Maxwell Garnett theory limitations in the analysis of bi-anisotropic composites

The constitutive parameters of metamaterials composed of asymmetrical inclusions are inaccurate when calculated using Maxwell Garnett theory. In this study, the authors discuss some particular cases of metamaterials composed of asymmetrical inclusions to demonstrate this statement. The unit cell single element dyadic is derived numerically using the induced currents by incident plane waves and is computed by point matching method of moments. The composite effective parameters approximated by Maxwell Garnett model were used to obtain the reflection and transmission coefficients from a bulk slab. The derived results were compared to the simulated numerical results with High Frequency Structure Simulator (HFSS) software. The scattering parameters from symmetrical and asymmetrical inclusions were compared and a parametric study was conducted. The scattering parameters are in good agreement when the material under consideration is composed of symmetrical inclusions and hold even for higher frequencies than Maxwell Garnett model theory limits. For asymmetrical inclusions the model provides inaccurate scattering parameters results. This discrepancy is especially pronounced when the illuminating field polarisation coincides with the inclusion asymmetry direction. These observations should be considered when Maxwell Garnett model is used for effective parameters analytical approximation.