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-ce ntred elliptic waveguide are analysed using the mode-matching method. Two t ypes of junction are considered, where the larger waveguide that forms the junction is circular or elliptic in cross-section. General cases are studie d that include both translational and rotational displacement between the w aveguides. Using generalised expressions for the coupling coefficients, tog ether with the addition theorem for Mathieu functions, series form solution s for evaluating the coupling integrals have been derived. For circular-to- elliptic junctions, an efficient method is shown for recomputing the coupli ng matrix due to an additional rotation between the waveguides.