The Role of Second-Order Symmetries in Waveguide Propagation and its Peculiarities on the Mode-Matching Problem Using the 2D Finite Element Method

In microwave engineering, first-order or axial symmetries are typically considered as a tool to control mode propagation in the design of devices such as antennas, antenna feeders, polarization selective surfaces, and orthomode transducers. Despite being known for a long time [1], second-order, or discrete rotational symmetries, have had a marginal presence in the field, even though they exhibit advantageous theoretical properties when compared to axial symmetries, like enhanced mode classes, degeneracy discrimination, rotationally symmetric mode, suitable for circular polarization, and possibly extended mode class monomode bandwidth.