Steshenko S. Generalization and development of numerical-analytical methods in problems of electrodynamics with piecewise coordinate boundaries

The aim of the work is to generalize the mode-matching technique in order to obtain a universal algorithm for calculating the scattering matrices of inhomogeneities with piecewise coordinate boundaries in Cartesian or cylindrical coordinate systems. The object of research is the process of propagation and scattering of electromagnetic waves in the guiding and resonance structures. Research methods: mode-matching technique, method of generalized scattering matrices, method of singular integral equations, method of discrete singularities, the Green's function method, array scanning method, Ewald method, Euler method, steepest descent method, gradient-search method, genetic algorithms, B-splines. Theoretical results: it is shown that the presence of eigen-oscillations provides the rotation of the polarization plane by objects with dihedral symmetry. Novelty: the generalization of the mode-matching technique for calculation of bases of eigenmodes and plane junctions in the case of waveguides with cross-sections of arbitrary complexshape is built. Degree of implementation: the received models are used for design of devices of waveguide and antenna equipment and vacuum electronics. Scope of application: development of new devices of waveguide and antenna equipment, and vacuum electronics with advanced characteristics.