optical media is calculated. The systems is composed of metallic and weak absorbent dielect ric films between glass and vacuum. The dielectric constant and the thickne ss of the dielectric film are chosen in such a way that in the absence of r oughness the system supports eight transverse magnetic guided modes, whose wave numbers are q(1)((TM))(lambda) , q(2)((TM)) (lambda),..., q(8)((TM)) ( lambda), or nine transverse electric (TE) guided models, whose wave numbers are q(1)((TE)) (lambda), q(2)((TE)) (lambda), ..., q(9)((TE)) (lambda), at the wavelength lambda. The Rayleigh hypothesis is used to obtain an integr al equation relating the amplitudes of the reflected fields to the incident wave. The scattering integral is solved both by perturbation and numerical ly. Results are obtained by assuming a Gaussian roughness spectrum for the surface, and the formalism is applied to simulate the scattering from the s ystem in the attenuated total reflection configuration, allowing the excita tion of guided waves. The angular dependence of the scattering shows four p eaks, in addition to the backscattering effect. The angular positions of th ese peaks are given by (2 pi/lambda)n(1) sin theta(k)((t)) = +/-q(k)((t)) w ith k = 7, 8 when t = {p, TM} or k = 8, 9, when t = {s, TE}; they are also independent of the angle of incidence and are due to single-scattering effe cts. (C) 1999 Optical Society of America [S0740-3232(99)01111-4].