The main objective of the thesis is to understand the parameters that contribute in limiting the pulse energy and spectral bandwidth of the mode-locked femtosecond fiber lasers. I have focused on studying the impact of the parameters of the saturable absorber and the bandwidth of the lumped spectral filter on the temporal and spectral profiles of the pulse. Therefore, I developed two models that can help us to optimize the pulse characteristics such as the pulse energy, spectral bandwidth and de-chirped pulse width. I also introduce two techniques that result in increasing the pulse peak power and spectral bandwidth. The nonlinear transmission coefficient of the saturable absorber is one of the main limitations to achieving high-energy pulses. Throughout my research, I have used two types of saturable absorbers. The first is a lumped semiconductor saturable absorber mirror (SESAM) and the second is based on the nonlinear polarization rotation (NPR) that is considered an artificial saturable absorber with distributed effect. The first model introduced in this thesis is an analytical model, which provides closed form relations for the pulse characteristics of all-normal dispersion fiber laser. It shows how the spectral bandwidth of the lumped filter inserted inside the cavity affects the pulse characteristics. Also, it illustrates the influence of the saturable absorber parameters on the pulse characteristics. I show that increasing the small signal saturable absorber loss and decreasing the saturation power leads to the increase in pulse energy and spectral bandwidth. Numerical simulation and experimental results are in agreement with the results of the analytical models. The second model, which is called the semi-vector model, is applicable to all-normal dispersion mode-locked fiber laser with high output coupling ratio. Nonlinear polarization rotation is employed for mode-locking. The model shows the relationship between the location of the overdriving point of the saturable absorber and the output pulse energy. The results of this model are in agreement with those of the full-vector model, but with a much reduced simulation time. In addition, the experimental results show the accuracy of the proposed model. In this thesis, I mitigate the peak power limitation, caused by the accumulated nonlinear phase shift, by replacing the short high-doped Yb3+ fiber with a long low-doped one. This results in an increase of the peak power by a factor that depends on the ratio between the gain coefficient of the high- and low-doped Yb3+ fiber. The length of the nonlinear section is kept unchanged by reducing the length of the single mode fiber after the long low-doped Yb3+ fiber. Numerical simulation and experimental results validate the idea. The location of narrow bandwidth lumped spectral filter, in an active Similariton laser, has proved to have a distinct effect on the pulse energy, spectral bandwidth and de-chirped pulse width and peak power. The proximity of the spectral filter to the input of the Yb3+-doped fiber leads to increasing the pulse spectral bandwidth and peak power of the de-chirped pulse as well as shortening the de-chirped pulse, but at the expense of reducing the pulse energy.

A spatial soliton is a shape invariant self guided beam of light or a self induced waveguide. Spatial solitons appear as a result of the balance of diffraction and nonlinear focusing in a system. They have been observed in many different conservative media in the last couple of years. Solitons are ubiquitous, because of the probability of using their interactions in optical data processing, communications etc. Up to now due to the power required to generate the solitons, and the response times of the soliton supporting media, these special waves of nature could not penetrate the applications arena. Semiconductors, with their resonant nonlinearities, are thought to be ideal candidates for fast switching, low power spatial solitons. In this dissertation it is shown theoretically and experimentally that it is possible to observe stable spatial solitons in a periodically patterned semiconductor optical amplifier (PPSOA). The solitons have unique beam profiles that change only with system parameters, like pumping current, etc. Their coherent and incoherent interactions which could lead to all optical devices have been investigated experimentally and theoretically. The formation of filaments or modulational instability has been studied theoretically and yielded analytical formulae for evaluating the filament gain and the maximum spatial frequencies in PPSOA devices. Furthermore, discrete array amplifiers have been analyzed numerically for discrete solitons, and the prospect of using multi peak discrete solitons as laser amplifiers is discussed.

In this thesis, we apply a recently developed technique to comprehensively categorize all possible families of solitary wave solutions in two models of topical interest. The models considered are: a) the Generalized Pochhammer-Chree Equations, which govern the propagation of longitudinal waves in elastic rods, and b) a generalized microstructure PDE. Limited analytic results exist for the occurrence of one family of solitary wave solutions for each of these equations. Since, as mentioned above, solitary wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions of both models here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves for each model, we find a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. For the microstructure equation, the new family of solutions occur in regions of parameter space distinct from the known solitary wave solutions and are thus entirely new. Directions for future work, including the dynamics of each family of solitary waves using exponential asymptotics techniques, are also mentioned.

<p> An optical time division multiplexing (TDM) scheme using soliton interaction is proposed in the thesis to save the time-bandwidth prduct (TBP). The soliton multiplexer (MUX) consisting of a highly nonlinear fiber (HNLF) combines two adjacent solitons to form a composite soliton, while the soliton demultiplexer (DEMUX) consisting of a similar HNLF restores the component solitons. The case of interaction between identical fundamental solitons is discussed first. However, when this scheme is used in the conventional TDM system, the total bit rate transmitted over the channel is limited by the time interval between the two adjacent component solitons. Therefore, a modified multiplexing scheme using interaction between different solitons is proposed to satisfy more practical engineering applications. The theoretical analysis and numerical simulation results demonstrate that the modified optical TDM scheme offers a higher TBP efficiency and suitable for conventional TDM, which makes it an attractive candidate for meeting the challenge of increasing demand on frequency bandwidth in modern optical communications. </p> / Thesis / Master of Applied Science (MASc)

The nonlinear propagation of a visible, continuous wave laser beam was studied in three types of polymer systems that harness photochemical reactions: (i) a photopolymerization to create permanent self-written structures, (ii) a photo-oxidation hosted within a polymer matrix and (iii) a reversible photoisomerization that triggers the contraction of a photoresponsive hydrogel. The process of self-trapping was characterized by monitoring the spatial intensity profiles over time. The mechanism of each material was determined with a series of control experiments in order to confirm the nature of the nonlinear response, including their reversibility and intensity-dependence. These observations led to the study of interactions between self-trapped beams. Two beams under linear conditions will pass through one another, but two beams travelling in a nonlinear medium will interact and influence one another. The interactions of two beams introduced into the aforementioned photochemical systems were investigated and revealed a rich diversity of phenomena including: (i) the attraction between beams, (ii) merging of beams into a single waveguide, (iii) nonlocal attraction between beams, (iv) orbiting of beams, (v) switching of beam positions, and (vi) inhibition of the self-trapping of a neighbouring beam. Each observation is dependent on a detailed understanding of the underlying mechanism of refractive index change. Numerical simulations supplement some of these experiments and provide further evidence for the nonlinear mechanisms. The formation of permanent self-written structures with these nonlinear waves offers the opportunity to create seamless 3D printed materials with prismatic geometries. Several macroscopic objects were constructed using nonlinear waves from incoherent LEDs and amplitude masks. Decomposition of 3D objects into prismatic elements was carried out using an algorithm that breaks an object into individual pieces. Using a multi-step printing process, several prismatic elements can be combined to form a target object. The results of these experimental and theoretical studies improve upon the current understanding of the dynamics of nonlinear light propagation in photochemical systems. These insights may allow us to harness other nonlinear effects and develop new materials for applications such as optical communication, computing and 3D printing. / Thesis / Doctor of Science (PhD) / The nonlinear propagation of a visible, continuous wave laser beam was studied in three types of polymer systems that harness photochemical reactions: (i) a photopolymerization to create permanent self-written structures, (ii) a photo-oxidation hosted within a polymer matrix and (iii) a reversible photoisomerization that triggers the contraction of a photoresponsive hydrogel. Photochemical changes to the material lead to self-induced light-guiding structures that influence the behaviour of light. These self-trapped beams can interact with one another inside of a nonlinear medium, giving rise to a rich diversity of phenomena including: (i) the attraction between beams, (ii) merging of beams into a single waveguide, (iii) nonlocal attraction between beams, (iv) orbiting of beams, (v) switching of beam positions, and (vi) inhibition of the self-trapping of a neighbouring beam. Each observation is dependent on a detailed understanding of the underlying mechanism of refractive index change. Numerical simulations supplement some of these experiments and provide further evidence for the nonlinear mechanisms. The formation of permanent self-written structures with these nonlinear waves offers the opportunity to create seamless 3D printed materials with prismatic geometries. Several macroscopic objects were constructed using nonlinear waves from incoherent LEDs and amplitude masks. Decomposition of 3D objects into prismatic elements was carried out using an algorithm that breaks an object into individual pieces. Using a multi-step printing process, several prismatic elements can be combined to form a target object. The results of these experimental and theoretical studies improve upon the current understanding of the dynamics of nonlinear light propagation in photochemical systems. These insights may allow us to harness other nonlinear effects and develop new materials for applications such as optical communication, computing and 3D printing.

This thesis discusses the Ruijsenaars-Schneider model and its connection to Calogero-Moser systems and the sine-Gordon equation. The derivations and mathematical framework presented aims at making the model comprehensible to non-experts in the field. Two different methods, the Bäcklund transformation and Ruijsenaars-Schneider model, are used to find soliton solutions to the sine-Gordon equation.

Les systèmes non linéaires sont décrits pour la plupart avec des équations aux dérivées partiellesqui les caractérisent, comme la chaine de pendules couplés, la chaine de protéines comportant des molécules avec liaisons hydrogène, les réseaux atomiques ...etc. Ces modèles comportent le plus souvent des interactions inter particulaires anharmoniques et des potentiels de substrat déformables. En effet, aux conséquences importantes dues à la non linéarité et à la dispersion, ces autres phénomènes comme l’anharmonicité et la déformabilité conduisent à d’autres propriétés de propagation des ondes solitaires telles que les compactons, les kinks et les antikinks , les peakons , … ainsi qu’à la capacité du système à transmettre un signal. Nous utilisons ici la méthode de bifurcation pour tracer les différents portraits de phases obtenus par variation des paramètres du système. Nous mettons en évidence l’influence du facteur d’anharmonicité sur la transmissivité et la bistabilité du système: Il en ressort que l’amplitude du signal d’entrée qui produit la bistabilité augmente avec la valeur absolue du coefficient d’anharmonicité et la bistabilité est retardée. En tenant compte des propriétés importantes générées par de tels systèmes, il nous a paru intéressant de construire une ligne électrique caractérisée par les mêmes équations, mais en doublant sur un tronçon de 10 cellules la valeur de la capacité par rapport à celles des 10 condensateurs suivants, et en reproduisant ce motif avec une périodicité de 20 cellules. Nous réalisons ainsi un super réseau qui simule un neurone myélinisé. Les types de solitons obtenus semblent mieux adaptés pour décrire le signal électrique qui caractérise l’influx neuronal localisé dans l’espace avec un support compact. / Non-linear systems are almostly described by partial differential equations that characterize them. We have some systems such as the chain of coupled pebdelums, the protein chain comprising molecules with hydrogen bonds, atomic lattice, and so on .These systems are most often characterized by anharmonic inter particulate interactions and and then immersed in deformable potential substrates. In addition to nonlinearity and dispersion, these other phenomena namely anharmonicity and deformability are responsible for certain properties of propagation of solitary waves such as (compactons, kinks and anti-kinks, peackons, ...etc) and also the ability of the systems to transmit a signal . We used the bifurcation method to plot the different phase portraits obtained . For various parameters of such systems , we have highlighted the influence of anharmonicity on transmissivity and bistability of the system: It appears that the amplitude of the input signal which produces bistability increases with anharmonicity and the bistability is delayed.To considering these important properties generated by such systems, it seemed interesting to buildin an electrical line characterized by the same equations of the system. By alternately doubling the capacitance of the capacitors of a section of this line, we have realised a super-lattice that simulates a myelinised neuron. The types of solitons we get from this line are better adapted to describe the electrical signal which characterizes the neuron impulse located in space with a compact support.

Si les flux de données actuellement échangés sont traités par les systèmes électroniques, ils transitent depuis plusieurs années par des lignes de transmission optique. Elles présentent seules une bande passante répondant à la croissance des taux de transmission. En revanche, les applications de traitement tout-optique du signal ne parviennent pas à rivaliser avec les systèmes électroniques. Les recherches récentes en optique laissent à penser que l'utilisation des faisceaux solitons comme guides photo-induits permettra à des dispositifs tout-optiques d'effectuer les opérations dévolues à l'électronique. La stabilité de ces solitons résulte de l'équilibre entre diffraction et auto-focalisation causée par la non-linéarité du milieu qu'ils traversent. Se propageant sans déformation, ils peuvent être considérés comme des canaux porteurs d'information. De tels dispositifs pourraient assurer les interconnexions dans les réseaux de communication.<br /><br />L'objectif de cette thèse est d'étudier théoriquement et expérimentalement une nouvelle classe de solitons, les solitons vectoriels, qui consitent en la superposition d'enveloppes de polarisations distinctes mutuellement piégées. Pour comprendre l'existence de ces solitons à composantes multiples, il suffit d'imaginer un guide supportant plusieurs modes photo-induits par effet soliton. Lorsque plusieurs modes se propagent simultanément, un d'eux peut jouer le rôle de guide d'onde effectif pour d'autres modes supérieurs et former un soliton multicomposante. Dans notre travail, nous étudierons différents membres de cette famille ainsi que leur stabilité. Nous analyserons leurs dynamiques dans un guide planaire non linéaire.

Ce mémoire de thèse présente une approche semi-analytique des différentes solutions solitons spatio-temporelles de l'équation cubique quintique de Ginzburg-Landau complexe étendue à (3+1)D (GL3D).La méthode semi-analytique choisie est celle des coordonnées collectives qui permet d'approcher le champ exact, dont l'expression analytique est inconnue, par une fonction d'essai, qui comporte un nombre limité de paramètres physiques.En appliquant cette procédure à l'équation GL3D, nous obtenons un système d'équations variationnelles qui gouverne l'évolution des paramètres de la balle de lumière. Nous montrons que cette approche des coordonnées collectives est incomparablement plus rapide que la procédure de résolution directe de l'équation GL3D. cette rapidité permet d'obtenir, en un temps record, une cartographie générale des comportements dynamiques des balles de lumière. Cette cartographie révèle une riche variété d'états dynamiques faite de balles de lumière stationnaires, oscillantes et rotatives.Finalement, les résultats de cette thèse prédisent l'existence de plusieurs familles de balles de lumière, et précisent les domaines respectifs de leurs paramètres physiques. Cette prédiction constitue un pas en avant dans les efforts entrepris ces dernières années en vue d'une démonstration expérimentale de ce type d'impulsions.

Submitted by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-30T07:33:27Z No. of bitstreams: 2 Tese - Márcio Lemes de Sousa - 2015.pdf: 2626758 bytes, checksum: 1e9e1b9d216bad33d6b5919afa54a4e4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-11-30T07:35:41Z (GMT) No. of bitstreams: 2 Tese - Márcio Lemes de Sousa - 2015.pdf: 2626758 bytes, checksum: 1e9e1b9d216bad33d6b5919afa54a4e4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-11-30T07:35:41Z (GMT). No. of bitstreams: 2 Tese - Márcio Lemes de Sousa - 2015.pdf: 2626758 bytes, checksum: 1e9e1b9d216bad33d6b5919afa54a4e4 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2015-07-03 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this thesis, primarily, we studied warped products semi-Riemannian Einstein manifolds. We considered the case in that the base is conformal to an n-dimensional pseudo- Euclidean space and invariant under the action of an (n 􀀀 1)-dimensional translation group. We constructed new examples of Einstein warped products with zero Ricci curvature when the fiber is Ricci-flat. In particular, we obtain explicit solutions, in the case vacuum, for Einstein field equation. Furthermore, we consider M = B f F warped product gradient Ricci solitons. We proved that the potential function depends only on the base and the fiber F is necessarily Einstein manifold. We provide all such solutions in the case of steady gradient Ricci solitons when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an (n􀀀1)-dimensional translation group, and the fiber F is Ricci-flat. / Nesta tese, primeiramente, estudamos variedades produto torcido semi-Riemannianas de Einstein, considerando-se o caso em que a base é conforme ao espaço pseudo- Euclidiano n -dimensional e invariante sob a ação de um grupo de translações (n􀀀1)-dimensional. Construímos novos exemplos de métricas produto torcido Einstein com curvatura de Ricci zero quando a fibra é Ricci -flat. Em particular, obtemos soluções explícitas, no caso de vácuo, para a equação de campo de Einstein. Em seguida, provamos que quando a variedade M = B f F é um Ricci soliton gradiente a função potencial depende apenas da base e a fibra F é necessariamente uma variedade de Einstein. Fornecemos todas as soluções, no caso de Ricci soliton gradiente steady, quando a base é conforme ao espaço pseudo- Euclidiano n -dimensional, invariante sob a ação de um grupo translações (n􀀀1) - dimensional, e a fibra F é Ricci -flat.