Successive matching as the technique for scalarisation of waveguide vector problems

Considers the simple example of the junction of two rectangular waveguides of different cross-sections. In accordance with the mode matching technique the authors use the two-step procedure of mode matching in the junction plane. The first step consists of matching of the field of the first waveguide with the unknown intermediate field assigned in the region possessing the width of the first waveguide and the height of the second one. The second step is the matching of that intermediate field with the field of the output waveguide. The boundary conditions on the metal junction plane are satisfied at every step