LIMITS OF VALIDITY OF 3 PERTURBATION THEORIES OF THE SPECULAR SCATTERING OF LIGHT FROM ONE-DIMENSIONAL, RANDOMLY ROUGH, DIELECTRIC SURFACES

The reflectivity of p- and s-polarized light incident upon a one-dimensional, randomly rough, dielectric surface is calculated for several angles of incidence, when the plane of incidence is normal to the generators of the surface, by a second-order small-amplitude perturbation theory, by a second-order self-energy perturbation theory, and by a second-order phase perturbation theory. The wavelength of the incident light is lambda = 0.6328 mu m, and the dielectric constant of the scattering medium is epsilon = 2.25. The surface roughness is characterized by a rms height delta and a transverse correlation length a. From a comparison of the results of these approximate calculations with those obtained by a numerical simulation approach for each polarization of the incident light, and for several angles of incidence, curves of delta/lambda as a function of a/lambda are constructed, below which each perturbative method is valid with an error that is smaller than 2.5%. It is found that, for a given value of a/lambda, the reflectivity of s- and p-polarized light is given most accurately by the phase perturbation theory and least accurately by small-amplitude perturbation theory.