Limits of validity of three perturbation theories of the specular scattering of light from one-dimensional, randomly rough, dielectric surfaces

Abstract

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 λ = 0.6328 μm, and the dielectric constant of the scattering medium is ∊ = 2.25. The surface roughness is characterized by a rms height δ 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 δ/λ as a function of a/λ 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/λ, 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.