Propagation in periodically loaded waveguides with higher symmetries

A generalization of Floquet´s theorem is presented for periodically loaded closed waveguides possessing a certain class of higher symmetries which includes the screw and glide symmetries. These symmetries frequently appear in microwave structures such as filters, traveling-wave tubes, and traveling-wave antennas. The theorem states that the natural modes are eigenvectors of the symmetry operator characterizing the structure. An alternative derivation of the theorem using an equivalent network representation leads naturally to a simple method for constructing the qualitative dispersion (Brillouin) diagrams for structures with screw or glide symmetry.