The waveguiding effect of spatial solitary waves in nonlinear optical media has been suggested as a potential basis for future all-optical devices, such as optical interconnects. It has been shown that low power (∼ mW) beams, which can encode information, can be optically steered using external electric fields or through interactions with other beams. This opens up the possibility of creating reconfigurable optical interconnects. Nematic liquid crystals are a potential medium for such future optical interconnects, possessing many advantageous properties, including a “huge” nonlinear response at comparatively low input power levels. Consequently, a thorough understanding of the behaviour of spatial optical solitary waves in nematic liquid crystals, termed nematicons, is needed. The investigation of multiple beam interaction behaviour will form an essential part of this understanding due to the possibility of beam-on-beam control. Here, the interactions of two nematicons of different wavelengths in nematic liquid crystals, and the optical steering of nematicons in dye-doped nematic liquid crystals will be investigated with the aim of achieving a broader understanding of nematicon interaction and steering. The governing equations modelling nematicon interactions are nonintegrable, which means that nematicon collisions are inelastic and radiative losses occur during and after collision. Consequently numerical techniques have been employed to solve these equations. However, to fully understand the physical dynamics of nematicon interactions in a simple manner, an approximate variational method is used here which reduces the infinite-dimensional partial differential equation problem to a finite dynamical system of comparatively simple ordinary differential equations. The resulting ordinary differential equations are modified to include radiative losses due to beam evolution and interaction, and are then quickly solved numerically, in contrast to the original governing partial differential equations. N¨other’s Theorem is applied to find various conservation laws which determine the final steady states, aid in calculating shed radiation and accurately compute the trajectories of nematicons. Solutions of the approximate equations are compared with numerical solutions of the original governing equations to determine the accuracy of the approximation. Excellent agreement is found between full numerical solutions and approximate solutions for each physical situation modelled. Furthermore, the results obtained not only confirm, but explain theoretically, the interaction phenomena observed experimentally. Finally, the relationship between the nature of the nonlinear response of the medium, the trajectories of the beams and radiation shed as the beams evolve is investigated.

Surface waves exist along the interfaces between two different media and are known to display properties that have no analogue in continuous systems. In years past, they have been the subject of many studies in a diverse collection of scientific disciplines. In optics, one of the mechanisms through which optical surface waves can exist is material nonlinearity. Until recently, most of the activity in this area was focused on interfaces between continuous media but no successful experiments have been reported. However, the growing interest that nonlinear discrete optics has attracted in the last two decades has raised the question of whether nonlinear surface waves can exist in discrete optical systems. In this work, a detailed experimental study of linear and nonlinear optical wave propagation at the interface between a discrete one-dimensional Kerr-nonlinear system and a continuous medium (slab waveguide) as well as at the interface between two dissimilar waveguide lattices is presented. The major part of this dissertation is devoted to the first experimental observation of discrete surface solitons in AlGaAs Kerr-nonlinear arrays of weakly coupled waveguides. These nonlinear surface waves are found to localize in the channels at and near the boundary of the waveguide array. The key unique property of discrete surface solitons, namely the existence of a power threshold, is investigated in detail. The second part of this work deals with the linear light propagation properties at the interface between two dissimilar waveguide arrays (so-called waveguide array hetero-junction). The possibility of three different types of linear interface modes is theoretically predicted and the existence of one of them, namely the staggered/staggered mode, is confirmed experimentally. The last part of the dissertation is dedicated to the investigation of the nonlinear properties of AlGaAs waveguide array hetero-junctions. The predicted three different types of discrete hybrid surface solitons are analyzed theoretically. The experimental results on observation of in-phase/in-phase hybrid surface solitons localized at channels on either side of the interface are presented and different nature of their formation is discussed.

Esta tesis constituye un estudio detallado y exhaustivo de las propiedades de una variedad específica de ondas ópticas solitarias. Observadas experimentalmente por primera vez en 1995, estas ondas estan formadas por un haz óptico a frecuencia fundamental y su segundo armónico que están ligados entre sí y viajan juntos en el material cuadrático; y son debidas al equilibrio entre la difracción lineal que sufre el haz al propagarse y un término no lineal de segundo orden en la susceptibilidad del medio. Las llamamos por eso solitones ópticos en medios cuadráticos o simplemente 'solitones cuadráticos'. También se les conoce como 'Solitones Multicolor' aludiendo al hecho de que requieren de haces a diferentes frecuencias para formarse.Un medio no-lineal cuadrático tiene por fuerza que ser no-centrosimétrico, lo cual es una variedad de anisotropía. Una gran parte de los materiales no-lineales cuadráticos (los que tienen mayor interés para la industria) son uniaxiales lo que significa que presentan un eje de simetría que suele llamarse eje óptico. De la dirección de un haz relativa a ese eje óptico dependen las características de la propagación del haz en el medio cuadrático no-lineal. Una consecuencia de eso en configuraciones de interés es un desvío ('walk-off') sufrido por el haz respecto a su dirección de propagación inicial al entrar en el material no-lineal.Las propiedades de los solitones cuadráticos 'caminantes' son también estudiadas en la tesis, estableciendo que existe una relación entre la potencia inyectada en el medio y el ángulo de desvío (walking angle).Una parte importante de la tesis está dedicada al estudio a través de exhaustivos experimentos numéricos del potencial de estas ondas solitarias para constituir la base de dispositivos de conmutación y encaminamiento totalmente ópticos que puedan hacer realidad la promesa de la red transparente totalmente óptica. Los experimentos han permitido identificar varias configuraciones de interés con niveles de potencia y dimensiones que permiten plantearse el diseño y construcción de dispositivos comerciales de conmutación y encaminamiento totalmente ópticos basados en solitones ópticos cuadráticos. / This thesis is a comprehensive study of the fundamental properties of a specific kind of optical spatial solitary waves. First observed experimentally in 1995, these solitary waves are formed by an optical beam at a fundamental frequency and its second harmonic which propagate together and are mutually entangled; and are due to a balanced interplay between the beams' linear diffraction and a second-order nonlinear susceptibility of the medium. They are thereby referred as 'Optical Solitons in Quadratic Nonlinear Media' or simply 'Quadratic Solitons', They are also known as 'Multicolor Solitons' recalling that they are formed by beams at different frequencies.A quadratic nonlinear media needs to be non centrosymmetric which is a special kind of anisotropy. A great deal of quadratic nonlinear materials (the most used by industry such as lithim niobate, KTP, etc.) are uniaxial meaning that they feature a symmetry axis known as 'optical axis'. The direction of propagation of an optical beam relative to that axis determines the characteristics of the beam's propagation through the quadratic nonlinear material. A main result of that in some configurations of interest is a walk-off suffered by the beam as it enters the quadratic material.The properties of the families of quadratic solitons in the presence of a linear walk-off (quadratic walking solitons) are studied as well in the thesis stating that there is a relationship between the power injected into the medium and the walking angle, suitable to applications of all-optical switching and routing.An important last part of the thesis is devoted to the study from a practical viewpoint and through extensive numerical experiments of the potential of these solitary waves as the basis of practical all-optical switches and routers which could take the all-optical transparent network to a reality. The experiments have allowed to identify several configurations of interest with power level and dimensions suited to practical applications which could allow the production of commercial all-optical switching and routing devices based on quadratic solitons.

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The reflection and transmission of an electromagnetic TE-polarized plane wave at a dielectric film between two linear semi-infinite media (substrate and cladding) is considered. All media are assumed to be homogeneous in x- and z- direction, isotropic, and non-magnetic. The permittivity of the film is assumed to be characterized by a continuously differentiable function of the transverse coordinate and the field. To obtain solutions of Maxwell´s equations that satisfy the boundary conditions the problem is reduced to a Helmholtz equation, which is transformed to a Volterra integral equation for the field intensity inside the film. The Volterra equation is solved by iteration subject to the appropriate boundary conditions. The (iteration) solutions for the linear case and for the nonlinear case are expressed in terms of a uniformly convergent series and a uniformly convergent sequence, respectively. The uniform convergence is proved using the Banach Fixed-Point Theorem. The condition for its applicability leads to a condition for the parameters of the problem. By iterating the Volterra equation an approximate solution for the intensity inside the film is presented. The mathematical basis of the procedure is outlined in detail. Using an approximate solution, the phase function,the phase shifts on reflection and transmission, the reflectivity and the absorptance are determined.Further iterations of the Volterra equation are possible.Semianalytical and numerical examples illustrate the main features of the approach. The method is succesfully applied to different permittivity functions (real, complex, Kerr-like and saturable nonlinear). The agreement between the approximate analytical solutions and numerical solutions is satisfactory. It seems that the method proposed can serve as a means to optimize certain parameters of the problem (material and/or geometrical) for particular purposes.

Un des problèmes à résoudre lors de la réalisation d'un endoscope non linéaire pour des applications biomédicales concerne la propagation d'impulsions ultra courtes dans une fibre optique. Les processus non linéaires concernés nécessitent de grandes puissances d'excitation, réalisables seulement pour des impulsions de très courte durée qui sont déformés et allongés par la dispersion et les non linéarités des fibres. La plupart des techniques d'illumination fibrées pour la microscopie non linéaire emploient des systèmes de pré-compensation pour neutraliser les effets de ces phénomènes. Dans ce travail, nous explorons les possibilités offertes par la formation de solitons de grande énergie dans une fibre à bandes interdites photoniques à coeur solide. Les solitons optiques ont la propriété de conserver leur forme lors de leur propagation, et leur durée reste proche de la valeur minimum définie par la limite physique imposée par leur largeur spectrale, sans avoir besoin de recourir à un système de pré-compensation. De plus, la longueur d'onde et le retard relatif des solitons peuvent être accordés en changeant la puissance lumineuse en entrée de fibre. Plusieurs sources de lumière ont été conçues et réalisées, pour générer de nombreux contrastes non linéaires. Des images d'échantillons biologiques ont d'abord été réalisées en tirant profit de la courte durée des solitons. Puis, des mesures d'absorption transitoire ont été menées dans une configuration pompe-sonde en contrôlant le retard des solitons dans la fibre. Enfin, un montage de CRS basé sur le principe de focalisation spectrale a été réalisé, et son utilité a été démontrée en suivant un équilibre chimique. / One of the issues that has to be overcome to realize a nonlinear endoscope for biomedical applications is the propagation of ultra-short pulses in an optical fiber. Nonlinear processes require high peak powers in the focal volume in order to generate observable signals, so the pulses should be as short as possible. This makes them sensitive to the dispersion and nonlinearities of the fibers. Most of the existing techniques of ultra-short pulses fiber-delivery rely on complex pre-compensation systems to counteract these effects. In this work, we explore the possibilities offered by the generation of high-energy solitons in a custom-built solid-core photonic bandgap fiber, for nonlinear microscopy and spectroscopy. Optical solitons preserve their shape when they propagate in a fiber, and their duration remains close to the minimum value physically allowed by their bandwidth, without the need of any pre-compensation. Moreover, the wavelength and delay of the soliton can be tuned by changing the power at the input of the fiber. Several soliton-based light sources were designed and realized, generating contrast in the most prevalent nonlinear microscopy modalities. TPEF and SHG images of biological samples were first realized by taking advantage of the short duration of the solitons. By controlling the delay of the soliton, transient absorption measurements were then realized in a pump-probe configuration. Finally, the wavelength tunability of the soliton was used to generate the Stokes beam in a CRS setup based on the spectral focusing technique. The capabilities of this scheme were demonstrated by performing CRS microspectroscopy to monitor a chemical equilibrium.

Dans cette thèse nous étudions les propriétés d'ondes stationnaires dans des structures composées d'une couche diélectrique nonlinéaire de type Kerr et des couches métalliques et diélectriques linéaires. Nous élaborons différents modèles pour étudier les propriétées de plasmons-solitons dans deux types de structures : (i) une région diélectrique nonlinéaire semi-infinie, des couches de métal et de diélectrique linéaires et (ii) une couche de diélectrique nonlinéaire d'épaisseur finie entre deux régions métalliques (guide d'onde métallique à coeur nonlinéaire). Pour le premier type de structures, nous montrons qu'en utilisant une structure à quatre couches, il est possible d'obtenir des plasmons-solitons de basses puissance. Pour des guides d'onde métalliques à coeur nonlinéaire, nous trouvons de modes d'ordres supérieurs. Pour certains des modes symétriques, nous observons une bifurcation par brisure de symétrie donnant naissance à des modes asymétriques dans une structure symétrique. / In this PhD thesis, we study the properties of stationary transverse magnetic polarized waves in structures composed of a Kerr-type nonlinear dielectric layer, metal and linear dielectric layers. We develop several models to study the properties of plasmon-soliton waves in two types of structures: a semi-infinite nonlinear dielectric in contact with metal and linear dielectric layers and a finite-size nonlinear dielectric layer sandwiched between two metal regions (nonlinear slot waveguide). Our models allow us to compute the nonlinear dispersion relations and the corresponding field profiles. For the first type of structure, we prove that using the four-layer structures that we propose, it is possible to obtain plasmon-soliton waves at the power levels. For nonlinear slot waveguide structures, we discover the existence of new, higher order modes. For some of the symmetric modes, we observe a symmetry breaking bifurcation giving birth to asymmetric modes in symmetric structure.

Les cristaux liquides ont été tout le long un terrain fertile pour la recherche scientifique, des mathématiques à la science des matériaux, à l'optique. Leur utilisation ne se limite pas seulement à l'optique d'afficheurs mais s'étend à l'optique non linéaire, par exemple, à la commutation et au routage de faisceaux optiques. En raison de leur extrême sensibilité aux champs électriques, et ce sur une plage de fréquences allant du continu aux fréquences optiques, ils sont aussi utilises comme milieu non linéaires aptes à générer des faisceaux optiques auto-confinés, appelés solitons spatiaux optiques, à de très faibles puissances. Ces faisceaux ont la propriété de se propager sans diffraction, du fait que cette dernière est compensée par l’auto-focalisation non linéaire du milieu, avec formation de guides d'onde auto-induites. Dans les cristaux liquides nématiques, ces guides d'ondes peuvent à leur tours confiner et guider d’autres signaux optiques et peuvent être reconfigurés, soit optiquement, soit électriquement, du fait que la trajectoire des solitons peut être contrôlée par d'autres champs, ouvrant ainsi la voie à la manipulation tout-optique. Récemment, les cristaux liquides nématiques ont été également utilisés avec succès dans l'optique dite singulière, dans laquelle le paramètre clef est la singularité topologique portée par la phase de l'onde électromagnétique. Dans cette thèse, je rendrai compte de mon travail sur les solitons optiques spatiaux et les singularités optiques dans les cristaux liquides nématiques. / Liquid crystals have been all along a fertile background for scientific research, from mathematics to material science and optics; their use is not limited to displays but extends to nonlinear optics, for instance, to switching and routing of optical beams. Due to their extreme sensitivity to electric fields, and this at frequencies ranging from continuous to optical ones, they are also nonlinear media supporting the generation and propagation of self confined beams, called spatial optical solitons, at very low powers. Spatial optical solitons have the property to propagate without diffraction, since this is compensated by nonlinear self-focusing in the medium, resulting in self-induced waveguides. In nematic liquid crystals, these waveguides can in turn confine and route other optical signals and can be reconfigured, either optically or electrically, as soliton trajectories can be controlled by other fields, paving the way to all-optical manipulation. Nematic liquid crystals have also been recently employed with success in the so-called singular optics, in which the key parameter is the topologic singularity carried by the phase of an electromagnetic wave. In this thesis I will report on my work on spatial optical solitons and optical singularities in nematic liquid crystals.