Long-wavelength electromagnetic propagation in heterogeneous media

Existing effective-medium-type theories for the propagation of long-wavelength electromagnetic radiation in heterogeneous media are examined, and structural effects, neglected by such theories, are introduced by a multiple-scattering approach that yields an effective propagation wave vector. Results are presented for propagation through an infinite periodic array of small spheres immersed in a host of different permittivity (or permeability). The procedure is generalized to aperiodic systems to include the lowest-order corrections for small-sphere volume fill fraction $\eta$ (for arbitrary scattering strength) and for weak scattering (for arbitrary $\eta$). In all cases significant effects due to structure-induced multipole fields are seen to occur. A simple parametrization of deviations from the lowest-order result, the Maxwell-Garnett expression, is proposed in order to extract information on structural multipoles or clustering effects from experimental data. We present the results of calculations for mixtures of real dielectrics and for small metal spheres embedded quasirandomly in a dielectric host, and describe generalizations to include the effects of particle coating and size distributions on optical properties.