Enhanced backscattering of light from a random grating

Abstract

By the use of Green's second integral theorem we have obtained exact expressions for the scattered electromagnetic field produced by a p- or s-polarized beam of finite width incident from the vacuum side onto a random grating whose grooves are perpendicular to the plane of incidence. The scattered field is expressed in terms of the total magnetic (electric) field in the vacuum and its normal derivative, evaluated on the surface of the grating in the case of p- ( s-) polarization. The coupled pair of inhomogeneous integral equations satisfied by these source functions is solved numerically for each of several thousand realizations of the surface profile, which are generated numerically and possess a Gaussian spectrum. The incoherent component of the differential reflection coefficient averaged over these realizations of the surface profile displays a well-defined peak in the retroreflection direction in the scattering of s-polarized light from a large amplitude random metallic grating but not in the scattering of s-polarized light from a small amplitude random metallic grating. The mean scattering amplitude, regarded as a function of the component of the wave vector of the scattered light parallel to the mean surface at the frequency of the incident light, displays a pole in the nonradiative region in the former case but not in the latter. This suggests that electromagnetic waves of s-polarization are trapped by large amplitude roughness but not by small amplitude roughness. Enhanced backscattering is also observed in the scattering of s-polarized light from a large amplitude random grating on the surface of a nearly transparent dielectric medium. Evidence is presented that the enhanced backscattering observed in the scattering of both p- and s-polarized light from a large amplitude random grating on a perfect conductor is not a single-scattering effect, but is already present in a double-scattering approximation. Finally, it is demonstrated that the enhanced backscattering present in our simulation results is an effect that lies outside the statistical errors caused by our use of a finite number of surface profiles in our calculations.