Periodic Structures with Higher Symmetries

In this article, we described the latest discoveries related to higher symmetries and opportunities to incorporate them into electromagnetic device designs. There are two known types of spatial higher symmetries: glide and twist. Glide symmetry has been the most broadly studied since it can be implemented in planar structures, which are easy to manufacture. For example, glide symmetry has been proposed to reduce the dispersion properties of the first propagating mode in parallel-plate configurations. This creates possibilities for increasing the bandwidth of metasurface lens antennas. More recently, glide symmetry was proposed to reduce the cost of low-dispersive, leakywave antennas. Additionally, glide symmetry has been reported to increase the operation bandwidth of conventional EBGs. This presents opportunities, for example, in cost-effective and robust gap waveguide technology and filters and to avoid undesireable leakage in flanges. Glide symmetry has also been proposed to produce tunable stopbands and increase the bandwidth of filters. In more recent works, glide symmetry has been found suitable for increasing the anisotropy of periodic structures, which can be used to reduce the dimensions of lens antennas. Finally, glide symmetry has been proposed for reducing the reflections at the contour of hyperbolic lenses ; this can be used to increase the total efficiency of lens antennas. Twist symmetries have been less studied than glide symmetries due to the complexity of their practical implementation. However, like glide symmetries, they have been proposed to reduce the dispersion of propagating modes and to control stopbands in transmission lines, waveguides, and flat metasurfaces.