Optical Properties of a Two-Dimensional Array of Metallic Spheres on a Substrate
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We describe a method for the calculation of the optical properties of a two-dimensional array of non-overlapping metallic particles (approximated by spheres) adsorbed on a dielectric slab. The interest in such systems arises to a large degree from their possible use as coatings, e.g. for solar energy absorbers and similar technological purposes. The formalism is an extension of the methods which have been developed in relation to electron scattering by two-dimensional atomic layers and takes fully into account multiple scattering of light between the particles of the overlayer and between the overlayer and the substrate. Scattering of light by multilayers or by an infinite crystal of non-overlapping spheres can be dealt with by a straightforward extension of the theory as in the theory of low-energy electron diffraction. Our calculations show that the usual approximation of replacement of the metallic particles by effective dipoles fails when the size of the particles or the concentration of particles increases beyond a limit and that l-pole contribution in interparticle scattering beyond the dipolar (l=1) one introduces new structure in the absorbance versus frequency curve. The reflection and absorption of light as a function of frequency is obtained numerically for selected examples. We consider in particular the variation of these quantities with concentration coverage. We examine also the effect of disorder.
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