Waveguide modes via an integral equation leading to a linear matrix eigenvalue problem

A numerical method for determining the modes of a rectangular or a circular waveguide strongly perturbed by axial cylindrical conducting objects is presented. The approach uses a real kernel given by recently determined forms of the dyadic Green's function for two-dimensional circular and rectangular resonators instead of the commonly used free-space Green's function. This procedure leads to a small-size linear matrix eigenvalue problem. Cutoff wavenumbers are simultaneously calculated with very good precision for a number of modes near the order of the matrix eigenvalue problem. Excellent results are also obtained when the perturbed waveguide section exhibits reentrant parts or edges. Computing time is short and storage requirements are moderate. The method is also applicable to waveguides of arbitrary cross section.