Influence of the rectangular helical and toroidal waveguides on the curvature and the torsion and the technique to solve circular hollow core with dielectric material in the cross section

The first objective of this research is to present the influence of the rectangular helical and toroidal waveguides on the curvature and the torsion. The second objective is to propose a technique for a practical example where the circular hollow core is located in the center of the cross-section and the dielectric material is located between the circular hollow core and the metal, by using a complementary shapes. This example shows the discontinuous cross section, that cannot be solved by analytical methods. The technique is based on subtracting the cross section with the dielectric material in the circular core from the cross section of the dielectric profile of the waveguide filled entirely with the dielectric material. The third objective is to demonstrate the influence of the bending (1/R) on the output power transmission and also to find the relevant parameters to obtain the Gaussian behavior of the output field in the interesting case of circular hollow core. The method is based on Laplace and Fourier transforms and the inverse Laplace and Fourier transforms. We will explain in detail how and where the technique can be integrated into the proposed mode model. The applications are useful for rectangular helical and toroidal waveguides in millimeter regimes, where the circular hollow core is located in the center of the cross section and the dielectric material is located between the circular hollow core and the metal.