Modeling of Periodic Rectangular Ladder-type Waveguide Systems

Ladder-type systems consisting of set of rectangular waveguides with different cross-sections are widely used for constructing microwave devices in THz range [1]. Mathematical models of these systems require solution of differential equation systems with bad-conditioned matrixes and as a consequence using of special methods for processing them. Another problem is a choice of matching conditions on abrupt change of the cross-sections because electromagnetic field may have singularity on metal edges. Mathematical model for infinite periodic hollow ladder-type waveguide with ideal metal walls is proposed. The model is based on incomplete Galerkin method and involves continuity in the mean of Poynting vector in cross-sections that ensure conservation of energy in this system. In each cross-section electromagnetic field is divided into two parts - waves propagating along the main waveguide axis in the one and the other direction. Considering one period of the system with Floquet's boundary conditions constructed algorithm takes into account multiple reflections and transits of waves and finally leads to a system with well-conditioned matrix. Thereby this method provides good speed and accuracy and allows to use more basis functions of incomplete Galerkin method in each cross-section for more precise field description in waveguide and in particularly near metal edges. As a result of modeling dispersion characteristics are calculated. For a case of weak transformation of regular waveguide into periodic ladder-type system with little difference of cross-sections results correspond to analytical investigation of this problem by asymptotic methods and show an interaction of different modes with appearing of prohibited gaps in spectrum [2].