A Comparison of Unit Cell Geometries for Lens Antenna Applications Using MMTMM

Lens antennas have long seen use in satellite communications due to their ability to steer electromagnetic waves, often realized as sizable structures composed of dielectric materials. In more recent times, a new class of lens antennas has emerged, utilizing metamaterials. Advancements in the research of electromagnetic structures have also introduced analytical techniques for determining the dispersion, impedance and effective constitutive parameters of periodic structures. These methods provide powerful tools for modeling complex metamaterial geometries without requiring extensive computational resources. This study analyzes various unit cell geometries for their potential use in lens antenna applications, by implementing the multimodal transfer matrix method. A parametric study of unit cell dimensions is performed, with results verified through a homogenization process. It is demonstrated that desired values of permittivity and permeability can be achieved by systematically varying dimensions and analytically solving for the material parameters. Furthermore, glide-symmetric metallic plates are shown to be particularly advantageous for lens applications, confirming trends observed in recent research.