On limitations of the Bruggeman formalism for inverse homogenization

The Bruggeman formalism provides an estimate is an element of(Br)(hcm) of the relative permittivity of a homogenized composite material (HCM), arising from two component materials with relative permittivities is an element of(a) and is an element of(b). It can be inverted to provide an estimate of is an element of(a), from a knowledge of is an element of(Br)(hcm) and is an element of(b). Numerical studies show that the inverse Bruggeman estimate is an element of(a) can be physically implausible when (i) Re {is an element of(Br)(hcm)}/Re {is an element of(b)} > 0 and the degree of HCM dissipation is moderate or greater; or (ii) Re {is an element of(Br)(hcm)}/Re {is an element of(b)} < 0 regardless of the degree of HCM dissipation. Furthermore, even when the inverse Bruggeman estimate is not obviously implausible, huge discrepancies can exist between this estimate and the corresponding estimate provided by the inverse Maxwell Garnett formalism.