Dispersion curve of the helically corrugated waveguide based on helicoidal coordinate transform

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