<p> Novel scalar and full-vectorial mode solvers based on quadratic spline collocation (QSC) method have been developed in MATLAB for optical dielectric waveguide with arbitrary two-dimensional cross-section and refractive index profile.</p> <p> Compared with the conventional finite difference mode solver in the literature and a commercial mode solver, the QSC mode solvers are simple and easy to implement in MATLAB without losing the accuracy of the mode solutions. The scalar mode solver is fast for solving weakly guiding waveguides. Three typical rib waveguides are calculated by the QSC scalar mode solver and compared with the numerical results of a finite difference scalar mode solver in the literature. The full-vectorial mode solver is capable of solving both weakly and strongly guiding waveguides. Typical numerical examples are calculated by the full-vectorial QSC mode solver and the solver is verified by comparing the results to a commercial mode solver.</p> <p> At the end of the thesis, methods of calculating leaky and radiation modes of general dielectric waveguides and possible methods of increasing the accuracy of the QSC mode solvers are proposed.</p> / Thesis / Master of Applied Science (MASc)

The advent of ultrafast lasers has enabled micromachining schemes that cannot be achieved by other current techniques. Laser direct writing has emerged as one of the possible routes for fabrication of optical waveguides in transparent materials. In this thesis, the advantages and limitations of this technique are explored. Two extended-cavity ultrafast lasers were built and characterized as the laser sources for this study, with improved performance over existing systems. Waveguides are fabricated in oxide glass, chalcogenide glass, and polymers, these being the three major classes of materials for the telecommunication industry. Standard waveguide metrology is performed on the fabricated waveguides, including refractive index profiling and mode analysis. Furthermore, a finite-difference beam propagation method for wave propagation in 3D-waveguides is proposed. The photo-structural modifications underlying the changes in the material optical properties after exposure are investigated. The highly nonlinear processes of the light/matter interaction during the writing process are described using a free electron model. UV/visible absorption spectroscopy, photoluminescence spectroscopy and Raman spectroscopy are used to assess the changes occurring at the atomic level. Finally, the impact of laser direct writing on nonlinear waveguide applications is discussed.