Bound state systems consisting of three nonrelativistic particles are numerically studied. Calculations are performed employing two-body and three-body forces as input in the Hamiltonian in order to study the role or contribution of three-body forces to the binding in these systems. The resulting differential Faddeev equations are solved as three-dimensional equations in the two Jacobi coordinates and the angle between them, as opposed to the usual partial wave expansion approach. By expanding the wave function as a sum of the products of spline functions in each of the three coordinates, and using the orthogonal collocation procedure, the equations are transformed into an eigenvalue problem. The matrices in the aforementioned eigenvalue equations are generally of large order. In order to solve these matrix equations with modest and optimal computer memory and storage, we employ the iterative Restarted Arnoldi Algorithm in conjunction with the so-called tensor trick method. Furthermore, we incorporate a polynomial accelerator in the algorithm to obtain rapid convergence. We applied the method to obtain the binding energies of Triton, Carbon-12, and Ozone molecule. / Physics / M.Sc (Physics)

Orientador: Newton Cesário Frateschi / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-17T01:57:53Z (GMT). No. of bitstreams: 1 Barea_LuisAlbertoMijam_M.pdf: 3934128 bytes, checksum: 9cd5c7861ac2af0dc42057f7f99ef89b (MD5) Previous issue date: 2010 / Resumo: As micro-cavidades ópticas são componentes essenciais em sistemas ópticos integrados, pois elas permitem capturar seletivamente, liberar e armazenar fótons, além de promoverem suas interações. Como exemplo, os micro-discos e micro-anéis são elementos que proporcionam tempos de vidas fotônicos extremamente longos, que podem ser utilizados tanto para filtros espectrais quanto para interações de fótons com alta eficiência não linear. Seu pequeno volume e seu alto tempo de vida fotônico são importantes para promoção eficiente de efeitos ópticos não lineares e, especialmente, o processo de mistura de quatro ondas com uma única freqüência de bombeio. No entanto, acoplar luz em um ressonador ainda é realizado com integrações híbridas utilizando fibras estranguladas. Nesta dissertação, nós apresentamos uma nova técnica para a fabricação de estruturas com ressonadores integrados monoliticamente a guias de ondas planares estrangulados, baseados em camadas de Si3N4/SiO2 depositadas sobre silício. Para isto, foi utilizada uma técnica que combina a nano fabricação, baseada em corrosões com um feixe de íons focalizados (FIB), com a técnica convencional de micro fabricação. Utilizando esta combinação, foi possível fabricar ressonadores acoplados a guias de ondas estrangulados e caracterizá-los. Para finalizar, nós observamos a geração de fótons em uma ressonância de um micro-anel devido ao efeito não linear de mistura de quatro ondas gerada pelo bombeio em uma ressonância subseqüente do anel / Abstract: Optical microcavities are essential components in optical integrated systems for they provide selective capture, release, and storage of photons as well as interaction with matter and other photons. As an example, micro-disks and micro-rings are elements that provide extremely long photon lifetime that can be used for spectral filtering as well for highly efficient non-linear photon interaction. For instance, its small volume and the high photonic lifetime are very important for the efficient promotion of nonlinear effects and, specially, the four wave-mixing (FWM) process with a single pumping frequency. However, coupling light to and from the resonator is still achieved with hybrid integration using tapered silica fibers. But, in this dissertation, we present a new technique for the fabrication of structures with monolithically integrated resonators and planar tapered waveguides, all based in Si3N4/SiO2 layers deposited on silicon. We use an approach that combines nano fabrication techniques based on focused ion beam (FIB) milling and conventional micro fabrication techniques. Using this approach, we could fabricate resonators coupled to tapered waveguides and characterize them. Finally, we observed the photon generation at a micro-ring resonance due to four-wave mixing generated by pumping at a subsequent micro-ring resonance / Mestrado / Física da Matéria Condensada / Mestre em Física

Orientador: Luiz Carlos Barbosa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-04T20:34:50Z (GMT). No. of bitstreams: 1 GarciaRivera_VictorAnthony_M.pdf: 15268986 bytes, checksum: 03f47604e1a522457d30d9fa547a024d (MD5) Previous issue date: 2005 / Resumo: Neste trabalho de pesquisa, reporto a fabricação e caracterização de vidros germano-telurito para amplificadores ópticos curtos. Estes são fabricados em guias de onda planar e canal pela técnica de troca iônica e fibra em vidro, dopados com altas concentrações de íons de Er3+ cuja composição é: 75TeO2 ¿ 2GeO2 ¿ (10+x)Na2O ¿ (12-x)ZnO ¿ 1Er2O3 (mol%, onde x=0, 2 e 5). São preparados guias multímodos e monomodos, as profundidades dos guias podem ser controladas pela variação do tempo e da temperatura no processo da troca iônica. Com o vidro de maior índice de refração consegui fabricar fibra óptica (só nucleo) e solda com outro vidro de menor índice de refração, pela técnica de fibra em vidro. A preparação dos vidros foi feita pela técnica convencional de fusão à temperatura de 7500C. Encontrou-se grande estabilidade térmica nos sistemas vítreos. Realizou-se as medidas de espectroscopia Raman, absorção, emissão e tempo de vida, onde se mostra a maior largura de banda de emissão dos vidros germano-teluritos dopados com íons Er3+ quando comparado com amplificadores comerciais feitos à base de vidros silicatos. Os vidros já polidos passaram pelo processo de fotolitografía, durante a fabricação dos guias de ondas se empregou a técnica de troca iônica dos íons Ag+. Na+, processo tomando por base a temperatura de início de cristalização Tg; neste processo os vidros foram submergidos num banho de sais que continha 2AgNaO3 ¿ 49NaNO3 ¿ 49KNO3. Os índices efetivos dos modos foram medidos pela técnica de acoplamento por prisma com o equipamento Metricom. Foram determinados o perfil do índice de refração e os parâmetros da difusão: coeficiente de difusão efetiva De e a energia de ativação ED. Conseguiu-se fabricar guias de onda planar e canais monomodos e multímodos pela técnica de troca iônica em vidros germano-teluritos dopados com altas concentrações de íons de Er3+. Empregando a técnica de fibra em vidro, consegui fabricar um guia de onda. Método totalemente novo que consiste na solda de uma fibra óptica (núcleo) com um substrato de menor índice de refração que é a casca para esta fibra mediante esta técnica. Neste processo deve-se ter em conta a região de temperatura Tg ¿ Tx, para evitar possiveis processos de cristalização no processo de solda da fibra óptica com o substrato / Abstract: In this work the production and characterization of germane-tellurite glasses for small optical amplifiers are reported. These materials were applied in the manufacture of planar e channel waveguide using the technique of ionic exchange in glasses and fiber on glass, doped with high concentrations of ions of Er3+ whose composition is: 75TeO2 ¿ 2GeO2 ¿ (10+x)Na2O - (12-x)ZnO ¿ 1Er2 O3 (mol%, x= 0, 2 e 5). Multimode and monomode guides have been prepared, and the depths of the guide can be controlled for the time and the temperature variation in the process of the ionic exchange. With the glass of high refraction index, manufacture of the optic fiber (only nucleus), and welding this with another glass of smaller refraction index were carried out for the fiber technique on glass purpose. The preparation of glasses was made by the conventional technique of fusing at the temperature of 7500C and glasses of great thermal stability were obtained characterization Raman, optical absorption, light emission and lifetime measurements were performed. The optical absorption of glasses doped tellurite with ions Er3+ has been considerably broader than those of the amplifiers of glass base silicate glasses. The polishing of glasses was done using the photo-lithographical process during the construction of the waveguides. The technique of Ag+. Na+ ion-exchange was applied near Tg and below Tx. In this process, the glasses have been submerged in a bath of melted 2AgNaO3 ¿ 49NaNO3 ¿ 49KNO3. The effective refraction index was measured by the coupled prism technique using the Metricom equipment. The refraction index profile and the diffusion parameters as the diffusion effective coefficient De and the energy of activation ED were determined. Planar monomode and multimode waveguide channel was manufactured using the ion-exchange technique in germane-tellurite glasses doped with high concentration of Er3+ ions. A new method of glass fiber preparation is introduced and consists of the soldering of a fiber optic (nucleus) to a substrate of smaller refraction index. In this process the temperature region between Tg and Tx was avoided in order to prevent against any possible crystallization soldering process / Mestrado / Física / Mestre em Física

Orientador: Luiz Carlos Barbosa / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-06T18:46:29Z (GMT). No. of bitstreams: 1 RamosGonzales_RoddyElky_M.pdf: 6808680 bytes, checksum: 483930056f42b4b00eb9026433b70044 (MD5) Previous issue date: 2003 / Resumo: Este trabalho informa a preparação de guias de onda planar por troca iônica em vidros teluritos dopado com íons de Érbio cujas composições são, 14Na2O-25W O3 - 60TeO2 - 1Er2O3 (mol%) e 2GeO2 - 10N a2O - 12ZnO - 75TeO2 - 1Er2 O3(mol%), foram preparados guias multimodos e monomodos, as profundidades dos guias podem ser controladas pela variação da temperatura e o tempo da troca iônica. Os vidros foram preparados pela técnica convencional de fusão. Os vidros foram cortados e as duas superfícies maiores foram polidas para a caracterização e para a troca iônica. A troca iônica Ag + - Na + foi realizada submergindo as amostras de vidro num banho de sais que continha 2AgN O3 - 49NaNO3 - 49KNO3 (%peso). As temperaturas de difusão foram de 290°C até 360°C e os tempos de difusão de 1h a 24h, dependendo do vidro. Os vidros foram quimicamente estáveis durante o processo da troca iônica. Os índices efetivos dos modos foram medidos pela técnica de acoplamento por prisma em 632,8nm, 1305,4nm e 1536nm na polarização TE. O perfil do índice foi calculado usando o método de WKB inverso e o perfil assumiu-se como uma função gaussiana. Dos perfis medidos das amostras a varias temperaturas e tempos, foram calculados os parâmetros da difusão: coeficientes de difusão efetiva De e sua dependência da temperatura assim como a energia de ativação ED / Abstract: This work reports the preparation of planar waveguides by ionic exchange in glasses tellurite doped with íons of erbium whose compositions are, 14Na2O-25W O3 - 60TeO2 - 1Er2O3 (mol%) and 2GeO2 - 10N a2O - 12ZnO - 75TeO2 - 1Er2 O3 (mol%), have been prepared multi-mode and single-mode waveguides, the depths of the waveguides can be controlled by the variation of ion-exchange temperatures and times. The glasses were prepared by a conventional melting and quenching technique. The glasses were cut and the two larger surfaces were polished for the ion-exchange and characterization. The Ag + - Na + ion-exchange was performed by submerging the glass samples in a molten salt bath containing 2AgN O3 - 49NaNO3 - 49KNO3 (%wt). The diffusion temperatures had been of 290°C to 360°C and diffusion times from 1h to 24h, depending on the glass. The glasses were chemically stable during the process of ion-exchange. The effective mode indices were measured by the prism coupler technique at 632,8nm, 1305,4nm and 1536nm at TE polarization. The index profile was calculated using the inverse WKB method and the profile by assuming as a gaussian function. From measured index profiles for the samples at various temperatures and times, were calculated the diffusion parameters, effective diffusion coefficients De and its temperature dependence as well as the activation energy ED / Mestrado / Física / Mestre em Física

Orientador: Jose Roberto de França Arruda / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-13T08:53:33Z (GMT). No. of bitstreams: 1 Nascimento_RangelFerreirado_D.pdf: 7547341 bytes, checksum: 0793f0ff7763f81b44868f59db73aab6 (MD5) Previous issue date: 2009 / Resumo: Esta tese estuda e investiga o problema de propagação de ondas em estruturas periódicas usando o método de elemento espectral, a relação entre a matriz dinâmica e a matriz de transferência é mostrada para alguns casos, tais como, viga, barra, placa de Levy e modelo de Minddlin Hermman. A partir destas teorias, o método de propagação de ondas usando um modelo de elementos finitos de uma fatia do guia de ondas, WFEM é apresentado e o problema de prever os modos de propagação e os números de onda correspondentes. O objetivo deste trabalho é mostrar que usando o método WFEM e uma fatia do guia de onda modelado com elementos finitos sólido é possível construir elementos finitos espectrais para ser usado em guias de ondas homogêneos sem precisar de malha de refinamento. Tais elementos podem ser usados para modelar guias de ondas com seção transversal constante. A matriz de rigidez dinâmica para o elemento de barra elementar e para o elemento de viga de Euler Bernoulli são obtidos usando a formulação espectral padrão e obtidas usando uma fatia do guia de onda modelado pelo método FEM, são mostrados resultados do método proposto. / Abstract: This thesis, studies and investigates wave propagation problem in periodic structures using the spectral element method, the relation between the dynamic matrix and the transfer matrix is shown for some cases, such as, beam, bar, Levy plate and Mindlin-Herrmann's model. From these theories, the Wave Finite Element Method, WFEM is presented and the problem of predicting the wave propagation modes and the respective wavenumbers. The purpose of this work is to show that using the WFEM method and a slice of the waveguide modeled with solid finite elements, it is possible to develop spectral finite elements to be used in long homogeneous waveguides without the need of mesh refinement. Such elements can be used to model waveguides with constant cross section and long spans. The dynamic stiffness matrix of a simple rod and Bernoulli Euler beam element obtained using the standard spectral formulation and obtained via the FEM model of a slice are shown to be similar, thus validating the proposed method. / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Dimensionnée de manière semi-empirique, la voie ferrée est un système mécanique dont le comportement dynamique reste difficile à appréhender et à quantifier. Un outil numérique peut alors être à la fois une aide à la conception, en évaluant la performance de nouvelles structures, et un élément de diagnostic sur les voies existantes, en complément de mesures terrain adaptées.L'outil développé dans ce travail s'appuie sur les techniques de résolution des équations de propagation dans les guides d'ondes dans le domaine des fréquences/nombres d'onde. Sa particularité est l'introduction d'un modèle réduit basé sur une sous-structuration périodique de la structure, en ne conservant, pour la résolution des équations de dispersion, que quelques nombres d'onde judicieusement choisis. En s'appuyant sur cette technique de réduction de modèle et son extension à des modèles temporels avec contact mobile, les coûts de calcul et de stockage sont largement diminués. Cela en fait un outil performant et utilisable dans des études d'ingénierie portant sur la voie ferrée.Des étapes de vérifications numériques sur les hypothèses sous-jacentes à la réduction ont été réalisées en construisant un modèle fréquentiel complet par transformée de Floquet. En parallèle, des campagnes d'essais dynamiques (mesures de réceptance et d'accélération sur traverse au passage des trains) ont été réalisées sur une zone de transition entre voie ballastée et voie sur dalle sur ligne à grande vitesse. Les résultats obtenus expérimentalement permettent de valider les simulations dans les domaines temporel et fréquentiel sur les différentes zones de la transition. Le modèle permet de mieux comprendre l'effet de la sous-structure sur le comportement dynamique. Une des grandes avancées de ce travail est également l'introduction d'une stratégie permettant d'utiliser la méthode de réduction pour coupler des zones présentant des tranches différentes. Des outils de post-traitement ont été développés pour mettre en lumière les effets dynamiques générés par la transition. / Railway tracks have evolved over years based on empirical results and their dynamic behavior still can be difficult to assess or to quantify. A numerical model can thus provide assistance in track design by assessing the mechanical performance of new structures, or allowing the diagnostic of existing track parts, as a complement to relevant in-situ measurements.The numerical model developed in this work combines a reduction strategy with numerical techniques used to solve the propagation equations in waveguides in the frequency / wave number domains. The peculiarity of the exposed methodology is the introduction of a model based on a periodic sub structuring of the track, keeping only a few wavelengths carefully chosen to solve dispersion equations. Based on this model reduction technique and its extension to time domain models with moving contact, the computational time and storage capacity required are greatly reduced. Thus, this model is efficient and useful for engineering purposes in railway tracks studies.Numerical validation of the reduction is carried out by building a complete reference model in the frequency domain. In parallel, measurement campaigns (receptance measurement and sleeper acceleration under passing trains) were performed on a transition zone between ballasted and slab tracks on a High Speed Line. These tests are compared to simulation results in both time and frequency domains on different areas of the transition. After successful validation, the model is used to improve understanding of the role of the substructure on the dynamic behavior.The final major development of this work is the introduction of a strategy to extend the reduction to piecewise periodic structures and the development of post-processing tools to highlight the dynamic effects generated by the transition zone.

Indiana University-Purdue University Indianapolis (IUPUI) / In the first part of this thesis, we investigate the propagation of quantum fluctuations in a nonlinear interferometer comprising under conditions of harmonic generation by computer simulations. This investigation assumes idealized conditions such as lossless and uniform nonlinear media, an ideal cavity and ideal photodetectors. After linearizing wave equations for harmonic generation with a coherent state input, we obtain equations for one dimensional spatial propagation of the mean field and quantum fluctuations for initial conditions set by arbitrary interferometer phase. We discover that fluctuations are de-squeezed in the X and Y quadratures as the interferometer phase is tuned. However, we discover that there is are quadratures P-Q obtained by rotating the X-Y quadratures for which squeezing is improved by factors of 10^9. We present a practical idea to implement rotation of X quadrature fluctuations to the Q quadrature by using an ideal empty optical cavity. Signal-to-Noise ratio of the nonlinear interferometer was calculated and compared with that of a linear interferometer with coherent state input. We calculated a maximum performance improvement of a factor of 60 for a normalized propagation length ζ0 = 3 under ideal conditions. In the second part of this thesis, we investigate experimentalarrangements to transfer atomic coherence from light to cesium atoms. We discuss the experimental arrangement to generate coherence under conditions of electromagnetically induced transparency (EIT). We measure a continuous wave EIT width of 7.18 MHz and present results for pulsed arrangements.

Microwave Photonics(MWP) has been defined as the study of photonic devices which operate at microwave frequencies and also their applications to microwave and optical systems. One or more electrical signals at microwave frequencies are transported over the optic link ,with electrical to optical and optical to electrical conversion on the transmission and receiving side respectively. The key advantages of microwave photonic links over conventional electrical transmission systems such as coaxial cables or waveguides ,includes reduced size, weight and cost, immunity to electromagnetic interference ,low dispersion and high data transfer capacity. Integrated Optics is the name given to a new generation of opto-electronic systems in which the familiar wires and cables are replaced by light-waveguiding optical fibers, and conventional integrated circuits are replaced by optical integrated circuits (OICs).Microwave Photonics with photonic integration can add the benefits of reduction in system size, losses, short path lengths leading to more efficient cost effective systems. In this thesis, a new approach for using 1-D linear arrays of curved waveguides as delay lines is presented. We propose a design for a passive phase shifter obtained by curved waveguide delay lines. The modulated RF signal obtains the phase shift in the optical domain which is transferred to the RF signal by heterodyning techniques .This phase shift is independent of the RF frequency and hence the Beam squinting which occurs in the conventional RF phase shifter systems is avoided in the proposed system. Switching between different lengths of the bent/curved waveguides can produce variable phase shifts ranging from 0 to 2 radians. The use of curved waveguides for delay generation and optimization of various parameters are the main topics of the research problem. The need for delay line is large and most of these were implemented previously using long optical fiber cables. More precise delays could be obtained by using waveguide delay lines as compared to fiber delay lines. Waveguides paves way for design in smaller dimensions ranging from m to nm in integrated optics. The differential phase shift for a signal propagating in a waveguide from waveguide theory is given as which clearly indicates that the differential phase shifts could be obtained in accordance with differential path lengths Δl with β as the propagation constant. S-bend waveguide sections of different lengths along with straight waveguide as reference for each section are employed. The phase delay is passively obtained by a differential path length change, where various phase shift values can be obtained by switching between different differential path lengths. Since the optical phase delay generated is in- dependent of the input RF frequency. A shift in the RF frequency, at the input will not change the phase or beam pointing angle when the phase shifter is employed for beam pointing in case of Phased Array Antenna applications. A 1-bit phase shifter is the firrst step in the design which could be further extended to n-bit phase shifter. Here 1-bit or n-bit ,is one where n can take any integer value. Each bit is composed of a reference phase signal pathway and a delayed phase signal pathway. When the optical signal goes every single bit through the reference phase the phase shift is ‘0’ radians ,the other is through the delayed path which is . For every n-bit, 2n delays can be obtained. For the 1-bit,2 delays are obtained. Switching between the path lengths is done using the directional coupler switches. Th optimization of different parameters of the S-bend waveguide delay line has been realized and studied. The design and optimisation of a 1-bit optical RF phase shifter is discussed which could be extended to n-bit phase shifters. These S-bends are studied analytically. Beam Propagation Method (BPM)is employed for modeling and simulation of the proposed device. An interferometric configuration is considered for practical measurement of optical phase. In this configuration the phase change is translated into amplitude or intensity measurement. One of the arms of the Maczehdner Interferometer has no path length change while the other arm has an S-bend structure which provides the path length difference as compared to the reference path, and hence produces the necessary phase shift at the output of the interferometer as required. By changing the path length difference between the two arms of the interferometer ,a change in intensity is produced at the output of the interferometer. In this study, integrated optic curved waveguide delay line phase shifters are designed and analyzed, considering the Titanium Di used Lithium Niobate Technology. This is because it has good electro-optic properties necessary for designing switches used for switching between delay segments. Practical parameters that can be fabricated are employed in the design and simulation studies reported here. Fabrication is also done using the Lithium Niobate Technology. However the fabrication studies are excluded from the main stream, as further fabrication studies are necessary to realise the actual devices de- signed. The fabrication aspects are left as scope for further development. The fabricated devices are shown as appendix to the thesis. Organisation of the thesis Chapter 1 gives the introduction to the fields of Microwave Photonics and Integrated optics and its applications. Chapter 2discusses the curved waveguide theory and design with coverage of materials and methods employed in the proposed system. Chapter 3 discusses the different types of delay lines and the design of the 1-bit phase shifter which can be extended to the design of a n-bit phase shifter with both analytical and simulation results. Chapter 4 discusses the method of phase measurement for the n-bit phase shifter and the possible applications where the phase shifter could be employed. Chapter 5 discusses conclusions and future work in the proposed area of work. Appendix A discusses the loss calculations for the Cosine S-bend waveguide. Appendix B gives the fabrication details. The references form the end part of the thesis.

The analysis of wave propagation in hyperelastic waveguides has significant applications in various branches of engineering like Non-Destructive Testing and Evaluation, impact analysis, material characterization and damage detection. Linear elastic models are typically used for wave analysis since they are sufficient for many applications. However, certain solids exhibit inherent nonlinear material properties that cannot be adequately described with linear models. In the presence of large deformations, geometric nonlinearity also needs to be incorporated in the analysis. These two forms of nonlinearity can have significant consequences on the propagation of stress waves in solids. A detailed analysis of nonlinear wave propagation in solids is thus necessary for a proper understanding of these phenomena. The current research focuses on the development of novel algorithms for nonlinear finite element analysis of stress wave propagation in hyperelastic waveguides. A full three-dimensional(3D) finite element analysis of stress wave propagation in waveguides is both computationally difficult and expensive, especially in the presence of nonlinearities. By definition, waveguides are solids with special geometric features that channel the propagation of stress waves along certain preferred directions. This suggests the use of kinematic waveguide models that take advantage of the special geometric features of the waveguide. The primary advantage of using waveguide models is the reduction of the problem dimension and hence the associated computational cost. Elementary waveguide models like the Euler-Bernoulli beam model, Kirchoff plate model etc., which are developed primarily within the context of linear elasticity, need to be modified appropriately in the presence of material/geometric nonlinearities and/or loads with high frequency content. This modification, besides being non-trivial, may be inadequate for studying nonlinear wave propagation and higher order waveguide models need to be developed. However, higher order models are difficult to formulate and typically have complex governing equations for the kinematic modes. This reflects in the relatively scarce research on the development of higher order waveguide models for studying nonlinear wave propagation. The formulation is difficult primarily because of the complexity of both the governing equations and their linearization, which is required as part of a nonlinear finite element analysis. One of the primary contributions of this thesis is the development and implementation of a general, flexible and efficient framework for automating the finite element analysis of higher order kinematic models for nonlinear waveguides. A hierarchic set of higher order waveguide models that are compatible with this formulation are proposed for this purpose. This hierarchic series of waveguide models are similar in form to the kinematic assumptions associated with standard waveguide models, but are different in the sense that no conditions related to the stress distribution specific to a waveguide are imposed since that is automatically handled by the proposed algorithm. The automation of the finite element analysis is accomplished with a dexterous combination of a nodal degrees-of-freedom based assembly algorithm, automatic differentiation and a novel procedure for numerically computing the finite element matrices directly from a given waveguide model. The algorithm, however, is quite general and is also developed for studying nonlinear plane stress configurations and inhomogeneous structures that require a coupling of continuum and waveguide elements. Significant features of the algorithm are the automatic numerical derivation of the finite element matrices for both linear and nonlinear problems, especially in the context of nonlinear plane stress and higher order waveguide models, without requiring an explicit derivation of their algebraic forms, automatic assembly of finite element matrices and the automatic handling of natural boundary conditions. Full geometric nonlinearity and the hyperelastic form of material nonlinearity are considered in this thesis. The procedures developed here are however quite general and can be extended for other types of material nonlinearities. Throughout this thesis, It is assumed that the solids under investigation are homogeneous and isotropic. The subject matter of the research is developed in four stages: First, a comparison of different finite element discretization schemes is carried out using a simple rod model to choose the most efficient computational scheme to study nonlinear wave propagation. As part of this, the frequency domain Fourier spectral finite element method is extended for a special class of weakly nonlinear problems. Based on this comparative study, the Legendre spectral element method is identified as the most efficient computational tool. The efficiency of the Legendre spectral element is also illustrated in the context of a nonlinear Timoshenko beam model. Since the spectral element method is a special case of the standard nonlinear finite element Method, differing primarily in the choice of the element basis functions and quadrature rules, the automation of the standard nonlinear finite element method is undertaken next. The automatic finite element formulation and assembly algorithm that constitutes the most significant contribution of this thesis is developed as an efficient numerical alternative to study the physics of wave propagation in nonlinear higher order structural models. The development of this algorithm and its extension to a general automatic framework for studying a large class of problems in nonlinear solid mechanics forms the second part of this research. Of special importance are the automatic handling of nonlinear plane stress configurations, hierarchic higher order waveguide models and the automatic coupling of continuum and higher order structural elements using specially designed transition elements that enable an efficient means to study waveguides with local inhomogeneities. In the third stage, the automatic algorithm is used to study wave propagation in hyperelastic waveguides using a few higher order 1D kinematic models. Two variants of a particular hyperelastic constitutive law – the6-constantMurnaghanmodel(for rock like solids) and the 9-constant Murnaghan model(for metallic solids) –are chosen for modeling the material nonlinearity in the analysis. Finally, the algorithm is extended to study energy-momentum conserving time integrators that are derived within a Hamiltonian framework, thus illustrating the extensibility of the algorithm for more complex finite element formulations. In short, the current research deals primarily with the identification and automation of finite element schemes that are most suited for studying wave propagation in hyper-elastic waveguides. Of special mention is the development of a novel unified computational framework that automates the finite element analysis of a large class of problems involving nonlinear plane stress/plane strain, higher order waveguide models and coupling of both continuum and waveguide elements. The thesis, which comprises of 10 chapters, provides a detailed account of various aspects of hyperelastic wave propagation, primarily for 1D waveguides.

Indiana University-Purdue University Indianapolis (IUPUI) / The tight-binding model that has been used for many years in condensed matter physics, due to its analytic and numerical tractability, has recently been used to describe light propagating through an array of evanescently coupled waveguides. This dissertation presents analytic and numerical simulation results of light propagating in a waveguide array. The first result presented is that photonic transport can be achieved in an array where the propagation constant is linearly increasing across the array. For an input at the center waveguide, the breathing modes of the system are observed, while for a phase displaced, asymmetric input, phase-controlled photonic transport is predicted. For an array with a waveguide-dependent, parity-symmetric coupling constant, the wave packet dynamics are predicted to be tunable. In addition to modifying the propagation constant, the coupling between waveguides can also be modified, and the quantum correlations are sensitive to the form of the tunneling function. In addition to modifying the waveguide array parameters in a structured manner, they can be randomized as to mimic the insertion of impurities during the fabrication process. When the refractive indices are randomized and real, the amount of light that localizes to the initial waveguide is found to be dependent on the initial waveguide when the waveguide coupling is non-uniform. In addition, when the variance of the refractive indices is small, light localizes in the initial waveguide as well as the parity-symmetric waveguide. In addition to real valued disorder, complex valued disorder can be introduced into the array through the imaginary component of the refractive index. It is shown that the two-particle correlation function is qualitatively similar to the case when the waveguide coupling is real and random, as both cases preserve the symmetry of the eigenvalues. Lastly, different input fields have been used to investigate the quantum statistical aspects of Anderson localization. It is found that the fluctuations in the output intensity are enhanced and the entropy of the system is reduced when disorder is present in the waveguides.