Generalized networks for waveguide step discontinuities

We have recently introduced an architecture for systematically dealing, in an efficient and rigorous manner, with electromagnetic fields representations and computations in complex structures. The approach is based on the topological partitioning of the complex structure into several subdomains joined together by interfaces. The suggested framework accommodates the use of different analytical/numerical methods (hybridization) when the latter are necessary, the choice of problem-matched alternative Green's functions and the selection of appropriate field quantities at the boundary between different regions. Some of these concepts are applied in this paper to the case of a waveguide step discontinuity problem: it is shown that, even for this rather well-investigated example, it is possible to select alternative Green's functions with improved convergence properties with respect to those commonly used. Moreover, a new canonical representation of the step discontinuity is derived and new original formulations of this problem are devised.