A new method called the Direct Method is developed to solve for the propagating modes in waveguides via the finite-element method. The variational form of the Direct method is derived to ensure that an extremum is reached. The Direct method uses Maxwell's equations directly, both zero and first-order, scalar and vector bases that are used in the finite-element formulation. The direct solution method solves for both the magnetic and electric fields simultaneously. Comparisons are made with the traditionally used vector-Helmholtz equation set. The advantages and disadvantages of the newly developed method is described as well as several results displayed using the WR-90 waveguide and a circular waveguide as test waveguides. Results include a partially filled dielectric loaded rectangular waveguide. The effects of including the divergence of the fields in the functional as penalty terms on the quality of results obtained by the Direct method and the vector-Helmholtz method is explored. The quality of results is gauged on the accuracy of the computed modes as well as the elimination or a significant reduction in the number of 'spurious modes' that are often encountered in solutions to waveguide problems. It is shown that computational time for the solution and computer storage requirements exceed the typically used Helmholtz equation method but the results obtained can be more accurate. Future work may include developing a sparse eigenvalue solution method that could reduce the solution time and storage requirements significantly. The Direct method of solution in dynamics resulted after an initial search in magnetostatics for methods to solve for the magnetic field without using the magnetic-vector potential using finite-element methods. A variational derivation that includes the boundary conditions is developed for the magnetic-vector potential method. Several techniques that were used to attempt accurate solutions for the magnetostatic fields with multiple materials and without the use of the magnetic-vector potential are described. It was found that some of the newly developed general techniques for magnetostatics are only accurate when homogeneous media are present. A method using two curl equations is developed which is a Direct method in magnetostatics and reveals the interaction between the bases used. The transition from magnetostatics to dynamics is made and similar Direct methods are applied to the waveguide problem using different bases. / Ph. D.

Guias de onda de luz foram fabricados por difusão térmica de Titânio em substratos de LiNbO3. Os índices efetivos dos modos guiados foram medidos usando o método de acoplamento por prismas e a equação de onda resolvida numericamente usando a aproximação WKB. Profundidade de difusão, variação máxima do índice de refração e o perfil da concentração de Titânio são calculados para um guia que suporta três modos TE / Optical waveguides have been fabricated by thermal diffusion of Titanium into LiNO3 substrate. The effective indices of guided modes have been measured using a prism coupling method and the wave equation has been solute numerically using the WKB approximation. The diffusion depth, maximum refractive index change and titanium concentration profited was calculated for one waveguide that support three TE modes

[pt] No presente trabalho o método de Rayleigh-Ritz é utilizado na determinação dos campos modais e dos números de onda de corte em guias de onda de seção arbitrária. Inicialmente, o método é aplicado com funções de base polinomiais, sendo a seção transversal do guia aproximada por um polígono convexo. Este tipo de função limitou o número de modos que podem ser calculados, uma vez que polinômios de grau alto geram instabilidades computacionais e overflow. Utilizando a mesma metodologia, os campos modais em guias de onda superquadráticos são analisados. Entretanto, as funções de base polinomiais são substituídas por funções trigonométricas, produzindo um modelo numérico capaz de computar um grande número de modos em um tempo de execução razoável. Os guias superquadráticos constituem uma classe de guias uniformes, incluindo guias circulares, elípticos, quase retangulares e outros de seções intermediárias. Conseqüentemente, eles são úteis na construção de diversos dispositivos em guias de onda, incluindo transições de diferentes seções, tais como circular para elíptica e circular para retangular. O método do casamento de modos é aplicado na determinação da matriz de espalhamento de descontinuidades entre guias superquadráticos. Diversas aplicações numéricas são apresentadas e comparadas com resultados obtidos através de outras técnicas. / [en] In the present work, the modal fields and cutoff wavenumbers of arbitrary cross section waveguides are determined using the Rayleigh-Ritz method. Initially, the method is applied to waveguides with cross section approximated by a convex polygon. Polynomial basis functions are used. Such basis functions limit the number of modes that can be computed, since polynomials of high degree generate computer instabilities and overflow. Using the same methodology, the modal fields of superquadric waveguides are analyzed. Polynomial basis functions are replaced by trigonometric functions, however, producing an efficient numerical model capable of computing a large number of modes with a reasonable computer time. Superquadric waveguides constitute a class of uniform waveguides that include circular, elliptical, almost rectangular waveguides and a series of intermediate cross section waveguides. As a consequence they are quite useful in the construction of several devices, including transitions between waveguides of different cross sections, such as circular to elliptical and circular to rectangular. The mode matching technique is applied to the determination of the scattering matrix of discontinuities between superquadric waveguides. Several numerical applications are presented and compared to results obtained from other techniques.

The conventional large radii bends used in large cross section silicon-on-insulator waveguides were replaced with novel wet etched corner mirrors, potentially allowing much smaller devices, therefore lower costs. If such corners had been based on reactive ion etch techniques they would have had the disadvantage of rougher surfaces and poor alignment in the vertical direction. Wet etching overcomes these two problems by providing smooth corner facets aligned precisely to the vertical {100} silicon crystallographic planes. The waveguides obtained had angled walls, and so numerical analysis was undertaken to establish the single mode condition for such trapezoidal structures. To show the relationship between fabrication tolerances and optical losses a three dimensional simulation tool was developed, based on expansion of the incident mode into plane waves. Various new fabrication techniques were are proposed, namely: the use of titanium as a mask for deep silicon wet anisotropic etching, a technique for aligning masks to the crystal plane on silicon-oninsulator wafers, a corner compensation method for sloping sidewalls, and the suppression of residues and pyramids with the use of acetic acid for KOH etching. Also, it was shown that isopropyl alcohol may be used in KOH etching of vertical walls if the concentration and temperature are sufficiently high. As the proposed corner mirrors were convex structures the problem of undercutting by high order crystal planes arose. This was uniquely overcome by the addition of some structures to effectively convert the convex structures into concave ones. The corner mirrors had higher optical losses than were originally hoped for, similar to those of mirrors in thin film waveguides made by RIE. The losses were possibly due to poor angular precision of the lithography process. The design also failed to provide adequate mechanisms to allow the etch to be stopped at the optimal time. The waveguides had the advantage over thin film technology of large, fibre-compatible cross sections. However the mirror losses must be reduced for the technology to compete with existing large cross section waveguides using large bends. Potential applications of the technology are also discussed. The geometry of the crystal planes places fundamental limits on the proximity of any two waveguides. This causes some increase in the length of MMI couplers used for channel splitting. The problem could possibly be overcome by integrating one of the mirrors into the end of the MMI coupler to form an L shaped junction.

This thesis explored the theory, design, fabrication and characterization of AlGaAs Bragg reflection waveguides (BRW) towards the goal of a platform for monolithic integration of active and optically nonlinear devices. Through integration of a diode laser and nonlinear phase-matched cavity, the possibility of on-chip nonlinear frequency generation was explored. Such integrated devices would be highly useful as a robust, alignment free, small footprint and electrically injected alternative to bulk optic systems. A theoretical framework for modal analysis of arbitrary 1-D photonic crystal defect waveguides is developed. This method relies on the transverse resonance condition. It is then demonstrated in the context of several types of Bragg reflection waveguides. The framework is then extended to phase-match second-order nonlinearities and incorporating quantum-wells for diode lasers. Experiments within a slab and ridge waveguide demonstrated phase-matched Type-I second harmonic generation at fundamental wavelength of 1587 and 1600 nm, respectively; a first for this type of waveguide. For the slab waveguide, conversion efficiency was 0.1 %/W. In the more strongly confined ridge waveguides, efficiency increased to 8.6 %/W owing to the increased intensity. The normalized conversion efficiency was estimated to be at 600 %/Wcm^2. Diode lasers emitting at 980 nm in the BRW mode were also fabricated. Verification of the Bragg mode was performed through imaging the near- field of the mode. Propagation loss of this type of mode was measured directly for the first time at 14 cm^-1. The lasers were found to be very insensitive with characteristic temperature at 215 K. Two designs incorporating both laser and phase-matched nonlinearity within the same cavity were fabricated, for degenerate and non-degenerate down-conversion. Though the lasers were sub-optimal, a parametric fluorescence signal was readily detected. Fluorescence power as high as 4 nW for the degenerate design and 5 nW for the non-degenerate design were detected. The conversion efficiency was 4176 %/Wcm^2 and 874 %/Wcm^2, respectively. Neither design was found to emit near the design wavelength. In general, the signal is between 1600-1800 nm and the idler is between 2200-2400 nm. Improvements in laser performance are expected to drastically increase the conversion efficiency.

This thesis explored the theory, design, fabrication and characterization of AlGaAs Bragg reflection waveguides (BRW) towards the goal of a platform for monolithic integration of active and optically nonlinear devices. Through integration of a diode laser and nonlinear phase-matched cavity, the possibility of on-chip nonlinear frequency generation was explored. Such integrated devices would be highly useful as a robust, alignment free, small footprint and electrically injected alternative to bulk optic systems. A theoretical framework for modal analysis of arbitrary 1-D photonic crystal defect waveguides is developed. This method relies on the transverse resonance condition. It is then demonstrated in the context of several types of Bragg reflection waveguides. The framework is then extended to phase-match second-order nonlinearities and incorporating quantum-wells for diode lasers. Experiments within a slab and ridge waveguide demonstrated phase-matched Type-I second harmonic generation at fundamental wavelength of 1587 and 1600 nm, respectively; a first for this type of waveguide. For the slab waveguide, conversion efficiency was 0.1 %/W. In the more strongly confined ridge waveguides, efficiency increased to 8.6 %/W owing to the increased intensity. The normalized conversion efficiency was estimated to be at 600 %/Wcm^2. Diode lasers emitting at 980 nm in the BRW mode were also fabricated. Verification of the Bragg mode was performed through imaging the near- field of the mode. Propagation loss of this type of mode was measured directly for the first time at 14 cm^-1. The lasers were found to be very insensitive with characteristic temperature at 215 K. Two designs incorporating both laser and phase-matched nonlinearity within the same cavity were fabricated, for degenerate and non-degenerate down-conversion. Though the lasers were sub-optimal, a parametric fluorescence signal was readily detected. Fluorescence power as high as 4 nW for the degenerate design and 5 nW for the non-degenerate design were detected. The conversion efficiency was 4176 %/Wcm^2 and 874 %/Wcm^2, respectively. Neither design was found to emit near the design wavelength. In general, the signal is between 1600-1800 nm and the idler is between 2200-2400 nm. Improvements in laser performance are expected to drastically increase the conversion efficiency.

The Multimode Interference (MMI) mechanism is a powerful toool used in the analysis and design of a certain class of optical, microwave and millimeter wave devices. The principles of the MMI method and the self-imaging principle is described. Using this method, NXM MMI couplers, MMI splitter/combiners are analyzed. Computer simulations for illustrating the &quot / Multimode Interference Mechanism&quot / are carried out. The MMI approach is used to analyze overmoded &#039 / rectangular metallic&#039 / and &#039 / dielectric slab&#039 / type of waveguides and devices. The application of the MMI technique is investigated experimentally by using a metallic waveguide structure operating in the X-band. The construction of the related structure and the related experimental work are reported.

Guias de onda de luz foram fabricados por difusão térmica de Titânio em substratos de LiNbO3. Os índices efetivos dos modos guiados foram medidos usando o método de acoplamento por prismas e a equação de onda resolvida numericamente usando a aproximação WKB. Profundidade de difusão, variação máxima do índice de refração e o perfil da concentração de Titânio são calculados para um guia que suporta três modos TE / Optical waveguides have been fabricated by thermal diffusion of Titanium into LiNO3 substrate. The effective indices of guided modes have been measured using a prism coupling method and the wave equation has been solute numerically using the WKB approximation. The diffusion depth, maximum refractive index change and titanium concentration profited was calculated for one waveguide that support three TE modes

This thesis presents the integration of atomic vapor cells with anti-resonant reflecting optical waveguides (ARROWs) fabricated on silicon chips. These potentially provide a compact platform for a number of optical applications, including the study of quantum coherence effects such as electromagnetically induced transparency and single-photon nonlinearities, as well as frequency stabilization standards. The use of hollow waveguides allows for light propagation in low index (vapor) media with compact mode areas. ARROWs make particularly attractive waveguides for this purpose because they can be interfaced with solid core waveguides, microfabricated on a planar substrate, and are effectively single mode. ARROW fabrication utilizes an acid-removed sacrificial core surrounded by alternating plasma deposited dielectric layers, which act as Fabry-Perot reflectors. To demonstrate the effectiveness of the ARROW as a vapor cell, a platform consisting of solid and hollow core waveguides integrated with rubidium vapor cells was developed. A variety of sealing techniques were tested for vapor cell integration with the ARROW chip and for compatibility with rubidium. Rubidium was used because it is of particular interest for studying quantum coherence effects. Liquefied rubidium was transferred from a bulk supply into an on-chip vapor cell in an anaerobic atmosphere glovebox. Optical absorption measurements confirmed the presence of rubidium vapor within the hollow waveguide platform. Further analysis of the measurements revealed high optical density of rubidium atoms in the hollow core. Saturated absorption spectroscopy measurements verified that the on-chip integrated vapor cell was suitable for common precision spectroscopy applications.

<p>This thesis reports work targeting the integration of Si light emitters with optical waveguides. Such integrated devices would find utility in a number of applications including telecommunications, optical interconnects, and biological and chemical sensors. Much research has been directed by others on how to improve the emission efficiency and achieve lasing in VLSI (very large scale integration) compatible sources. Here, the focus is on how such devices can be integrated with planar waveguides. Two enhancement techniques were selected for potential integration; defect engineering (DE), and Si nanocrystals (Si-nc) embedded in Si02• Defect engineered light emitting diodes (LEDs) made on silicon-on-insulator (SOI) and emitting at 1.1 μm were successfully demonstrated. In addition, surface photoluminescence from SOI was analyzed to account for interference from the SOI cavity. However, it was determined that the emission efficiency of defect engineered LEDs studied during the course of this work is below that which was reported previously, and that the fabrication procedure thus suffers from irreproducibility. Barring an enormous advancement in the DE technique, it is concluded that the emission efficiency is too small to make use of its integration potential. </p><p>A more successful approach was obtained from the Si-nc system fabricated using electron-cyclotron resonance plasma enhanced chemical vapor deposition (ECR-PECVD). Optically pumped edge emitting devices were designed, fabricated and characterized. The devices are comprised of Si-ncs emitting at 800 nm, integrated with slab silicon nitride waveguides. This work is the first report of edge emission from Si-ncs integrated with silicon nitride waveguides. Edge emission and waveguide properties were characterized in the ~850 nm emission band of the Si-ncs. The edge emission was well described as a propagating mode, attenuated primarily by the Si-nc film. Propagation losses of a typical air/Si-nc/SiNx/Si02 waveguide were measured to be 11 ± 2 dB/cm and 20 ± 2 dB/cm at 850 nm in the TE and TM polarizations respectively. A wavelength dependent loss of -0.14 ± 0.03 dB/(cm*nm) was found to exist in the material loss of Si-nc films. In addition, the Si-nc films were found to undergo a partially recoverable photo-induced degradation of PL efficiency during exposure to pump light. Processing techniques compatible with both high efficiency Si-nc and low loss silicon nitride were developed and described. A two-sectioned photonic device was also designed, fabricated and characterized. The device contained an optically pumped Si-nc emitting waveguide section integrated with a low loss silicon nitride slab waveguide. The potential for optically pumped Si-nc emitters integrated with silicon nitride photonic circuits thus appears promising.</p> / Thesis / Doctor of Philosophy (PhD)