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The Finite-Difference Time-Domain (FDTD) method has become a very powerful tool for the analysis of propagating electromagnetic waves. It involves the discretization of Maxwell's equations in both time and space that leads to a numerical solution of the wave propagation problem in the time domain. The technique's main benefits are that it permits the description of wave propagation in non-uniform media, it can easily accommodate a wide range of boundary conditions, and it can be used to model nonlinear effects as well as the wave behaviour near localized structures or material defects. In this study, we extend this technique to mechanical wave propagation in piezoelectric crystals. It is observed to give large reflection artefacts generated by the computational boundaries which interfere with the desired wave propagation. To solve this problem, the renowned absorbing boundary condition called perfectly matched layer (PML) is used. PML was first introduced in 1994 for electromagnetic wave propagation. Our research has further developed this idea for acoustic wave propagation in piezoelectric crystals. The need to improve the large reflection artefacts by introducing a finite thickness PML has reduced acoustic wave reflection occurring due to practical errors to less than 0.5 %. However, it is found that PML can generate numerical instabilities in the calculation of acoustic fields in piezoelectric crystals. Theses observations are also discussed in this report. / Thesis / Master of Applied Science (MASc)

Yes / The potentially broad application area in engineering design using Genetic Algorithm (GA) has been widely adopted by many researchers due to its high consistency and accuracy. Presented here is the initial design of a wideband non-dispersive wire bow-tie antenna using GA for breast cancer detection applications. The ultimate goal of this design is to achieve minimal late-time ringing but at higher frequencies such as that located from 4 to 8 GHz, in which is desire to penetrate human tissue for near field imaging. Resistively loading method to reduce minimal ringing caused by the antenna internal reflections is implemented and discussed when the antenna is located in free space and surrounded by lossy medium. Results with optimised antenna geometry and different number of resistive loads are presented and compared with and without existence of scatterers.

Prediction of the sound field in large urban environments has been limited thus far by the heavy computational requirements of conventional numerical methods such as boundary element (BE), finite-difference time-domain (FDTD), or ray-tracing methods. Recently, a considerable amount of work has been devoted to developing energy-based methods for this application, and results have shown the potential to compete with conventional methods. However, these developments have been limited to two-dimensional (2-D) studies (along street axes), and no real description of the phenomena at issue has been exposed (e.g., diffraction effects on the predictions). The main objectives of the present work were (i) to evaluate the feasibility of an energy-based method, the diffusion model (DM), for sound-field predictions in large, 3-D complex urban environments, (ii) to propose a numerical hybrid method that could improve the accuracy and computational time of these predictions, and (iii) to verify the proposed hybrid method against conventional numerical methods. The proposed numerical hybrid method consists of a full-wave model coupled with an energy-based model. The full-wave model is used for predicting sound propagation (i) near the source, where constructive and destructive interactions between waves are substantial, and (ii) outside the cluttered environment, where free-field-like conditions apply. The energy-based model is used in regions where diffusion conditions are met. The hybrid approach, as implemented in this work, is a combination of FDTD and DM models. Results from this work show the role played by diffraction near buildings edges close to the source and near the exterior boundaries of the computational domain, and its impact on the predictions. A wrong modeling of the diffraction effects in the environment leads to significant under or overpredictions of the sound levels in some regions, as compared to conventional numerical methods (in these regions, some differences are as high as 10 dB). The implementation of the hybrid method, verified against a full FDTD model, shows a significant improvement of the predictions. The mean error thus obtained inside the cluttered region of the environment is 1.5 dB. / Master of Science

Parmi les filières de cellules photovoltaïques, les cellules solaires organiques suscitent un intérêt industriel par leur faible coût financier et de production énergétique et leur application possible sur des substrats flexibles de type plastique. L'ITO (Indium Tin Oxide) est l'électrode transparente conductrice (ETC) la plus utilisée pour ces cellules ainsi que pour d'autres dispositifs optoélectroniques. Cependant, ce matériau n'est pas sans présenter certains inconvénients (rareté de l'indium, structure non adaptée à des substrats flexibles,…), et la recherche d'alternatives à l'ITO est une préoccupation actuelle de la communauté scientifique internationale. Une possibilité est alors offerte par des structures multicouches de type Oxyde|Métal|Oxyde. Le rôle des deux couches d’oxydes est d’accorder, en ajustant les épaisseurs, la position, l’intensité et la largeur de la fenêtre spectrale de transmission. Des travaux numériques et expérimentaux couplés ont été effectués en particulier sur les structures SnOx|Ag|SnOx, TiOx|Ag|TiOx et ZnS|Ag|ZnS. Par microstructuration de telles électrodes ou bien par incorporation d’un bicouche Cu|Ag comme feuillet métallique au coeur de la structure, il est possible d’améliorer leurs performances optiques en amplifiant et en élargissant la fenêtre spectrale de transmission, sans dégrader leur haute conductivité. L’intégration d’électrodes SnOx|Ag|SnOx et TiOx|Ag|TiOx au sein de cellules solaires organiques inverses a été entrepris. Des résultats photoélectriques très prometteurs ont été obtenus avec la structure TiOx|Ag|TiOx qui permet d’atteindre des performances de niveau quasi-équivalent aux cellules de référence à base d’ITO. / Among all variants of photovoltaic thins films, organic solar cells generate a major industrial interest due to low manufacturing costs, reasonable levels of energy production and suitability to flexible substrates like plastic. ITO (Indium Tin Oxide) is the most used Transparent Conductive Electrode (TCE) for organic solar cells as well as other optoelectronic devices. However, this material is not without drawbacks (scarcity of indium, non-suitability to flexible substrates...), and the search for alternatives to ITO is actively pursued by the international scientific community. One possibility is offered by Oxide|Metal|Oxide multilayer structures. By reaching the thin metal layer percolation threshold and by varying its thickness, it is possible to obtain very high conductivity and transparency of this multilayer in the visible spectral range. The role of both oxide layers is to tune the position, intensity and width of the spectral transmission window by adjusting the oxides’ thicknesses. Coupled experimental and numerical works were lead in particularly on SnOx|Ag|SnOx, TiOx|Ag|TiOx and ZnS|Ag|ZnS structures. By microstructuring such electrodes, or by incorporating a Cu|Ag bilayer as metal sheet at the core of the structure, it is possible to increase the optical performances by amplifying and expanding the spectral transmission window without degrading the high conductivity. The integration of SnOx|Ag|SnOx and TiOx|Ag|TiOx electrodes in inversed organic solar cells was undertaken. Very promising photoelectric results were obtained with the TiOx|Ag|TiOx structure which allows to reach performances close to that obtained with ITO-based reference cells.

Descargas atmosféricas representam uma das principais causas de interrupção no fornecimento de energia para os consumidores, e embora tenham efeitos mais intensos quando incidem diretamente nas redes elétricas, é o caso das descargas indiretas que chama mais atenção, já que elas ocorrem com maior frequência. Tanto as primeiras descargas que geralmente ocorrem com maior intensidade de corrente, quanto as descargas subsequentes que têm menor tempo de frente associado, irradiam campos eletromagnéticos que ao se acoplarem com as redes elétricas geram surtos que podem causar tanto a interrupção do fornecimento de energia quanto danos a equipamentos. A presença de edifícios na região de incidência da descarga atmosférica afeta a propagação das ondas irradiadas, criando diferentes padrões de campos resultantes, os quais são responsáveis por sobretensões induzidas. Embora tanto a descarga atmosférica em si quanto a caracterização do ambiente ao seu redor sejam de natureza complexa para sua representação, ferramentas computacionais bem estruturadas podem representar o fenômeno de forma satisfatória, como é o caso da ferramenta computacional desenvolvida neste trabalho utilizando o método das diferenças finitas no domínio do tempo. O presente trabalho apresenta dois estudos para verificação da influência de edificações na propagação de campo irradiado por descargas atmosféricas. O primeiro estudo avaliou o comportamento das componentes do campo elétrico e do campo magnético irradiados, comparando resultados obtidos com e sem a presença de edificações numa pequena região. Tanto os parâmetros geométricos dos três edifícios considerados neste estudo, como a permissividade e a condutividade elétrica do solo e dos edifícios, foram variados para identificar a sua influência nos campos irradiados. Os resultados mostraram diferentes comportamentos das componentes dos campos resultantes em função da variação desses parâmetros, observando-se inversão de polaridade, oscilações na forma de onda e tanto redução quanto aumento do valor de campo. O segundo estudo avaliou um caso mais geral em que a componente vertical de campo elétrico foi tomada em nove pontos diferentes de uma região tipicamente urbana, com a presença de 102 edifícios. Os valores de campo avaliados em cada ponto, dez metros acima do solo, consideraram a incidência aleatória de 28 descargas atmosféricas distintas, cada uma atingindo o topo de um dado edifício. Os resultados desse segundo estudo mostraram que exceto nos casos em que a descarga atmosférica ocorre próximo do ponto analisado, há reduções significativas do campo elétrico vertical. Desta forma é possível perceber que não apenas a existência de edifícios, mas a sua concentração com diferentes características elétricas e geométricas, podem influenciar significativamente a propagação de campo irradiado. Os valores calculados a partir da ferramenta desenvolvida podem ser usados em conjunto com modelos de acoplamento, para o cálculo de sobretensões induzidas em redes elétricas, em situações realistas com configurações mais complexas. / Atmospheric discharges represent one of the main causes of interruption in power supply to consumers, and although they have more intense effects when direct impact on energy lines, are the case of indirect discharges that draws more attention, since they occur more frequently. Both the first discharges, occurring generally with greater intensity of current, as subsequent discharges that have shorter front time associated, radiate electromagnetic fields which engage with the electrical networks generating surges that can cause so much disruption of power supply as damage to the equipment. The presence of buildings in the lightning incident area affects the propagation of the radiated waves, creating different patterns of resultant fields, which are responsible for induced overvoltages. Although both the lightning itself and characterization of the surrounding environment are of a complex nature for its representation, structured computational tools can represent satisfactorily the phenomenon, such as the software tool developed here using the finite difference time domain method. This work presents two studies to verify the influence of buildings in the propagation of lightning irradiated field. The first study assessed the behavior of the components of the electric field and magnetic field irradiated, by comparing results obtained with and without the presence of buildings in a small region. Both the geometric parameters of the three buildings considered in this study, as the permittivity and electrical conductivity of the soil and buildings, were changed to identify their influence on radiated fields. The results showed different behaviors of the components of the resulting field due to the variation of these parameters, observing polarity inversion, oscillations in the waveform and either a reduction or increase of the field value. The second study evaluated a more general case where the vertical component of the electric field was taken at nine different points of a typical urban area, in the presence of 102 buildings. The field values evaluated at each point, ten meters above the ground, considered the effect of 28 different random lightning, which hit the top of a given building. The results of this second study showed that except in cases where atmospheric discharge occurs near the analyzed point, there are significant reductions of the vertical electric field. Thus it can be seen that not only the existence of buildings, but its concentration with different electrical and geometrical characteristics, can significantly influence the propagation of irradiated field. The values calculated from the developed tool can be used in conjunction with coupling models for calculating induced overvoltages on power lines, in realistic situations with complex configurations.

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.