On limitations of the Bruggeman formalism for inverse homogenization

TL;DR

This paper investigates the limitations of the inverse Bruggeman formalism in estimating component permittivities of composite materials, revealing conditions under which it produces implausible or inaccurate results compared to other models.

Contribution

The study identifies specific conditions where the inverse Bruggeman formalism yields unreliable estimates, highlighting its limitations in inverse homogenization.

Findings

Inverse Bruggeman estimates can be physically implausible under certain permittivity ratios.

Significant discrepancies exist between inverse Bruggeman and inverse Maxwell Garnett estimates.

Limitations are pronounced when the real part of permittivity ratios exceeds or is less than zero.

Abstract

The Bruggeman formalism provides an estimate $\eps^{Br}_{hcm}$ of the relative permittivity of a homogenized composite material (HCM), arising from two component materials with relative permittivities $\eps_a$ and $\eps_b$. It can be inverted to provide an estimate of $\eps_a$, from a knowledge of $\eps^{Br}_{hcm}$ and $\eps_b$. Numerical studies show that the inverse Bruggeman estimate $\eps_a$ can be physically implausible when (i) $Re\{\eps^{Br}_{hcm}\}/Re\{\eps_b\} > 0 $ and the degree of HCM dissipation is moderate or greater; or (ii) $Re\{\eps^{Br}_{hcm}\}/Re\{\eps_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.