Incremental and differential Maxwell Garnett formalisms for bi-anisotropic composites

We present, compare and contextualize two approaches to the homogenization of bi-anisotropic-in-bi-anisotropic particulate composite medias: (i) the incremental Maxwell Garnett (IMG) formalism, in which the composite medium is built incrementally by adding the inclusions in N discrete steps to the host medium; and (ii) the differential Maxwell Garnett (DMG) formalism, which is obtained from the IMG in the limit N→∞. Both formalisms are applicable to arbitrary inclusion concentration and are well-suited for computational purposes. Either of the two formalisms may be used as an alternative to the well-known Bruggeman formalism. Numerical results for the homogenization of a uniaxial dielectric composite medium and of a chiroferrite are presented.