Finite-Element Analysis of Evanescent Modes in Circular Waveguides With Periodic and Metamaterial Walls

A new eigenmode calculation methodology is developed to investigate the behavior of existing modes in waveguided circular structures with periodic and metamaterial walls. The Finite Element Method (FEM) is applied on a unit-cell and then combined with a new eigenvalue reduced problem solving. This leads to a problem with no boundary terms for the evanescent case and enables a rapid calculation of the dispersion diagrams including both the propagating and the evanescent modes. The method is successfully validated on a conventional Perfect Electric Conductor (PEC) waveguide by comparison with the analytical solution. Then, the eigenmode algorithm is applied to compute dispersion diagrams of three metamaterial-based waveguides: with corrugated walls, with post-patterned walls and with mushroom-patterned walls.