In this article, a number of guiding structures are proposed which take advantage of higher symmetries to vastly reduce the dispersion. These higher symmetries are obtained by executing additional geometrical operations to introduce more than one period into the unit cell of a periodic structure. The specific symmetry operations employed here are a combination of p-fold twist and polar glide. Our dispersion analysis shows that a mode in a structure possessing higher symmetries is less dispersive than in a conventional structure. It is also demonstrated that, similar to the previously studied Cartesian glide-symmetric structures, polar glide-symmetric structures also exhibit a frequency independent response. Promising applications of these structures are leaky-wave antennas which utilize the low frequency dependence.

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In this article, we provide an overview of the current state of the research in the area of twist symmetry. This symmetry is obtained by introducing multiple periods into the unit cell of a periodic structure through a rotation of consecutive periodic deformations around a symmetry axis. Attractive properties such as significantly reduced frequency dispersion and increased optical density, compared to purely periodic structures, are observed. The direct link between the symmetry order and these properties is illustrated through numerical simulations. Moreover, polar glide symmetry is introduced, and is shown to provide even further control of the dispersion properties of periodic structures, especially when combined with twist symmetry. Twist symmetries can, with benefit, be employed in the development of devices for future communication networks and space applications, where fully metallic structures with accurate control of the dispersion properties are desired.

In this article, we demonstrate how twist symmetries can be employed in the design of flat lenses. A lens design is proposed, consisting of 13 perforated metallic sheets separated by an air gap. The perforation in the metal is a two-dimensional array of complementary split-ring resonators. In this specific design, the twist symmetry is local, as it is only applied to the unit cell of the array. Moreover, the twist symmetry is an approximation, as it is only applied to part of the unit cell. First, we demonstrate that, by varying the order of twist symmetry, the phase delay experienced by a wave propagating through the array can be accurately controlled. Secondly, a lens is designed by tailoring the unit cells throughout the aperture of the lens in order to obtain the desired phase delay. Simulation and measurement results demonstrate that the lens successfully transforms a spherical wave emanating from the focal point into a plane wave at the opposite side of the lens. The demonstrated concepts find application in future wireless communication networks where fully-metallic directive antennas are desired.