Bi-isotropic mixtures

Bi-isotropic heterogeneous media are analyzed. Bi-isotropic materials are characterized by four scalar parameters in the constitutive relations: permittivity, permeability, chirality, and nonreciprocity. These contain the reciprocal chiral (Pasteur) medium and nonreciprocal nonchiral (Tellegen) medium as special cases. The polarizabilities of general bi-isotropic spheres and ellipsoids are derived, and these results are used in the analysis of bi-isotropic mixtures. The generalized Maxwell-Garnett formulae are derived for mixtures with spherical or ellipsoidal inclusions in isotropic background medium. The ellipsoids are allowed also to have any orientation distribution. Rayleigh mixing rules are also presented and they are seen to be a natural extension of the Rayleigh rule in the dielectric case. Numerical illustrations show the effect of shape, amount, and nature of inclusions on the bi-isotropic mixture parameters; this is essential information in the engineering problem of tailoring bi-isotropic composite materials