Numerical determination of eigenmodes of an arbitrary waveguide with coordinate boundaries in cylindrical coordinate system

Waveguide units with coordinate boundaries in the cylindrical coordinate system are widely used in microwave devices based on circular and coaxial waveguides. Besides the universal finite element methods more accurate and efficient algorithms were built for the analysis waveguides of this kind. However, all of the currently available algorithms were developed for the analysis of individual structures of interest, mainly for ridge waveguides. So far the general algorithm suitable for the analysis of any waveguide of this class has not been developed yet. In this paper we eliminate this gap by a generalization of the mode matching technique to the waveguides with coordinate boundaries in the cylindrical coordinate system taking into account field singularities. The final goal was to obtain a tool for fast calculation of the mode spectrum (up to hundreds) as it was previously built for the waveguides with piesewise Cartesian coordinate boundaries.