Calculation of full-wave S-matrices of monoaxially uniform (2D) elements in rectangular waveguides

Discontinuities that are uniform along one of the transversal axes form a wide class of conventional elements of rectangular waveguides: H- and E-plane bends and steps, H- and E-plane tees and cross-junctions, and so on. On the other hand, their mathematical models in the S-matrix form are often used in the calculation of more complicated discontinuities, in particular 3D ones. There is another reason to consider such a class of elements in the calculation of full-wave S-matrices as a special group, but not as a particular case of corresponding 3D structures. The concern is that the 3D boundary-value problems for such structures may be reduced to a set of 2D ones. The investigation of the latter has a long history and there are sophisticated methods for solving such problems that take into account geometrical peculiarities and are much more efficient than general methods usually used for the analysis of 3D discontinuities. It is a well known fact that in the case of 2D structures the residue-calculus method is the most efficient one for waveguide steps, method of inversion of the difference part of the matrix operators is used for H-plane angled bends, standard mode-matching procedures are the best for 90° waveguide crosses, moment methods that take into account field singularities are well tailored for waveguide bifurcations, steps and other discontinuities, etc. In view of these reasons, in the development of modelling software based on the matrix technique, it makes sense to devise a special tool that produces full-wave S-matrices of the structures of interest by using well-known algorithms for a solution of corresponding scalar problems