Abstract
The scattering of polarized light incident from one dielectric medium on its two-dimensional randomly rough interface with a second dielectric medium is studied. A reduced Rayleigh equation for the scattering amplitudes is derived for the case where p- or s-polarized light is incident on this interface, with no assumptions being made regarding the dielectric functions of the media. Rigorous, purely numerical, nonperturbative solutions of this equation are obtained. They are used to calculate the reflectivity and reflectance of the interface, the mean differential reflection coefficient, and the full angular distribution of the intensity of the scattered light. These results are obtained for both the case where the medium of incidence is the optically less dense medium, and in the case where it is the optically more dense medium. Optical analogues of the Yoneda peaks observed in the scattering of x-rays from metal surfaces are present in the results obtained in the latter case. Brewster scattering angles for diffuse scattering are investigated, reminiscent of the Brewster angle for flat-interface reflection, but strongly dependent on the angle of incidence. When the contribution from the transmitted field is added to that from the scattered field it is found that the results of these calculations satisfy unitarity with an error smaller than $10^{-4}$.
Highlights
In the great majority of the theoretical studies of the scattering of light from a two-dimensional randomly rough surface of a dielectric medium, the medium of incidence has been vacuum
By comparing the curves obtained from small-amplitude perturbation theory to the results obtained from a purely numerical solution of the reduced Rayleigh equation (RRE) [Eq (27)] we conclude that smallamplitude perturbation theory (SAPT) for the considered level of roughness, even to lowest nonzero order in the surface profile function as in Eq (53), reproduces all the important features found in the mean differential reflection coefficients fairly well, but with a discrepancy in the amplitudes
We have presented a derivation of the RRE for the reflection amplitudes of light scattered from a two-dimensional, randomly rough, surface
Summary
In the great majority of the theoretical studies of the scattering of light from a two-dimensional randomly rough surface of a dielectric medium, the medium of incidence has been vacuum. Its use yielded interesting results, including the presence of Yoneda peaks in the angular dependence of the intensity of the light scattered back into the medium of incidence when the latter was the optically more dense medium These are sharp, asymmetric peaks occurring at the critical angle for total internal reflection for a fixed angle of incidence for both p- and s polarization of the incident light. It should be mentioned that in an earlier numerical investigation of light scattering from onedimensional dielectric rough surfaces, Nieto-Vesperinas and Sanchez-Gil [9] observed “sidelobes” in the angular intensity distributions These authors did not associate these features with the Yoneda peak phenomenon, even though we believe doing so would have been correct. It is hoped that the presentation of these results will stimulate and motivate experimental studies of such scattering systems
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