Reducing the Dispersion of Periodic Structures with Twist and Polar Glide Symmetries

Abstract

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.

Propagation characteristics of periodic structures possessing twist and polar glide symmetries

“…Similar properties have been demonstrated in twistsymmetric structures [6][7][8][9]. Moreover, the possibility of reaching m-fold symmetry, where m is any integer (in contrast to glide symmetry which is inherently of order 2 [4]), enables further control of the dispersion characteristics in twist-symmetric structures [6][7][8][9].…”

“…Similar properties have been demonstrated in twistsymmetric structures [6][7][8][9]. Moreover, the possibility of reaching m-fold symmetry, where m is any integer (in contrast to glide symmetry which is inherently of order 2 [4]), enables further control of the dispersion characteristics in twist-symmetric structures [6][7][8][9]. Such increased control has found applications in filters [7,8] and phase shifters [9], and has been proposed to be of use in fully metallic lowdispersive leaky-wave antenna designs [6][7][8].…”

“…Twist symmetry is one type of higher symmetry, where the additional geometrical operation is a rotation around a twist axis, called here a "twist operation" [6][7][8][9]. More specifically, a structure possesses an m-fold twist symmetry if the compound geometrical operation consists of a translation of p/m along a given axis (the periodicity axis) and a rotation of 2p/m around the same axis, where p is the periodicity of the unit cell, and m is an integer number.…”

“…The concept of polar glide symmetry was introduced in [6], where a structure is said to possess polar glide symmetry if its flat approximation of the structure possesses Cartesian glide symmetry, i.e., the additional geometric operation is a mirroring in a plane. However, it has been noted that this definition can be improved upon, and in [7], the true definition of polar glide symmetry is proposed.…”

“…Moreover, the possibility of reaching m-fold symmetry, where m is any integer (in contrast to glide symmetry which is inherently of order 2 [4]), enables further control of the dispersion characteristics in twist-symmetric structures [6][7][8][9]. Such increased control has found applications in filters [7,8] and phase shifters [9], and has been proposed to be of use in fully metallic lowdispersive leaky-wave antenna designs [6][7][8]. This article provides an overview of the recent results in twist symmetries; three studies are conducted, simulated with the Eigenmode Solver of CST Microwave Studio [29], in which the properties of twist symmetry are highlighted.…”