Effective electromagnetic properties of linear and nonlinear composites

Abstract

A composite structure consisting of randomly distributed two groups of non-magnetic spheres is investigated. The electric and magnetic polarizabilities of these spheres are determined using Mie scattering theory and then used to calculate the effective permittivity and the effective permeability of the composite. Based on these effective properties, the design procedures to obtain a negative refractive index at infrared frequencies are reported. Furthermore, the characteristics of the plane wave propagations in biaxial anisotropic lossy media are investigated. The general condition on the negative phase velocity for homogeneous plane waves is provided in terms of material parameters and the propagation direction. The nu¬merical calculations for the angles between the average Poynting vector and the phase velocity are performed in order to justify the theoretical analysis. In ad¬dition, the refraction between free space and the biaxial anisotropic lossy media are also considered and the general condition on the negative angle of refraction is derived. Finally the higher-order dielectric responses of composites composed of weakly nonlinear elliptic cylindrical inclusions randomly embedded in linear media are investigated. The general formulae for effective DC coefficients are derived by the average field method up to the ninth order and then applied to analyze the effects of inclusion shapes on the effective response. The quasi-static AC response of the composites under sinusoidal electric fields are also investigated. The general relationships between the effective DC and AC coefficients are established, which are applicable to all weakly nonlinear isotropic composites.