Modal analysis at the junction formed by a circular or an elliptic waveguide and a translated and rotated elliptic waveguide

The scattering characteristics of waveguide junctions with a smaller off-centred elliptic waveguide are analysed using the mode-matching method. Two types of junction are considered, where the larger waveguide that forms the junction is circular or elliptic in cross-section. General cases are studied that include both translational and rotational displacement between the waveguides. Using generalised expressions for the coupling coefficients, together with the addition theorem for Mathieu functions, series form solutions for evaluating the coupling integrals have been derived. For circular-to-elliptic junctions, an efficient method is shown for recomputing the coupling matrix due to an additional rotation between the waveguides