Analysis of Single and Coupled Dielectric Rib Waveguides and Discontinuities

Available from UMI in association with The British Library. This thesis considers the theoretical analysis of the rib waveguide, a waveguiding structure most favoured for integrated optics and in millimetre waves. The work begins by considering the application of the Transverse Resonance Diffraction method (TRD) to the rib waveguide in the pure LSE/LSM polarizations. In solving the TRD problem, a variational method of order one, i.e. that assumes at the transverse step discontinuity a single function 'trial field', which takes into explicit account the singularities at the dielectric corners, is used. The formulation leads to a scalar dispersion equation and a simple transverse equivalent network. Theoretical results for discrete bound mode propagation constant are compared with the vector finite element method. The agreement is found to be excellent and, hence, LSE/LSM provide an accurate approximation. The investigation is completed by considering a full hybrid rigorous analysis of the structure. The analysis of a single guide is extended to cover multiple coupled waveguides. The approach adopted to analyse this structure is to represent the uniform section of the coupled structure by its equivalent two-port network. In this way, the problem of multiple coupled guides is turned into a cascade of equivalent networks, which can be tackled by simple network method. The theory is applied to analyse directional couplers, three guide couplers, non symmetrical coupled waveguides and waveguide arrays. In order to complete the characterization of the modal spectrum of the rib waveguide, the continuum portion of the spectrum is derived. The approach adopted uses an eigenfunction in a manner analogous to the bound mode description of the guided fields. Finally, with knowledge of the complete spectrum, the problem of abruptly terminated rib waveguide and discontinuities between two rib waveguides are addressed. To avoid excessive computational effort a number of simplifications are employed giving results which agree quite well with those of FEM analysis.