On the application of homogenization formalisms to active dielectric composite materials

TL;DR

This paper investigates the use of Maxwell Garnett and Bruggeman homogenization formalisms to estimate the effective permittivity of active dielectric composites, highlighting conditions where estimates agree or diverge, especially with active quantum dot components.

Contribution

It compares the applicability of two homogenization formalisms to active dielectric composites containing quantum dots, revealing their agreement or divergence based on permittivity signs.

Findings

When permittivity signs match, estimates are close and physically plausible.

Divergence occurs when permittivity signs differ, especially with low imaginary parts.

Bruggeman estimate can become physically implausible under certain conditions.

Abstract

The Maxwell Garnett and Bruggeman formalisms were applied to estimate the effective permittivity dyadic of active dielectric composite materials. The active nature of the homogenized composite materials (HCMs) arises from one of the component materials which takes the form of InAs/GaAs quantum dots. Provided that the real parts of the permittivities of the component materials have the same sign, the Maxwell Garnett and Bruggeman formalisms give physically plausible estimates of the HCM permittivity dyadic that are in close agreement. However, if the real parts of the permittivities of the component materials have different signs then there are substantial differences between the Bruggeman and Maxwell Garnett estimates. Furthermore, these differences becomes enormous--with the Bruggeman estimate being physically implausible--as the imaginary parts of the permittivities of the component materials tend to zero.