Light scattering from a random rough interface with total internal reflection

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Abstract
The scattering of linearly polarized electromagnetic waves incident from a dielectric from a rough surface separating the dielectric from a vacuum is studied by using the extinction theorem. The angular distributions of the ensemble average of intensity of the reflected and transmitted fields are calculated numerically for several values of the angle of incidence, the surface statistical parameters, and the dielectric permittivity. To determine the effect of the corrugation on the transmitted evanescent waves, we also obtain the angular spectrum of the transmitted field as a function of the momentum parallel to the surface in the nonradiative zone. The total mean reflected and transmitted energies (reflectance and transmittance), as well as their incoherent parts in the case of slight corrugations, are derived by integrating the angular intensity distribution over the angle of observation. This permits the analysis of the influence of the corrugation and of the phenomenon of total internal reflection within two different systems of surface correlation length T namely, for T larger and smaller than the wavelength. In particular, enhanced backscattering and forward transmission are predicted for surfaces with both T and the rms deviation greater σ than the wavelength of the incident light.