In this thesis, an investigation into the modal characteristics of novel beam shapes is presented. Sculpting the phase profile of a Gaussian beam can result in the generation of a beam with unique properties. Described in this thesis are Laguerre-Gaussian (LG), Hermite-Gaussian (HG) and Bessel beams (BBs). The diffraction of LG beam modes from a triangular aperture is explored and this effect can be used for the efficient measurement of the azimuthal mode index l that indicates the number of multiples of 2π of phase changes that the field displays around one circumference of the optical axis. In this study, only LG beams with zero radial mode index p, with p + 1 denoting the number of bright high intensity concentric rings around the optical axis, were considered. Then, a powerful approach to simultaneously determine both mode indices of a pure LG beam using the principal component analysis (PCA) algorithm on the observed far-field diffraction patterns was demonstrated. Owing to PCA algorithm, the shape of the diffracting element used to measure the mode indices is in fact of little importance and the crucial step is ‘training' any diffracting optical system and transforming the observed far-field diffraction patterns into the uncorrelated variables (principal components). Our PCA method is generic and it was extended to other families of light fields such as HG, Bessel and superposed beams. This reinforces the widespread applicability of this method for various applications. Finally, both theoretically and experimentally investigations using interferometry show the definitive linkage between both the radial and azimuthal mode indices of a partially coherent LG beam and the dislocation rings in the far-field cross-correlation function (CCF).

In this doctoral thesis we investigate several experiments exploring the light orbital angular momentum and the Fraunhofer diffraction of light. Our investigations goes from coherent propagation, continue through incoherent propagation, arriving at semiclassical states used to explore one fundamental problem in quantum mechanics, i. e., the Born’s rule. Therefore, concerning coherent propagation of light with orbital angular momentum, we were first involved with studies about Fraunhofer diffraction of this type of light, by a single slit and by a square aperture. In the former work we studied the Fraunhofer diffraction when the slit center is aligned with the vortex center and when it is out of the vortex center. Concerning the work related to the square aperture, we show that the diffraction by such aperture is not sufficient to characterize the topological charge. Continuing the works, we also investigate the Fraunhofer diffraction of light with orbital angular momentum of fractional topological charge in the real space. An interesting phenomenon, the birth of a vortex, was studied at Fraunhofer plane, showing new conclusions in the study of fractional topological charges. Our studies continued with the Fraunhofer propagation of vortices in incoherent light, unveiling strong correlations between incoherent vortices. Finally, we explored semiclassical aspects of light with orbital angular momentum. Firstly, the topological charge determination via the spatial probability distribution of detection of photons diffracted by a triangular aperture. After, the validation of the Born’s rule using diffraction, by three slits disposed in a triangular configuration, of photons with an extra phase, i. e., the azimuthal phase added to the path phase. / Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nesta tese de doutorado investigamos diversos experimentos que exploram o momento angular orbital da luz e a difração de Fraunhofer. Nossas investigações abrangeram desde propagação coerente, passando por propagação incoerente, chegando a estados semiclássicos usados para explorar uma questão fundamental da mecânica quântica, a saber, a regra de Born. Portanto, no que concerne à propagação de luz coerente com momento angular orbital, estivemos envolvidos primeiramente com estudos da difração de Fraunhofer deste tipo de luz, por uma fenda simples e por uma abertura quadrada. No primeiro trabalho estudamos a difração de Fraunhofer quando o centro da fenda está alinhado com o centro do vórtice e quando está deslocado do centro do vórtice. Quanto ao trabalho relacionado à abertura quadrada, mostramos que a difração de Fraunhofer por tal abertura não permite caracterizar a carga topológica. Prosseguindo os trabalhos, investigamos também a difração no plano de Fraunhofer de luz com momento angular de carga fracionária no plano real. Um interessante fenômeno, o nascimento de um vórtice, foi estudado no plano de Fraunhofer, mostrando novas conclusões nos estudos relacionados à carga fracionária. Nossos estudos continuaram com a propagação de Fraunhofer de vórtices em luz incoerente, revelando fortes correlações entre vórtices incoerentes. Por fim, exploramos aspectos semiclássicos da luz com momento angular orbital. Primeiramente, a determinação da carga topológica via distribuição de probabilidade espacial de detecção de fótons difratados por uma abertura triangular. Posteriormente, a validação da regra de Born utilizando difração, por três fendas simples dispostas na forma triangular, de fótons com uma fase extra, ou seja, a fase azimutal, adicionada à fase de caminho.

Ce travail consiste en l'étude de phénomènes optomécaniques en d'interaction spin-orbite de la lumière, en utilisant des milieux inhomogènes et anisotropes comme systèmes modèles, différents types de systèmes matériels étant considérés en pratique. En particulier,nous avons utilisé des défauts de cristaux liquides nématiques pour lesquels nous avons identifié expérimentalement d'un couple optique de nature spin-orbite conduisant à des modifications de champ d'orientation moléculaire du cristal liquide. Aussi, grâce à l'utilisation de verres nanostructurés artificiellement permettant un contrôle de l'interaction spin-orbite à la demande,nous mettons en évidence un phénomène de couple optique inverse qui est l'analogue angulaire des forces optiques dites négatives. Cet effet optomécanique contre-intuitif est démontré expérimentalement, d'une manière indirecte, grâce à la mise en place de diverses expériences de décalage en fréquence Doppler associées aux degrés de liberté de rotation. Enfin, nous présentons nos tentatives en vue de réaliser expérimentalement l'observation directe d'un couple optique inverse. Plusieurs options sont envisagées, qui comprennent à la fois des approches à base de matériaux métalliques ou diélectriques. De manière générale, cela implique la miniaturisation des systèmes considérés, ce qui est effectué à la fois à l'échelle millimétrique et micrométrique. / This work focuses on angular optomechanics driven by the spin-orbit interaction of light, using inhomogeneous and anisotropic media as model systems and different kinds of such material systems are considered in practice. In particular, we use nematic liquid crystal defects and report on the direct experimental observation of spin-orbit optical radiation torque that leads to distortion of molecular orientation pattern of the defects. Then, by using solid-state spin-orbit couplers of arbitrary order made of artificially nanostructured glasses, we unveil an optical torque reversal phenomenon that is the angular counterpart of so-called optical negative forces. This counterintuitive optomechanical effect is experimentally retrieved, in an indirect manner, via rotational Doppler frequency shift experiments. Finally, we report on our attempts to build up an experimental framework allowing the direct observation of optical torque reversal. Several options are considered, which include both metallic and dielectric approaches and involve sample miniaturization that has been explored at the millimeter and micrometer scale.

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.

Le moment orbital angulaire (OAM) de la lumière est une grandeur quantifiée associée à la phase d’un vortex optique et est actuellement une des variables explorées pour les technologies quantiques.Dans ce contexte, cette thèse étudie expérimentalement la conversion de vortex optiques par une vapeur de rubidium, via la transition Raman stimulée à deux photons 5S₁/₂ − 5D₅/₂. Quand les atomes sont soumis à deux lasers respectivement à 780 nm et 776 nm, ils génèrent des rayonnements cohérents, infrarouge à 5,23 μm et bleu à 420 nm. On examine le rayonnement bleu lorsque l’un des lasers ou les deux sont des vortex, en particulier des modes de Laguerre-Gauss. Dans une première partie nous montrons que si l’OAM est porté par le laser à 776 nm, alors le rayonnement bleu émis porte un OAM qui respecte l’accord de phase azimutale et de phase de Gouy. Nous montrons aussi que la conversion est efficace sur une grande plage d’OAM allant de -50 à +50, que l’efficacité est gouvernée par le produit des intensités des lasers incidents et que le rayonnement bleu se comporte comme un mode de Laguerre-Gauss pur. Dans une deuxième partie nous montrons qu’il est possible de convertir une superposition de vortex ou une paire de vortex coaxiaux et que l’OAM du rayonnement bleu émis obéit à la règle de somme des OAM incidents. Pour les cas étudiés, nous proposons un modèle de mélange à quatre ondes qui établit les règles de sélection du processus de conversion d’OAM. Ce travail ouvre la voie vers la conversion d’OAM utilisant des transitions vers des niveaux atomiques plus élevés. / The orbital angular momentum of light (OAM) is a quantized quantity arising from the azimuthal phase carried by optical vortices and is well-known for quantum technology applications. Its set of values is theoretically infinite.In this context this thesis experimentally study the conversion of optical vortices in a rubidium vapor through the 5S₁/₂ − 5D₅/₂ stimulated Raman transition. When the atoms are illuminated with laser beams at 780 nm and 776 nm they generate two coherent light beams at 5,23 μm and 420 nm. We investigate the blue light when one laser or both are optical vortices, in particular Laguerre-Gaussian modes. In a first part we show that if the laser at 776 nm carries an OAM the blue light is an optical vortex with an OAM which respects azimutal and Gouy phase matchings. We further show that the conversion is efficient on a large set of OAM from -50 to +50, that the efficiency is governed by the product of the input laser intensities and that the blue light behaves like a pure Laguerre-Gaussian mode. In a second part we demonstrate the conversion of a vortex superposition or a pair of coaxial vortices and that the OAM of the emitted light obeys the conservation rule of total OAM. For each studied case we propose a four wave mixing model establishing selection rules for the conversion process. This work opens possibilities towards OAM conversion using higher atomic levels.

This dissertation thesis deals with the methods for processing image data in X-ray microtomography and digital holographic microscopy. The work aims to achieve significant acceleration of algorithms for tomographic reconstruction and image reconstruction in holographic microscopy by means of optimization and the use of massively parallel GPU. In the field of microtomography, the new GPU (graphic processing unit) accelerated implementations of filtered back projection and back projection filtration of derived data are presented. Another presented algorithm is the orientation normalization technique and evaluation of 3D tomographic data. In the part related to holographic microscopy, the individual steps of the complete image processing procedure are described. This part introduces the new orignal technique of phase unwrapping and correction of image phase damaged by the occurrence of optical vortices in the wrapped image phase. The implementation of the methods for the compensation of the phase deformation and for tracking of cells is then described. In conclusion, there is briefly introduced the Q-PHASE software, which is the complete bundle of all the algorithms necessary for the holographic microscope control, and holographic image processing.