Les guides à cristaux photoniques sont des guides optiques structurés à des échelles inférieures à la longueur d’onde. La vitesse de groupe de l’onde guidée y est ralentie. L’intensité du champ électromagnétique est ainsi exaltée et permet d’envisager de nombreuses applications pour le traitement optique de l'information. Cependant cette exaltation rend aussi les guides particulièrement sensibles aux imperfections de fabrication. Nous réalisons ici une étude théorique, numérique et expérimentale du transport de la lumière lente dans ces guides en présence de désordre. Le travail théorique propose une extension des méthodes perturbatives (de type Born) au cas des modes de Bloch électromagnétiques et un outil numérique original pour prendre en compte la diffusion multiple, qui devient déterminante lorsque la vitesse diminue. Les prédictions de ces deux types d'analyse ont été confrontées à des résultats expérimentaux. Pour la première fois dans les guides à cristaux photoniques, nous avons mesuré les statistiques d'ensemble du transport, en recoupant des mesures réalisées sur 18 échantillons identiques au désordre de fabrication près. Nous mettons en évidence les véritables limites de fonctionnement de ces guides. Ils ne sont limités ni par la dispersion, ni par leur atténuation moyenne. Les phénomènes de diffusion multiple modifient par contre considérablement la loi de probabilité de transmission. Pour pouvoir utiliser les guides à cristaux photoniques, il faut donc rester dans des régimes de fonctionnement où la diffusion multiple est négligeable, c’est-à-dire soit pour des vitesses de groupe relativement grandes (vg > c/20), soit pour des longueurs de guide faibles. / Photonic crystals are optical materials in which patterning of dielectric materials on a sub-wavelength scale creates unusual optical properties such as propagation speeds that are much slower than the speed of light. Electromagnetic fields are locally enhanced and light-matter interactions are thereby increased. However, because of this enhancement, the waveguides are much more sensitive to fabrication disorder. In this manuscript, we develop a theoretical, numerical and experimental analysis of the light transport in disordered waveguides. The theoretical work proposes an extension of the Born approximation to the case of electromagnetic Bloch modes and a new numerical tool which considers the multiple-scattering that becomes dominant when the group velocity decreases. Predictions of both models have been compared to experimental results. For the first time in photonic crystal waveguides, we measured ensemble-averaged quantities of photonic transport, collected on a series of 18 waveguides that are nominally identical and that only differ by statistical structural imperfections. We deduced the actual working limitations of these guides: they are limited neither by their GVD nor by their averaged losses. However multiple-scattering processes change the transmission probability density function dramatically. In order to use photonic crystal waveguides, it is therefore necessary to keep within regimes, where multiple scattering can be neglected, i.e. for relatively high group velocities (vg > c/20), or for short waveguide lengths.

Cette thèse de doctorat a pour but de fabriquer des systèmes électro-optiques compacts en utilisant les propriétés des cristaux photoniques (CP).). Le niobate de lithium (LiNbO3) est très attractif pour les applications optiques (télécommunications optiques, biomédical, astrophysique) car il a de faibles pertes en propagation (0.1 dB/cm ou moins), une faible dispersion en longueur d’onde, une large bande de transparence (350-5000 nm), et des forts coefficients Electro-optiques, non-linéaires et acousto-optiques. Cependant, les composants optiques utilisant ce matériau présentent classiquement un encombrement supérieur au centimètre, ce qui est dommageable pour leur intégration dans des circuits optiques compacts. Nous cherchons à démontrer plus précisément la faisabilité de modulateurs électro-optiques ultra-compacts tout en gardant les performances des modulateurs de type Mach-Zehnder, telles que de faibles pertes d'insertion, une faible tension de commande et un fort taux d'extinction. Nous proposons de remplir ces objectifs par l'usinage de cristaux photoniques à haut facteur de forme sur des guides LiNbO3, en associant découpe à la scie circulaire de précision et gravure par faisceau d'ion focalisé. La configuration s’appuie d’une part sur une tranche fine (ridge) de LiNbO3 qui confine la lumière transversalement, et d’autre part sur l'usinage du CP à haut facteur de forme pour favoriser une forte sensibilité à la présence de champs électriques externes sur des longueurs actives de l'ordre du micromètre. Les hauts facteurs de forme seront obtenus en usinant les ridges sur leur sommet et sur leurs flancs. Un premier enjeu, technologique, est destiné à optimiser les technologies développées à l’institut FEMTO-ST en vue d’applications à l’optique intégrée. Le deuxième enjeu, scientifique, s’agit de mettre en oeuvre une nouvelle configuration de contrôle de la lumière à l’aide d’un cristal photonique, présentant un double usinage sur les flancs et le sommet. C'est la première démonstration expérimentale de nanostructures LiNbO3 à haut facteur de forme. / The main goal of this PhD thesis is to fabricate compact electro-optical devices in exploiting the properties of photoniccrystal (PhC). Lithium niobate (LiNbO3) is a very attractive material for optical applications (such as opticaltelecommunication, biomedicine, astrophysics) thanks to its low propagation losses (0.1 dB/cm or less), its weakwavelength dispersion, its large optical bandwidth (350-5000 nm), and its strong electro-optical, non linear and acoustoopticalcoefficients. However, classical LiNbO3-based optical components possess active lengths of several centimers,which is not benefic for their good integration in compact optical circuits.We will focus this study more precisely on the feasibility of ultra-compact electro-optical modulators while keeping theperformances of commercialized LiNbO3 Mach-Zehnder type modulators, like their low insertion losses, their high extinctionratios, and their low power consumptions. To overcome this challenge, we will structure high aspect ratio photonic crystalson lithium niobate waveguides by combining optical grade dicing and focused ion beam milling. The main configuration isbased on the technology of LiNbO3 ridge waveguide in order to confine the light laterally and on the nano-structuration ofhigh aspect ratio photonic crystal on the ridge waveguide to enhance the sensibility to electric field stimuli on a fewmicrometers only. Structuring such high aspect ratio PhC will be possible thanks to focused ion beam milling from thetopside and the lateral side of the waveguide.The first issue is to optimize the technology developed in FEMTO-ST Institute for the fabrication of LiNbO3 integratedcomponents. The second issue is to create new configurations to control the propagation of light. This will be the firstexperimental demonstration of high aspect ratio LiNbO3 nanostructures.

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.

SWIFTS (Stationary Wave Integrated Fourier Transform Spectrometer) est une nouvelle technologie innovante de spectrométrie qui permet une réduction radicale de la taille des spectromètres à Transformée de Fourier, tout en conservant, et même en améliorant leurs performances. Grâce aux avancées de l'optique intégrée et des nanotechnologies, SWIFTS repose sur une méthode de détection optique originale, sans aucune partie mobile, où des nanoplots métalliques échantillonnent directement le champ évanescent d'une onde stationnaire dans un guide d'onde.Dans cette thèse, nous proposons de présenter le cheminement complet qui a mené, en partant du concept original, au développement puis à la mise en pratique de la technologie SWIFTS. Le document illustre notamment les caractérisations optiques, les choix technologiques et les optimisations entrepris pour la réalisation de spectromètres fonctionnels dans le domaine visible et proche-infrarouge. Des procédures de calibrages novatrices et complémentaires, basées sur du multiplexage fréquentiel et sur de l'interférométrie à faible cohérence temporelle, ont été développées pour déterminer avec précision les différentes irrégularités de fabrication et de comportement de l'appareil complètement intégré. Les spectromètres calibrés permettent à présent d'aborder des applications diverses en industrie et en recherche, de la caractérisation hautes performances de lasers, à l'interrogation de capteurs fibrés à réseaux de Bragg, aux techniques de spectrométries Raman et LIBS, et de tomographie optique OCT, jusqu'aux sciences de l'Univers (géophysique, astrophysique).SWIFTS est une innovation de rupture qui, de part sa miniaturisation obtenue sans compromis avec de hautes performances d'analyse spectrale, a la capacité de faire passer la spectrométrie du stade de la mesure complexe en laboratoire à celle d'un simple composant intégré pour des applications exigeantes. / SWIFTS (Stationary Wave Integrated Fourier Transform Spectrometer) is a new innovative technology of spectrometry that allows a drastic reduction of the size of Fourier transform spectrometers, while maintaining, and even improving their performance. With advances in integrated optics and nanotechnology, SWIFTS is based on an original method of optical detection, without any moving part, where metallic nanodots directly sample the evanescent field of a standing wave in a waveguide.In this thesis, we propose to present the complete process that led, starting from the original concept, to the development and the applications of the technology. The document illustrates the optical characterizations, the technological choices and the optimizations made for the realization of functional spectrometers in the visible and near-infrared range. Innovative and complementary procedures of calibrations, based on frequency multiplexing and low coherence interferometry, have been developed to accurately determine the various irregularities of the manufacturing and of the behavior of the integrated device. The calibrated spectrometers allow to address various applications in industry and research, such as high performance characterization of lasers, interrogation of fiber Bragg gratings sensors, Raman and LIBS spectrometry, optical coherence tomography OCT, and sciences of the Universe (geophysics, astrophysics).SWIFTS is a breakthrough innovation in spectrometry, without trade-off between miniaturization and high performance, that opens the way for product development based on the most demanding applications currently performed in research laboratories.

Este trabalho tem por objetivo a extensão de métodos numéricos baseados em diferenças finitas no domínio do tempo (FDTD) e no domínio da freqüência (FD-BPM) para a simulação da propagação de ondas eletromagnéticas em materiais com propriedades ópticas diversas, por exemplo, isotrópicos, anisotrópicos, lineares, não-lineares, bem como a combinação destes em uma mesma estrutura. Inicialmente foram elaborados formalismos bidimensionais (FDTD e FD-BPM), dos quais foram investigados modos com polarização TM (Magnético Transversal) que se propagam em estruturas planares magnetoópticas/não-lineares/lineares. Esta polarização foi escolhida tendo em vista o campo magnetostático dc adotado, o qual possibilitou a observação do fenômeno não-recíproco associado ao não-linear simultaneamente. Por outro lado, é bem sabido que o método FDTD é computacionalmente muito intensivo. Portanto, um grande esforço foi dedicado aos formalismos no domínio da freqüência, os quais foram implementados em duas e três dimensões. Este último foi estendido para um formalismo totalmente vetorial, capaz de simular modos híbridos ou até mesmo a transferência de energia entre modos de polarizações ortogonais. Isto nos permitiu investigar geometrias ainda mais complexas, tais como um isolador óptico baseado em um guia de onda tip rib utilizando material magnetooptico. Adicionalmente, fenômenos de natureza complexa, tais como a dinâmica dos condensados de luz em materiais com não-lineares do tipo Kerr com saturação, também conhecidos como meios não-lineares cúbico-qüínticos, foram investigados pela primeira vez com um formalismo vetorial. Finalmente, métodos numéricos capazes de considerar qualquer combinação de materiais com propriedades ópticas distintas (linear e/ou não-linear e/ou magnetoóptico) são uma ferramenta extraordinária para a comunidade científica para o projeto de novos dispositivos ópticos, bem como a investigação de novos efeitos físicos com vistas à aplicações em computação óptica, que podem resultar em um menor e mais eficiente número de componentes para sistemas de comunicações ópticos. / This work introduces three improved formalisms for the analysis of electromagnetic wave propagation through materials with distinct optical properties, i.e., isotropic, anisotropic, linear, nonlinear, or any combination of them. Two finite difference approaches were extensively investigated in this work for this purpose, namely the finite difference in time domain (FDTD), and the finite difference beam propagation method (2D and 3D FD-BPM), these in frequency domain. Initially, a TM (transverse magnetic) mode propagating through a planar magnetooptic/nonlinear/linear waveguide was investigated by way of a two-dimensional formalism (FDTD and FD-BPM). This mode polarization was chosen based on the orientation of the external magnetostatic field adopted, which favored the observation of non-reciprocal and nonlinear effects simultaneously. On the other hand, it is well known that FDTD formalisms are computationally intensives. Therefore, a great effort was dedicated to its frequency domain counterpart (FD-BPM), which was implemented in two and three dimensions. The later was further extended to a fully vectorial formalism, which is capable of simulating hybrid modes or even the energy transfer between orthogonal modes. This enabled us to investigate more complex geometries, such as an optical isolator based on magnetooptic rib waveguide. Additionally, complex phenomena, such as the dynamic of light condensates in bulk nonlinear Kerr media with saturation, also known as cubic-quintic nonlinear media, were investigated for the first time with a 3D vectorial formalism. Finally, numerical methods capable of handling any combination of materials with distinct optical properties (linear and/or nonlinear and/or magnetooptic) are an extraordinary tool for the scientific community for the design of new optical devices, as well as the investigation of new physical effects aimed for optical computing, that may result in fewer and more efficient components for optical communication systems.