Periodic Structures with Higher Symmetries: Analysis and Applications

Abstract: In this thesis, periodic structures with higher symmetries are studied. Their wave propagation characteristics are investigated and their potential applications are discussed. Higher-symmetric periodic structures are described with an additional geometrical operation beyond a translation operator. Two particular types of higher symmetry are glide and twist symmetries. Glide-symmetric periodic structures remain invariant under a translation of half a period followed by a reflection with respect to a glide plane. Twist-symmetric periodic structures remain invariant under a translation along followed by a rotation around a twist axis. In a periodic structure with a higher symmetry, in which the higher order modes are excited, the frequency dispersion of the first mode is dramatically reduced. This feature overcomes the bandwidth limitations of conventional periodic structures. Therefore, higher-symmetric periodic structures can be employed for designing wideband metasurface-based antennas. For example, holey glide-symmetric metallic structures can be used to design low loss, wideband flat Luneburg lens antennas at millimeter waves, which find application in 5G communication systems. In addition, holey glide-symmetric structures can be exploited as low cost electromagnetic band gap (EBG) structures at millimeter waves, due to a wider stop-band achievable compared to non-glide-symmetric surfaces. However, these attractive dispersive features can be obtained if holey surfaces are strongly coupled, so higher-order modes produce a considerable coupling between glide-symmetric holes. Hence, these structures cannot be analyzed using common homogenization methods based on the transverse resonance method. Thus, in this thesis, a mode matching formulation, taking the generalized Floquet theorem into account, is applied to analyze glide-symmetric holey periodic structures with arbitrary shape of the hole. Applying the generalized Floquet theorem, the computational domain is reduced to half of the unit cell. The method is faster and more efficient than the commercial software such as CST Microwave Studio. In addition, the proposed method provides a physical insight about the symmetry of Floquet modes propagating in these structures. Moreover, in this thesis, the effect of twist symmetry and polar glide symmetry applied to a coaxial line loaded with holes is explained. A rigorous definition of polar glide symmetry, which is equivalent to glide symmetry in a cylindrical coordinate, is presented. It is demonstrated that the twist and polar glide symmetries provide an additional degree of freedom to engineer the dispersion characteristics of periodic structures. In addition, it is demonstrated that the combination of these two symmetries provides the possibility of designing reconfigurable filters. Finally, mimicking the twist symmetry effect in a flat structure possessing glide symmetry is investigated. The results demonstrate that the dispersion properties associated with twist symmetry can be mimicked in flat structures.