Effective Medium Modeling of Anisotropic Perforated Composites: Electromagnetic Equivalence of Elliptical and Capsule Structure

This paper presents an analytical, numerical, and optimization-based study of the effective permittivity and permeability of dielectric slabs perforated with elliptical and capsule-shaped cylindrical microstructures. Based on a quasi-static approximation, the two-dimensional Mori–Tanaka (M-T) 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, especially up to 70% porosity, beyond which capsule structures exhibit superior stability and modeling consistency even at extreme porosities (82%, 97%) with M-T model. Additionally, to validate the study, efficient absorber and shielding structures are designed using capsule-perforated ferrite substrates, thereby demonstrating that the capsule geometry can accurately replicate the EM properties of its elliptical-shaped inclusions. The designs, optimized through the integration of the M-T model with the objective function, confirm the feasibility of realizing high-performance EM structures within thickness constraints, while maintaining analytical-numerical consistency with full-wave simulations. The extracted effective parameters are directly compatible with EM simulation tools formulated for homogeneous media, facilitating their deployment in lightweight absorbers, shielding systems, sensors, and other functional EM devices.