Optimisation of the coupled-mode method for the analysis of waveguides partially filled with dielectrics of high permittivity: Application to the study of discontinuities

The differences between two distinct formulations of the coupled-mode method are analysed and justified. The difference, the mathematical basis of which is the different ways used to calculate the axial components of the electromagnetic field, is interpreted in terms of the continuity of the functions that affect the calculation of these components. The original formulation of the coupled-modes method is shown to converge in a more efficient way than the Ogusu formulation, although it is less efficient from a numerical viewpoint. Results of the propagation constant in isotropic dielectric waveguides are presented which confirm the better convergence of the original formulation. Applying this formulation in conjunction with the modal matching method allows an improvement in the accuracy of the analysis of dielectric discontinuities between materials of high permittivity. Then, this formulation is useful for designing isotropic dielectric structures as mode launchers or filters, as well as nonreciprocal elements constructed with ferrites