Effects of the dispersion of sizes in the dielectric response of composites

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Abstract
We extend the method of the renormalized polarizability in the Maxwell Garnett theory recently developed in order to obtain a dielectric function of composite systems consisting of a host matrix with inclusions of small metallic spheres of two different sizes. We introduce two renormalized polarizabilities, one for each size, and we obtain the result that they obey two coupled quadratic equations. We obtain three peaks in the imaginary part of the dielectric function and we identify its physical origin.