Effective medium model for multilayered anisotropic media with different orientations

Anisotropic property is very popular among modern engineering materials such as composites, fibers, crystals, wood and so on. These kinds of materials have a lot of usages as housings and casings in aerospace, transportation, civil infrastructure, electronics, appliance and marine. In aerospace industry, composites can be replacements for metals due to its good features that they are not as electrically conductive as traditional. It becomes more and more important to understand the electromagnetic interactions (i.e., reflection, transmission) of composites. Multilayered anisotropic material with different orientations is very common in composites. However, electromagnetic modelling of multilayered anisotropic material needs huge CPU time and memory requirements. Using effective medium theory, by replacing multilayered anisotropic medium with a single equivalent layer for the permittivity, permeability and orientation, CPU time and memory requirements can be significantly reduced. In this paper, effective medium theory is applied to model two-layer biaxial anisotropic material with different orientations. The reflection and transmission matrices are derived for both single and two layers of biaxial anisotropic materials for a plane wave incidence at the normal direction. Basing on the same reflection and transmission coefficients, effective anisotropic permittivity, permeability and orientation angle are extracted, similar to the approach used to extract effective parameters from measurements and numerical modeling of periodic structures as isotropic materials. With the low frequency (LF) limit, analytical expressions for effective parameters and orientation angle are derived and result in a frequency-independent equivalent model. The low frequency approximations also give a non-magnetic effective anisotropic model if each layer is non-magnetic anisotropic dielectric. Finally, effective parameters using low frequency approximation are compared with the ones from parameter extraction method. Good agreements in effective parameters and angle are observed between with and without the approximations for the frequency up to several GHz.