Dynamic polarizability tensor for cylindrical rods and their application to the homogenization of uniaxial metamaterials

We develop fully dynamic expressions for the parallel and transverse components of the polarizability tensor characterizing circular cylinders of arbitrary electrical size and material properties. Our results show the importance of spatial dispersion effects in modeling cylindrical rods within the dipolar approximation, and extend the range of validity of existing models to arbitrary incidence angle and moderately large electrical sizes. We have also derived passivity conditions for all the components of the polarizability tensor and arbitrary incidence angle, which are satisfied by our expressions. Finally, we numerically study the effect of size and material variation on the relevant polarizability components, and we apply our formulation to analyze the effective parameters of uniaxial metamaterials composed of arrays of cylindrical rods. We expect that this result may be applied to the correct modeling of artificial uniaxial materials and their applications.