Calculation of anomalous permeability and permittivity spectra

An extended model for calculating the permeability and permittivity spectra of granular materials, which is able to predict resonances, relaxations, and complex spectra that have been explained previously either by a combination of multiple sources or simply labeled as anomalous, is presented. Using the Clausius-Mossotti relation complex spectra are predicted by taking into account the relative size of the internal wavelength and by assigning the individual grains frequency-dependent electromagnetic properties. Scattered multipolar fields about a single sphere are related to the polarizability of a cubic array of such spheres. Using the Clausius-Mossotti relation the effective permeability and permittivity spectra of a polycrystalline (or amorphous) material for arbitrary permittivity and permeability of the individual spheres, packing density, and sphere size, are determined. Although the product of the external wave vector and sphere radius is kept small, typically less than one-tenth, the product of the internal wave vector and sphere radius is unconstrained and seen to have a large effect on predicted spectra.