Effective medium theory: Mathematical determination of the physical solution for the dielectric constant

The complex effective dielectric constant of an inhomogeneous medium, as calculated with the Effective Medium Theory (E.M.T.), is the solution of a quadratic equation and is therefore a multiple-valued function. In most cases, physical criteria alone are not sufficient to select the solution which has a physical meaning. By using the properties of complex functions and Riemann surfaces together with physical criteria, one can readily define a single solution with physical meaning. The method is applied to a cermet-like material with metallic Cr inclusions.