Electromagnetic Properties of Disordered Three-Dimensional Mixtures

The electromagnetic (EM) properties of two-component mixtures involving many disordered regularly and irregularly shaped crystals are studied. The effective relative permittivities are calculated utilizing the time-domain finite integration technique. The effective permittivity of disordered mixtures deviates from established mixing theories especially in cases of high permittivity contrast between inclusions and matrix material, and is strongly correlated to the cross-sectional area of the inclusion crystals. Electric energy density localizes at the edges and corners of inclusions in a manner independent of inclusion shape and influenced by EM propagation direction and surrounding inclusions. For mixtures with both disordered irregular and more organized cube inclusions, energy localization increases as the EM signal travels through the mixture before decreasing due to attenuation of the propagating EM signal. With a large number of inclusion crystals (here in the hundreds), it is found that the impact on effective permittivity from differences in individual inclusion shapes is negligible.