Method for calculation of helical-waveguide eigenmodes on the basis of solving the equivalent two-dimensional problem by field expansion in circular-waveguide modes

We present a method for calculating the dispersion characteristics of eigenmodes of metal waveguides with helical corrugations on the inner surface, which is based on the transition to a new nonorthogonal system of coordinates. In the new coordinate system, the problem of finding helical-waveguide modes is rigorously equivalent to the problem of finding the modes of a circular unitradius waveguide which has an anisotropic filling and is homogenous in the longitudinal direction. To solve the equivalent problem, we expand the field of the desired eigenmode in the modes of an empty circular unit-radius waveguide. As a result, the problem is reduced to solving a generalized algebraic eigenvalue problem. The comparison with the results of earlier three-dimensional calculations shows that the developed method allows one to determine characteristics of helical-waveguides with sufficient accuracy for many important applications and requires much lower calculation costs.