RF/microwave terrestrial point-to-point and satellite communication systems employ a large number of waveguide components operating at microwave and millimeter wave frequencies. Accurate design of these components for optimum performance of the overall system is critical. To achieve this, computationally efficient and accurate numerical methods are indispensable tools in the design and optimization of components and subsystems. Among the large variety of potentially suitable numerical methods, the mode matching method in conjunction with the generalized scattering matrix technique has been found to be one of the most reliable and straightforward techniques to design waveguide components. In the past the method has been mainly applied to eigenvalue and scattering problems in rectangular waveguides. In this thesis, the mode matching method is extended to ridge waveguide problems in circular waveguides and thus closes a gap in the literature that has existed for a long time. The thesis begins with a study of the basic principles of the mode matching method as it is known from rectangular waveguides. These principles are then applied to the analysis of the rectangular ridged and coaxial waveguide, followed by an eigenvalue analysis of ridged circular waveguide. Rather than rectangular ridges, ridges of uniform angular thickness (conically shaped) are used in the circular waveguide to avoid a mixed coordinate system which would render the mode matching method computationally very inefficient. On the other hand, conically shaped ridges are as easy to fabricate as rectangular ridges and are not detrimental to the electrical performance of the component. The thesis then continues to treat the discontinuity problem at the interface between the empty circular waveguide and ridged circular waveguide. To verify the computed scattering parameters, measurements were performed and good agreement was found. By cascading several discontinuities transformers and evanescent mode filters were designed. A fifth order filter was designed and fabricated and also here good agreement between measured and computed data was found. The final chapter in the thesis analyses the coupling between orthogonal modes in the presence of an asymmetric discontinuity. Determining the coupling factor between orthogonal modes is an integral part of the design of polarizers and dual mode filters and for conically shaped ridges, has not been published in the open literature yet. To realize various coupling coefficients, a single or double ridges must be placed at an arbitrary angle to the exciting wave. The mode matching method is extended to include also this case and various convergence tests have been performed to validate the algorithm . As a final example, the algorithm has been applied to design a circular polarizer with two ridges. Although only two-port problems are treated in this thesis, the basic framework for the mode matching method in circular waveguide has been established and can now be extended to three-port problems. This will be the subject of future work to analyze and design power dividers and orthomode transducers. / Graduate

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The rigorous descriptions of linear and nonlinear guided wave theory are given together with a geometrical description that helps in the understanding of the physical phenomena taking place. The nonlinear waveguide discussed in this dissertation is composed of a linear thin film and substrate with a cladding material whose refractive index varies with the intensity of the light. Experimentally, this was accomplished, by placing an oriented liquid crystal (highly nonlinear but extremely slow) on top of a thin film glass waveguide. When the liquid crystal used was K15, light-induced mode cutoff was observed. The TE(,0) mode became leaky as the guided wave power was increased. This was a consequence of the light-induced increase in refractive index due to thermal effects. This behaviour was studied as a function of temperature. Light by light modulation was also accomplished with this setup. The theory of the linear and nonlinear prism coupler and the first experimental investigations on the nonlinear prism coupler are given. The nonlinear prism coupler used was obtained by depositing a small amount of MBBA liquid crystal in the gap beween the input coupling prism and the thin film. The basic properties of the nonlinear prism coupler were demonstrated experimentally and the results obtained were verified to have their origin in the temperature component of the nonlinear index of refraction. Good qualitative agreement between the theory developed and experiments were obtained. Bistability and switching in a thin film waveguide with a K18 liquid crystal cladding has been demonstrated for the first time. These experiments made use of the interesting phenomena associated with the nematic to isotropic phase transition. Such behaviour was satisfactorily explained by the intense light scattering associated with the critical opalescence that accompanies such a phase transition in a liquid crystal. Both the TE(,0) and the TM(,0) modes were found to exhibit such behaviour.

Because of their compatibility with the planar concept of integrated optics, grating couplers offer the most satisfactory means of coupling light into thin film optical waveguides. The purpose of this dissertation has been to study the behaviour, both theoretically and experimentally, and fabrication of grating couplers in nonlinear waveguides. A theory of nonlinear grating couplers is presented based on a coupled-mode approach. The dependence of coupling efficiency on incident beam intensity, beam size, beam position, incident angle, chirp rate, and waveguide losses have been examined all in the presence of nonlinearities in the waveguide. It is reported that, in the presence of nonlinearities, the coupling efficiency decreases with increasing incident power. Different ways of optimizing the coupling efficiency at high incident power levels are presented. These include adjusting the beam size, the coupling angle, and chirping the grating. A new technique is reported for fabrication of regular period, chirped, and curved photoresist gratings. The experimental arrangement is essentially based on Lloyd's mirror fringes and is characterized by its stability, simplicity, and versatility. We also report on successful use of Reactive Ion-Beam Etching (RIBE) with C₂F₆ gas in producing very smooth and deep gratings with high aspect ratios in different waveguide structures. Experimental coupling efficiencies of up to 40% are reported in polystyrene waveguides using etched grating couplers. Experiments are reported in support of the theoretical findings of this dissertation using a polystyrene waveguide with thermal nonlinearity.

The properties of all-optical nonlinear waveguide devices are investigated. In particular, the nonlinear directional coupler (NLDC) and nonlinear Mach-Zehnder interferometer (NLMZ) are analyzed using perturbation theory. The perturbation theory provides differential equations that describe the amplitude of the waveguide modes as a function of the propagation distance. To be practical, these waveguide devices require nonlinear phase shifts of π or more. Therefore, the theoretical investigation of these devices emphasizes their fabrication in bulk and multiple-quantum-well (MQW) gallium arsenide (GaAs). For the first time, absorption, carrier diffusion, and thermal effects are included in the theoretical investigation of the NLMZ and NLDC. The nonlinear dependence of the coupling terms, which has been neglected in all previous work, is shown to be significant for semiconductor based NLDC's. The effects of carrier diffusion on the nonlinear response of a GaAs waveguide is demonstrated using a self-consistent numerical method. The effects are heavily dependent on the waveguide geometry, and, therefore, should be included in the analysis of nonlinear semiconductor waveguide devices. However, if the diffusion length is large compared to the mode width, carrier diffusion simplifies the investigation since the nonlinear absorption and index change are uniform across the mode. This important conclusion is used in the models for the NLMZ and NLDC. The theoretical models predict the NLMZ and NLDC should work in bulk and MQW GaAs. To demonstrate that the required nonlinear phase shifts for the NLMZ and NLDC are indeed possible in bulk and MQW GaAs, the first experimental observation of electronic optical bistability in a MQW GaAs strip-loaded waveguide is recounted. This original research illustrated that phase shifts in excess of 2π are possible in MQW GaAs waveguides and, therefore, the future of all-optical waveguide devices in semiconductors is optimistic.