Consequences of symmetry in periodic structures

Abstract

Periodic guiding or radiating structures at microwave frequencies frequently possess symmetry properties in addition to their axial periodicity. These include rotation and reflection symmetries, wither occurring alone or in conjunction with translations. These symmetries influence the characteristics of the electromagnetic fields associated with the structures.Therefore, useful information concerning the fields can be obtained from the symmetry properties without resorting to detailed field solutions or to equivalent circuit analogs. These symmetry properties are conveniently analyzed by introducing symmetry operators under which the structure is invariant.This paper showsthat two symmetries, the screw and the glide, are particularly important in determining the characteristics of the fields. Some of the implications of these symmetries for leaky wave antennas and microwave tube interaction circuits are explored. The consequences of screw and glide symmetries, together with five other possible symmetries, are examined to facilitate the analysis and synthesis of periodic microwave structures.

One-Plane Glide-Symmetric Holey Structures for Stop-Band and Refraction Index Reconfiguration

“…The recent study of higher symmetries [1][2][3][4][5] was driven by a growing interest in the use of periodic structures to improve the electromagnetic properties of antennas and microwave devices. These symmetries were first investigated in the 1960s and 1970s for one-dimensional periodic structures [6][7][8], introducing the concepts of glide and screw (twist) symmetry. More recently, two-dimensional glide symmetries were proposed and studied, which are a particular case of higher symmetries, demonstrating great potential for modifying the dispersion properties of periodic structures [9,10].…”

Dirac leaky-wave antennas for continuous beam scanning from photonic crystals

“…Continuous leaky structures such as slot waveguides are only capable of forward scanning above the cut-off (broadside) of the leaky mode 10 . Periodically perturbed waveguides, such as periodically loaded dielectric waveguides 15,16 are capable of both forward and backward scanning away from broadside, but typically have an open stopband around broadside due to mode coupling 10,17 . Hence, such structures so far could never achieve true broadside radiation and could only radiate 'close' to broadside 10 .…”

Evidence of Mode Coupling on Periodic Traveling‐Wave Dipole Arrays

“…Figure l shows an exploded view of such a structure. The dipoles are connected to the transmission line in a glide-symmetric configuration (Crepeau and Mcisaac, 1964), producing a phase reversal between adjacent elements, which favors back-fire radiation. The dipoles are flat strips of copper etched from a copper-clad dielectric sheet (.004 in.…”