Generalization of the mode-matching technique to the problems of scattering by semi-infinite slow-wave structures

Abstract

Subject and purpose. The scattering matrix of a semi-infinite slow-wave structure formed by grooves in a rectangular waveguide is investigated. The purpose was to develop a method for calculating a semi-infinite periodic structure. Methods and methodology. A generalization of the mode-matching technique to semi-infinite periodic structures is built. The fields of the periodic part of the structure are expanded in series of the eigenmodes of the periodic structure, taking into account the condition at infinity, which makes it possible to obtain a linear matrix equation for finding the scattering matrix. Only the propagating modes of the periodic structure were considered. To make these expansions reliable the fields were matched at a period somewhat distant from the junction of the regular waveguide with the periodic one. Results. Matrix equations for determining the blocks of the scattering matrix of a semi-infinite structure are obtained. A number of investigations are carried out to check the reliability of the equations obtained. These include test of convergence, reciprocity, energy balance, and conservation of the scattering matrix while adding one period to a semi-infinite structure. The main confirmation was obtained by comparing the scattering matrix of a finite fragment of the slow-wave structure, obtained in two ways: through the scattering matrices of semi-infinite slow-wave structure and through a cascade assembly of the scattering matrices of the waveguide elements that make up the structure. Conclusions. An algorithm for calculating the scattering matrix of a semi-infinite structure is obtained. It can be used to build a rigorous hot model of vacuum electronics devices using slow-wave structures.