Mathematical model of periodic waveguide systems with rectangular cross-section

A mathematical model of an ideally conducting periodic waveguide system with piecewise constant rectangular cross-section is proposed. This type of geometry is finding application in the development of terahertz devices more often recently. The problem to solve is a system of Maxwell equations supplemented by metal boundary conditions and Floquet conditions on cross-sections spaced by one period of the structure. The solution of the problem is based on incomplete Galerkin's method and projection field conjunction in the region of cross-sections jumps. Direct use of this approach leads to matrix problems with ill-conditioned matrices due to simultaneous presence of exponentially increasing and decreasing matrix coefficients. In this context the method to be proposed additionally takes into account the directions of wave propagation in any regular section in the system, which makes it possible to eliminate exponentially increasing elements and make the matrices well-conditioned. Internal wave reflections occurring within the considering period of the system are taken into account explicitly. Based on the proposed model the dispersion characteristics of various structures are constructed. The convergence of the method to the limiting cases is investigated.