Electromagnetic properties of random material

This work addresses the relationship between grain properties and the permeability and permittivity spectra of non-crystalline materials or aerosols.

The scattered multipolar fields about a single sphere are related to the polarizability of a random collection of such spheres. Using the Clausius-Mossotti relation the effective permeability and permittivity spectra of an amorphous material is determined for arbitrary permittivity and permeability of the individual spheres, packing density, and sphere size. Although the author considers the spectra over a range where the product of the external wavevector and sphere radius is kept small, typically less than one-tenth, the product of the internal wavevector and sphere radius is unconstrained and seen to have a large effect on predicted spectra.

The result is a variety of possible spectral types which include resonances, relaxations and certain complex. conglomerate spectra that have been measured and far which no direct explanation is otherwise available.