Light scattering and transmission by rough surfaces are of considerable interest in a variety of applications including remote sensing and characterization of surfaces. In this work, the finite-difference time-domain technique is applied to calculate the scattered and transmitted electromagnetic fields of an infinite periodic rough surface. The elements of the Mueller matrix for scattered light are calculated by an integral of the near fields over a significant number of periods of the surface. The normalized Mueller matrix elements of the scattered light and the spatial distribution of the transmitted flux for a monolayer of micrometer-sized dielectric spheres on a silicon substrate are presented. The numerical results show that the nonzero Mueller matrix elements for scattering from a surface consisting of a monolayer of dielectric spheres on a silicon substrate have specific maxima at some scattering angles. These maxima may be used in the characterization of features of the surface. For light transmitted through the monolayer of spheres, our results show that the transmitted energy focuses around the ray passing through centers of the spheres. At other locations, the transmitted flux is very small. Therefore, micrometer-sized dielectric spheres might be placed on a semiconductor surface to burn nanometer-sized holes in a layer using laser pulses. The method may also be useful in the assembly of periodic microstructures on surfaces.
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