A diagrammatic approach to the optical properties of composites

We formulate a diagrammatic approach for the calculation of the effective dielectric response of a collection of spheres located at random positions and embedded in a homogeneous medium. Through infinite summations of specific classes of diagrams we derive Maxwell Garnett's theory and an expression given by Felderhof, Ford and Cohen [1]. Extending the diagrammatic procedure developed by Matsubara and Toyozawa [2] in their theory of impurity band conduction in semiconductors we obtain an improved version of the Clausius-Mossotti relation with a renormalized polarizability instead of the bare polarizability of the spheres. We compare our results with other theories and with experiment. We also find that the simple theory of a renormalized polarizability in the Maxwell Garnett theory developed by us [3] corresponds to the choice of a specific class of diagrams.