Analysis on Chiral Mixtures

Abstract

This paper discusses the macroscopic properties of heterogeneous media containing chiral components. Starting with the derivation of the polarizability matrix of a chiral sphere, the components of this matrix are used in calculating the effective constitutive parameters of a mixture consisting of a nonchiral background material in which chiral spherical scatterers are immersed. The analysis is quasistatic, i.e., the spatial variation of the fields is neglected in the scale of the particle dimensions, and the scattering effects are neglected, limiting the applicability of the results to low frequencies. Generalized Lorenz-Lorentz formulae and Maxwell-Garnett formulae are given, and all three effective material parameters of the mixture are seen to be dependent on all the material parameters of the components and their volume fractions. Still, there is symmetry in the mixing relations, and through perturbation analysis, it is shown that the chirality effect on the permittivity and permeability is of the second order. In later sections, ellipsoidal chiral inclusions and multiphase chiral mixtures are discussed, and finally the derived expressions are illustrated with graphs.