On the Calculation of Electromagnetic Fields in Closed Waveguides with Inhomogeneous Filling

The paper investigates waveguides of constant cross-section with ideally conducting walls and arbitrary filling. The problem of finding the normal modes of a waveguide in a full vector formulation has been set and discretized. In the framework of numerical experiments, the guiding and evanescent modes of the waveguide are calculated for several variants of the fillings. The problem of diffraction of the normal waveguide mode incident on the joint of two waveguides, the cross-sections of which coincide, and the filling at the junction varies abruptly, is set and discretized. The results of numerical experiments for specific configurations of waveguide joints are presented, and the transmission and reflection coefficients of the guided modes are calculated. The solution of the Maxwell equations system is based on the decomposition of fields with the help of four potentials, and in the present work a symbolic-numerical method is realized that uses this approach. The numerical experiments presented in this paper show that the proposed approach and the method on its basis allow the effective calculation of various characteristics of waveguide systems. The adequacy of the approach used is also evidenced by comparing the results obtained with the results of V.V. Shevchenko for the diffraction problem at the junction of two open waveguides The symbolic-numerical method used in the work is implemented in the computer algebra system Maple, in particular, the calculations of matrix elements in the framework of the incomplete Galerkin method are carried out in symbolic form to accelerate further calculations using numerical methods.