In this work, we study the nonlinear propagation of light in liquid crystals (LCs) and the optical gain provided by LCs when they are polymer- or dye-doped.We will focus on nematic LCs, which are characterized by a mean orientation (also called director) of the elongated molecules and by a subsequent birefringence. After a general introduction on LCs, we focus on the nonlinear propagation of light in nematic LCs, and in particular the soliton-like propagation (nematicon). Indeed, if the light injected in the cell is intense enough, it can create a waveguide that counteracts the diffraction of the light. The light then propagates with an almost constant (or periodic) transverse profile.Our contribution to the subject starts with the numerical modeling of the thermal noise that characterizes the nematic LCs and the study of spatial instabilities of the soliton propagation caused by that noise. In Ch.3 we show that, by explicitly implementing the spatial correlation of the director in the LC thermal noise, it is possible to reproduce some of the features that characterize the LC response, such as the speckle generation or the fluctuating trajectory of the spatial optical soliton in LCs. Indeed, when the nematicon diameter is of the same order ofmagnitude as or smaller than the refractive index perturbations caused by the thermal noise, the nematicon starts to fluctuate in space. These fluctuations are not present when the noise is not correlated, indicating that the long-range interactions in LCs are crucial to explain the fluctuations. The model also allows us to introduce the propagation losses experienced by the nematicon without the use of an ad-hoc term. The simulations are in agreement with the experimental results. This method could also help the modeling of complex nonlinear phenomena in LCs that rely on noise, such as modulation instabilities or filamentation.Then, the optical gain is included in the LCs by dissolving photoluminescent polymers or dyes in it. In particular, we show that a particular polymer, the polyfuorene, when dissolved in nematic LCs, creates an intricate supramolecular pattern composed by homogeneous LC-rich regions surrounded by polymer-rich boundaries. The study of these structures through an ultra-fast spectroscopic technique (the pump-probe technique) and confocal microscopy reveals that the boundaries are composed by ordered and isolated chains of polymers. This particular morphology allows the observation of the optical gain from an oxidized unit of the polymeric chain (keto defects). This signal is usually covered by the absorption caused by the chain aggregation in solid state samples, while in LCs it is clearly visible. The optical gain from the keto defects appears also to be polarized orthogonal to the LC director, which is also the orientation of most of the boundaries. When a dye, one of the pyrromethenes, is dissolved in the LCs, the sample appears to be homogeneous. The optical gain from the dye ispolarized along the LC director and it shows an important spectral blue-shift (10 nm) passing from a polarization parallel to orthogonal to the LC director. The amplified spontaneous emission (ASE) shows the same shift when changing the direction of the sample excitation.When the ASE and the nematicon are generated in the same sample, it is possible to study the interaction between the two. In particular, the waveguide induced by the soliton can be used to guide another signal at another wavelength. We show that the nematicon can collect the ASE generated in the same device and guide it to the same fiber used to inject the nematicon in the LC cell. The extraction of the ASE from the device increases almost one order of magnitude when the soliton is present. However, due to the nematicon spatial fluctuations in LCs, an optimal nematicon power has to be found. Indeed, by increasing the soliton power, the light guiding is improved since the refractive index contrast of the nematicon-induced waveguide is increased. However, very high soliton powers have to be avoided, since the power-dependent soliton fluctuations prevent an optimal collection of the light. The nematicon is also found to increase the spectral purity and the polarization degree of the guided signal.Another LC system is studied, the chiral nematic LCs. In this system, the molecules are disposed following an helicoidal distribution. Due to their optical anisotropy and the periodic distribution, the system presents an optical band-gap. If the LC is also dye-doped, the combination of optical band-gap and gain generates laser emission. We are interested in a fast (sub-ms) reorientation of the helix, with the aim of studying the effect of this reorientation on the laser emission. The first step is the alignment of the LC helix (without the dye) with its axis parallel to the glass plates that constitute the cell, which is difficult to obtain with a high optical quality. For this reason, an innovative method is developed to align LCs through directional solvent evaporation. The solvent-induced method allows us to obtain particularly homogeneous textures, with a contrast ratio between the bright and the dark states that is a factor of 4 greater than that obtained with traditional methods. The LC samples based on solvent-induced alignment are then stabilized via two-photon photo-polymerization. This technique allows us to polymerize small regions of the device while the rest of the sample can be washed out in a solvent bath. When an achiral material is used to refill the device, it assumes a chiral alignment in the polymerized regions and an achiral nematic distribution in the rest. The first characterization of the laser emission is then presented in the last Chapter, with the aim of achieving sub-ms electrical tuning in future works.In this work a wide range of aspects have been investigated, leading to the realization of novel techniques for the fabrication of liquid crystal devices, the demonstration of novel phenomena for light amplification in liquid crystals and the experimental verification of new numerical modeling tools for light propagation in liquid crystals. The three key aspects of the work are nonlinear propagation, optical amplification and electrical response of different LC-based mixtures. Although the first few chapters deal with some of the aspects separately, in the last chapter these aspects are combined, revealing interesting new phenomena and pointing out a number of new aspects that could be part of future work. The results in this work have potential applications in fast tunable lasers, optical communication systems and lab-on-chip components. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

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.