Abstract

A new approach for the evaluation of the effective permittivity of a mixture of dielectric particles in a background matrix of a dielectric with relative permittivity m is formulated. The approach is much more precise in relating the singularity in the Green’s function of the wave equation for the electric field to the shape of the particles. Unlike other treatments, this approach first formulates rigorous wave equations for a collection of N particles, and it collects repeated scatterings inside one particle into a transition operator for a particle with nonzero volume vα. From there, an approximate integral equation in an averaged continuous medium leading to an effective permittivity, with error terms ~vα1/3/λ, is formulated for waves at wavelength λ. The approach is able, through differing assumptions about the kernel of the wave equation, to reproduce most of the formulations for the effective permittivity in the literature.

© 1993 Optical Society of America

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