Consequences of symmetry in periodic structures

Periodic guiding or radiating structures at microwave frequencies often possess symmetry properties in addition to their axial periodicity. These include rotation and reflection symmetries, either 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 circuits. These symmetry properties are conveniently analyzed by introducing symmetry operators for which the structure is invariant. This paper shows that two symmetry operators, the screw and the glide, are particularly important in determining the dispersion characteristics of the structures. Some of the implications of these symmetries for leaky wave antennas and microwave tube interaction circuits are explored, and their consequences are examined to facilitate the analysis and synthesis of periodic microwave structures.