Rigorous Modal Characterization of First- and Second-Order Symmetric Waveguides Using Specular Periodic Boundary Conditions in 2D-FEM

Symmetries are widely exploited in the electromagnetic characterization of millimeter-wave devices and antennas, as they usually bring an improvement in resource usage and accuracy in full-wave simulations. Given the rising relevance of higher order symmetric devices, a challenge of integrating many different symmetries into compact formulations appears, with the objective of finding synergies and combining the strengths each one separately brings. In this work, we present a 2-D finite element method (FEM) formulation that fulfills this task for arbitrary waveguide cross sections presenting at the same time specular first-order and rotational second-order symmetries. It is based on newly introduced specular periodic boundary conditions (SPBCs), which effectively exploit the best case simulation domain for this problem. Furthermore, they avoid the need of using a mesh matching or projection procedure for periodic boundaries, while also bringing an improvement to mode classification.