Dispersion Curve of the Helically Corrugated Waveguide Based on Helicoidal Coordinate Transform

This article presents the dispersion curve study of the helically corrugated waveguide (HCW) using the 2-D finite element method (FEM) method based on the helicoidal coordinate transform. Calculation of the dispersion curve is 60 times faster compared with 3-D FEM simulation while maintaining similar accuracy. The 2-D method was used to investigate the relative error between it and a 1-D analytical method based on perturbation theory. Over a narrow parametric range, the 1-D method has a similar dispersion (within a relative error of 3%) in comparison to the 2-D/3-D methods but the error greatly increased when the parameter space was expanded. Correction factors were determined to greatly enhance the 1-D method accuracy over the wider parametric range. Assisted by the improved 1-D method, it allows identifying the desired operating mode automatically within the multiple eigenvalues from the 2-D simulation results. Therefore, it can be integrated into an optimization routine to explore the applications of the HCWs at wider parameter ranges.