An Effective Permittivity Tensor of Cylindrically Perforated Dielectrics

In the letter, we propose a simple analytical effective permittivity model of perforated dielectrics composed of through-hole cylindrical perforations. As the perforated dielectrics are uni-axial media, the model respects the anisotropic properties of the material and the results are simple engineering formulas for effective permittivities of ordinary and extraordinary wave for polarization corresponding to parallel and perpendicular orientation with respect to the axis of perforations. The model is based on the 2-D Maxwell Garnett approximation of inhomogeneous media valid for circularly shaped perforations. The analytical results obtained for propagation of transverse electromagnetic wave are verified by unit-cell full-wave simulations of triangular perforations lattice, and a very good agreement is obtained.