Abstract Optical fiber communications have been become one of the most popular researches since 1970s. In this field, there are many studies on the coupling between semiconductor lasers and fibers and many conclusions are demonstrated. In this thesis we build a 2-D numerical model to simulate energy coupling between laser diodes (LDs) and tapered optical fibers. Our model is based on the spectral domain integral equation (SDIE) formulation which is derived from Maxwell equations and the principle of mode matching. Through this numerical model we will be able to show the field distribution in LD waveguide junctions. We may also use this tool to study the coupling parameters such as the separation distance and tapered fiber geometry.

The limit of current technology for mobile base station filters is the multimode filter, in which each cavity supports two (or possibly three) independent degenerate resonances. Shielded dielectric resonators with a rectangular cross-section are useful in this application. In the design of these filters, manufacturers are using software packages employing finite element or finite difference time domain techniques. However, for sufficient accuracy these procedures require large numbers of points or elements and can be very time consuming. Over the last decade research using the mode matching technique has been used to solve this kind of difficulty for various types of filter design and waveguide problems. In this thesis a mode matching method and computer program is developed to calculate the propagation coefficients and field patterns of the modes in a shielded rectangular dielectric rod waveguide. Propagating, complex, evanescent and backward wave modes are included and the work shows the presence of a dominant mode, and other fundamental modes, not previously identified. The effect of the shield proximity on the propagation characteristics and mode spectrum is investigated, together with the limitations on the accuracy of the mode matching method. In addition, the fields within the shielded rectangular dielectric rod waveguide, are used to calculate the attenuation coefficient of the dominant and fundamental modes. The influence on the attenuation coefficient of the proximity of the shield to the rod is also evaluated for these modes and limitations on accuracy are discussed. The calculated numerical results for the propagation and attenuation coefficient values are verified by measurement. The propagation coefficients results are typically within 2% of those measured. Verification of the attenuation coefficient results is achieved by comparing calculated and measured Q at the resonant frequencies of a number of shielded rectangular dielectric rod resonators. The difference between calculated and measured Q values is on average less than 4%. In the absence of a full solution of the shielded rectangular dielectric rod resonator, these results provide useful design information for this structure. In addition, the work reported in this thesis provides a basis for a full electromagnetic solution of this type of resonator. This would encompass the cubic dielectric resonator in a cubical cavity.

Finite-Difference (FD) based complex modes solver and Complex Mode Matching Method (CMMM) is one of the most popular combinations in modeling and simulation of opti- cal waveguides. This thesis covers the basic theories behind the approaches and impor- tant implementation details. Weighted Optical Path Distance is proposed to speed up convergence and improve numerical accuracy to deal with asymmetric structures. An improved formula is derived for Complex Mode Matching Method expansion process based on matrix optimization. The latter part applies the above approach in the mod- eling of bending structures and grating structures. Typical structures, including bend- ing structures, straight-bend-straight structures, long-period gratings, gratings with de- posited layer, gratings with deep corrugations, are investigated and analyzed. / Thesis / Master of Science in Electrical and Computer Engineering (MSECE)

During the past 60 years fluid-structure interaction in a wide range of three dimensional circular cylinder problems have been studied. Initial problems considered a rigid wall structure which were solved using impedance model comparisons. Soon after, further solution techniques were used, such as computer simulation, transfer matrix methods and finite element techniques. However such problems were only valid for low frequencies when compared with experiments, this was because that did not include higher order modes. The importance of higher order modes was then established and studies have since included these modes. More recently, mode matching methods have been used to find the amplitudes of waves in structures comprising two or more ducts. This has been done with using an orthogonality relation to find integrals which occur from the application this method. This methodology is demonstrated in as background information and is applied to prototype problems formed of rigid ducts. The rigid duct theory led to the consideration of elastic shells, of which several shell modelling equations were available from the vibration theory. In this thesis, the Donnell-Mustari equations of motion are used to model thin, elastic, fluid-loaded shells of circular cross-section. It is demonstrated that generalised orthogonality relations exist for such shells. Two such relations are found: one for shells subject to axisymmetric motion and one for shells subject to non-axisymmetric motion. These generalised orthogonality relations are new to the field of acoustics and are specific to shells modelled with the Donnell-Mustari equations of motion. The mode matching method is used to find the amplitudes of waves propagating in prototype problems and the generalised orthogonality relations are used to find integrals which occur through this method. Expressions for energy for all considered structure types are used to find the resulting energy for each prototype problem and results for equivalent problems are compared. In addition, verification of the resulting amplitudes is done by ensuring that the matching conditions are suitably satisfied. It is anticipated that the method will have application to the understanding and control of the vibration of cylindrical casings such as those enclosing turbo-machinery. Another application of the method would be the tuning of cylindrical casings, such as those featured on car exhaust systems or HVAC (heating, ventilation and air conditioning) systems.

<p>The main contributions of this thesis include two points: firstly, we originally establish Complex STM to semi-analytically calculate the mode profiles of multi-layer planar waveguide terminated with both PML and PRB ; secondly, although CMMM has been generally applied to the simulation of waveguide facets, Bragg gratings, etc[52-53], we for the first time demonstrate that CMMM can also be utilized for the modeling of couplings of radiation field outgoing perpendicularly to the waveguide axis with an incident wave launched in the examples of high-index-contrast waveguide crossings and corners. CMMM is proved to be able to estimate the field profiles and power flows accurately through the validation with FDTD.</p> / <p>Optical waveguides are basic building blocks of high-density photonic integrated circuits and play crucial roles in optical access networks, biomedical system, sensors and so on. Various kinds of dielectric waveguides apply the total internal reflection condition to transmit optical field [9] and even more complicated structures based on waveguide interconnects, Bragg grating, photonic crystals are actively developed by corporations and academic institutes. Especially, the fast developing pace of Metal-Organic Chemical Vapor Deposition (MOCVD), Molecular Beam Epitaxy (MBE) and other fabrication techniques has predicted the increasing complication and thus more advanced function of modern optics integrated circuits. Under such circumstances, convenient and accurate modeling and simulation schemes are necessary for the exploration, designing and optimization of photonic devices, systems and networks before the time-consuming and expensive fabrication process.</p> <p>The thesis summarizes several frequency-domain modeling schemes for the calculation of mode profile or beam propagation in 2D dielectric waveguide. The thesis mainly covers conventional Smooth Transition Method (STM), High Order Finite Difference (HOFD) scheme, Complex STM, and Complex Mode Matching Method (CMMM) based on the 2D waveguide model terminated with Perfect Matching Layer (PML) and Perfect Reflection Boundary (PRB). The mode spectrums and modal patterns obtained from Complex STM are compared with those of HOFD, and the simulation of waveguide crossings and corners with CMMM is validated with Finite-Difference-Time-Domain (FDTD) Method.</p> <p><strong> </strong></p> / Master of Applied Science (MASc)

La tesis estudia cinco formulaciones del método de modos acoplados para analizar guías con medios magnéticos en su interior. La formulación indirecta, de tipo general, se ha aplicado al análisis de desfasadores toroidales obteniéndose resultados similares a los obtenidos mediante un método numérico puro como es el de diferencias finitas. La tesis introduce igualmente una formulación del método de adaptación que junto con el método de modos acoplados permite analizar discontinuidades simples. La combinación de los métodos anteriores con la matriz de dispersión generalizada ha permitido analizar discontinuidades en guías de onda con ferritas transversalmente magnetizadas con discontinuidades en las tres direcciones del sistema de coordenadas.