On the application of homogenization formalisms to active dielectric composite materials

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. These differences are slightly less pronounced if the relative permittivity of the metallic component material is described by the extended version of the Drude formula appropriate to very small particles. However, these differences become enormous – with the Bruggeman estimate being physically implausible – as the imaginary parts of the permittivities of the component materials tend to zero.