Equivalent Effective Permittivity Modeling of Anisotropic Composite Structures with Perforations

This paper presents an analytical and numerical investigation of the effective permittivity of dielectric slabs perforated with elliptical and capsule-shaped cylindrical microstructures arranged in square and triangular lattice configurations. Based on a quasi-static approximation, the two-dimensional Mori–Tanaka mixing model is employed to calculate the anisotropic effective permittivity tensor by incorporating direction-dependent depolarization factors for both parallel and perpendicular field orientations. An elliptical-based microstructure is first analyzed, followed by the introduction of a capsule-shaped alternative that simplifies fabrication while maintaining comparable electromagnetic (EM) properties with over 95% accuracy. The EM behavior of both geometries is validated through full-wave unit cell simulations across a broad frequency range (5–48 GHz) and porosity levels. The results demonstrate excellent agreement between analytical predictions and full-wave simulations, particularly up to 70% porosity, beyond which capsule structures exhibit superior stability and modeling consistency even at extreme porosities (82%, 97%). Additionally, the model captures angular field misalignments up to 20°, preserving accurate predictions of permittivity. The calculated effective properties can serve as inputs for EM simulation tools designed for homogeneous media, enabling their application in various practical EM designs.