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<p> A quantum particle moving in a periodic potential, with periodicity d, when acted by an external constant force F undergoes the dynamical phenomenon of Bloch-Zener oscillations (BZO). We investigate BZO of a neutral cold atom in an optical cavity pumped by a laser. We find that the single mode electromagnetic field of the optical cavity is affected by the atomic dynamics and propose the idea that a measurement of the electromagnetic field leaking out of the cavity will reflect the BZO frequency WB = Fd/h, and can be used for a precision measurement of F. The motivation for such a study comes from the fact that if the force F is gravity, then one can probe gravitational forces on sub-millimeter scales since the size of these systems are generally a few hundreds of microns. Such a study can be used to detect deviations from Newtonian gravity at short range proposed by some theories beyond the standard model of particle physics. </p> / Thesis / Master of Science (MSc)

Les structures à cristaux photoniques bidimentionnels ont permis la fabrication d'une large variété de composants nanophotoniques. En particulier, dans les PC parfaits, la densité locale d'états optiques se trouve exacerbée au niveau des points de symétrie du diagramme de bande. Près de ces points, où la vitesse de groupe tend vers zéro, la faible courbure de bande courbure de bande donne lieu à des modes stationnaires, dits de lumière "lente" (ou modes de Bloch lents). Les propriétés de la lumière lente en font de bons candidats pour améliorer l'effet Purcell, pour produire des effets non-linéaires ou pour concevoir des lasers à faible seuil. Parmi ces modes, les modes de Bloch lent émettant dans la direction verticale, c'est à dire situé au niveau du point Γ de la zone de Brillouin, sont particulièrement intéressants pour intégrer des architectures 2D avec de l'optique en espace libre. En particulier, certains de ces modes ont permis la réalisation d'émission laser dans la 3e direction avec des propriétés de polarisation particulières. D'autres applications prometteuses concernent le désordre : en introduisant un désordre aléatoire mais contrôlé dans la structure photonique, il est possible d'induire une transition entre le mode de Bloch lent de la structure ordonnée vers un mode localisé par le désordre, de type localisation d'Anderson dans une structure faiblement désordonnée.Dans cette thèse, les modes de Bloch lents ont été étudiés et caractérisés en Microscopie optique en champ proche. Nous nous sommes concentrés sur les modes en Gamma de la structure graphite. Le SNOM a permis de visualiser la composante évanescente du mode avec une résolution spatiale inférieure à la limite de diffraction. Dans ce travail, nous avons montré que le champ lointain et de l'image en champ proche du mode à la surface du cristal photonique sont différentes et que seules les mesures en champ proche permettent de rendre compte du mode réel à l'intérieur de la membrane de cristal photonique, en accord avec prédiction théorique. L'importance du choix de la sonde (silice, pointe métallisée, Nano-antenne) pour l'étude des structures à cristaux photoniques a également été démontrée. Outre la mesure d'intensité du champ électromagnétique, la polarisation du champ électrique a été mesurée à l'échelle nanométrique pour la première fois par l'aide d'une antenne à ouverture papillon. Ces résultats permettent d'identifier sans équivoque des modes avec les simulations 3D-FDTD.Dans ce travail est également rapporté la première observation de la localisation de la lumière dans deux types de lasers aléatoires à base de cristaux photoniques bidimensionnels. Le caractère aléatoire est introduit soit en déplaçant les positions des motifs du cristal (trous d'air), soit en faisant varier de façon aléatoire le diamètre des trous. Pour la première fois nous avons observé directement par SNOM la localisation de la lumière dans le cristal désordonné. Cela nous a permis d'observer la transition de morphologie du mode de Bloch lent entre le cristal ordonné et le cristal désordonné. / 2D-Photonic crystal (PC) structures have enabled the fabrication of a wide variety of nanophotonic components. In perfect PCs, the exploitation of the enhanced local density of states at critical points of the band diagram has attracted considerable attention. Near these points, where the group velocity vanished, low curvature flat bands give rise to delocalized and stationary optical slow Bloch modes (or slow light modes). Properties of slow light make them good candidates to enhance Purcell or various non-linear effects or to design low-threshold lasers. Among these modes, slow Bloch modes (SBMs) emitting in the vertical direction, i.e. located at the Γ- point of the Brillouin zone are particularly interesting for integrating 2D PC architectures with free space optics. In particular, some SBMs proved to be suitable for achieving strong vertical emission with peculiar polarization properties. Other promising applications concern disorder: by introducing a controlled randomness into the PC structure, it is possible to induce a transition from slow Bloch mode (in ordered PC) to Anderson’s localization (in disordered PC) as a function of disorder degree. In this PhD dissertation, Slow Bloch modes have been studied and characterized by the means of Near-field Scanning Optical microscopy (NSOM). We particularly focused on Slow Bloch laser mode at Γ- point of a honeycomb 2DPC. This NSOM technique enables to visualize the evanescent component of the mode with a spatial resolution below the diffraction limit. In this work, we showed that the far-field and the near-field image of the mode at the 2D-PC surface are different and that near-field results yield a better insight in the real mode structure inside the PC slab in agreement with theoretical prediction. The importance of the probe selection (bare silica, metallized tip and bow-tie aperture nanoantenna) for studying III-V photonic crystal structures was also demonstrated. Besides intensity measurement of the electromagnetic field, the polarization of the electric field has been measured at the nanoscale for the first time by using a bow-tie nano-antenna probe. These results enable the unambiguous identification of the modes with the 3D-FDTD simulations.In this work is also reported the first observation of two-dimensional localization of light in two types of 2D random photonic crystal lasers, where Slow Bloch Mode (SBM) is scattered by artificial structural randomness in triangular PCs. The structural randomness is introduced whether by nanometer displacements in the positions of lattice elements (air holes), whether by variation of the hole diameters. The direct near-field imaging of the lasing mode by use of NSOM for the first time, allowed us to observe the transition of the extended planar SBM to be Anderson localized.

Le champ électromagnétique térahertz (THz) se situe dans l'intervalle de fréquence entre l'infrarouge et les micro-ondes, à peu près entre 1 THz à 10 THz. Ce domaine est hautement souhaitable tant pour la recherche fondamentale que pour les applications. Pourtant des sources THz compacts et accordables ne sont pas encore disponibles. Depuis la première proposition en 1970, les superréseaux semiconducteurs, dans lequel deux couches semi-conductrices atomiques avec bande interdite différente sont disposés périodiquement, fournissent de nouvelles possibilités. De nouvelles techniques et de nouveaux dispositifs deviennent réalisables. Dans cette thèse, les oscillations de Bloch dans des mini-bandes électroniques d’un superréseau polarise et la dispersion du gain associée sont utilisées pour réaliser une source THz compacte et accordable : l’oscillateur de Bloch THz. Un premier ensemble de dispositifs utilisent des réseaux dopes spécifiquement conçus pour éviter la formation de domaine d’accumulation de charges. Ces dispositifs utilisent une surface semi-isolante ou deux surfaces métalliques permettant un guidage par plasmon de surface. Cependant, malgré la réalisation de couplage par les bords ou par un réseau diffractant en surface et des mesures directes ou avec un interféromètre a transformation de Fourrier (FTIR), l’électroluminescence a été observée dans le domaine térahertz, avec un gain qui n’a pas pu etre relie aux oscillations de Bloch. Avec des superréseaux non dope, l'émission THz des oscillations de Bloch a été détectée par spectroscopie dans le domaine temporel. La dépendance de la fréquence d’émission avec le champ électrique appliqué constitue une preuve directe des oscillations de Bloch. L’échelle de Wannier Stark des trous sous pompage optique continu a aussi été observe dans les superréseaux non dopes. Avec l’augmentation de la puissance de pompage optique, les pics du photocourant se décalent et leurs formes deviennent asymétriques. L’évolution est attribue a l’accumulation des porteurs photogénérés dans les deux couches encadrant le superréseau. En outre, pour une puissance de pompage élevée, la bistabilité du photocourant a été également observée. / Terahertz (THz) electromagnetic field, which lies in the frequency gap between the infrared and microwave, roughly between 1 THz to 10 THz, is highly desirable for both fundamental research and application. Yet tuneable compact THz sources are still not available. On the other hand, ever since first proposed in 1970, semiconductor superlattice provides new playground for various new technique and devices of tremendous research and application interest. In this thesis, an innovative theme, relying on Bloch oscillations in a dc biased semiconductor superlattice, is explored to realize tunable compact THz source THz Bloch oscillator. For doped superlattice Bloch oscillator, we designed quantum cascade super-superlattice structure to realize Bloch oscillations whilst prohibit electrical domain formation. The designed structures were processed into various waveguide and grating devices for electroluminescence detection using Fourier transform infrared spectroscopy (FTIR). The Bloch gain of semi-insulating surface plasmon waveguide device was also measured using THz time domain spectroscopy. Even though the electroluminescence and gain at THz regime were observed, no direct evidence of Bloch emission was confirmed. For undoped superlattice, the THz emission from Bloch oscillations was observed by time domain spectroscopy. At last, the photocurrent corresponding to heavy hole and Wannier Stark Ladder (WSL) states transitions in undoped superlattice was studied. Under CW laser pumping, the photocurrent as function of the applied voltage showed multiple WSL peaks, which indicated laser induced and controllable negative differential conductance (NDC). With increasing pumping power, the nonlinear NDC regime and bistable states were investigated as well.

Le piégeage optique se présente maintenant, depuis quelques décennies, comme une thématique majeure à l'intersection de diverses disciplines. Depuis les résultats d'Ashkin, de nombreux travaux ont été effectués dans le piégeage et le guidage d'objets physiques (particules, molécules, bactéries, etc.) de toutes tailles. Ces derniers caractériseront alors, devant la longueur d'onde, le domaine optique dans lequel nous nous placerons (Rayleigh, Mie, Optique géométrique).Notre travail porte donc sur l'étude des propriétés de chaînes linéaires périodiques de gouttelettes (huile), placées dans l'eau, et soumises à deux faisceaux laser horizontaux contra-propageants de profil gaussien. Nous démontrons qu'il est possible d'établir un ordre spatial sur un ensemble de grosses gouttes (devant la longueur d'onde) suivant une structure périodique. L'originalité d'un tel système réside dans le fait que la lumière peut alors être refocalisée par l'ensemble des gouttes espacées périodiquement. Cette périodicité peut ainsi, dans certains cas, conférer au faisceau une refocalisation périodique au sein du réseau. Cette première étude, en limite statique, nous permet ainsi de mettre en évidence les conditions de couplage des modes liés aux chaînes de gouttes. En particulier, nous caractérisons la présence de modes de Bloch où le faisceau se propage avec une périodicité équivalente à celle du réseau. Cela nous amène à remarquer que ces conditions modales sont soumises au paramètre de phase gaussien "Thêta" (phase de Gouy). Ainsi, bien que structuré à une échelle largement supérieure, nous mettons en évidence théoriquement des propriétés analogues à celle des cristaux photoniques, conférées par la périodicité des chaînes de gouttes. Ce qui nous permet, en conséquence, de démontrer l'existence de bandes interdites, nous amenant à définir un ensemble de modes guidants/nonguidants de cette chaîne. Cette étude statique est, par la suite, étendue d'un point de vue dynamique en considérant l'effet des forces optiques sur les gouttes. Nous démontrons ainsi qu'il est possible de piéger optiquement de telles gouttes sur des états d'équilibres stables. Au-delà desquels nous mettons en évidence, à travers une étude paramétrique, l'existence de modes oscillants périodiques ou pseudo-périodiques. Enfin, nous prenons en compte les phénomènes de collisions par coalescence, entraînant une réorganisation des répartitions de champs optiques qui peuvent se traduire par de nouvelles configurations de piégeage / Optical trapping appears now, since a few decades, as a major theme at the intersection of variousdisciplines. Since the results of Ashkin, many works were made in the trapping and the guidance of physical objects (particles, molecules, bacteria, etc.) of any sizes. The latter will characterize then, in front of the wavelength, the optical domain in which we shall take place (Rayleigh, Mie, Geometrical Optics).Our work thus concerns the study of the properties of periodic linear chains of droplets (oil), placed in water, and submitted to two counter-propagating horizontal laser beams of gaussian profile. We show that it is possible to establish a spatial order of a set of large drops (in front of the wavelength) in a periodic structure. The originality of such a system lies in the fact that the light can then be refocused by the set of periodically spaced drops. This periodicity may thus, in some cases, confer on the beam a periodic refocusing within the network. This first study, in static limit, allows us to identify the conditions of coupling modes associated with drop channels. In particular, we characterize the presence of Bloch modes where the beam propagates with similar frequency to that of the network. This leads us to note that these modal conditions are submitt to the gaussian phase parameter "Thêta" (Gouy phase). Thus, although structured at a widely higher scale, we highlight theoretically similar properties to that of the photonic crystals, conferred by the periodicity of the chains of drops. This allows us, consequently, to demonstrate the existence of bandgaps, leading us to define a set of guiding/not-guiding modes of this chain. This static study, thereafter, is extended from a dynamic point of view by taking into account the effect of the optical forces on the drops. We show that it is possible to optically trap such drops on stable equilibrium states. Beyond of which we highlight, through a parametric study, the existence of periodic or pseudo-periodic oscillating modes.Finally, we take into account the phenomena of collisions by coalescence, involving a reorganization of the distributions of optical fields which can result in new configurations of trapping.

Bloch analysis was originally developed by Felix Bloch to solve Schrödinger's equation for the electron wave function in a periodic potential field, such as that found in a pristine crystalline solid. His method has since been adapted to study elastic wave propagation in periodic structures. The absence of a rigorous mathematical analysis of the approach, as applied to periodic structures, has resulted in mistreatment of internal forces and misapplication to nonlinear media. In this thesis, we detail a mathematical basis for Bloch analysis and thereby shed important light on the proper application of the technique. We show conclusively that translational invariance is not a proper justification for invoking the existence of a "propagation constant," and that in nonlinear media this results in a flawed analysis. Next, we propose a general framework for applying Bloch analysis in damped systems and investigate the effect of damping on dispersion curves. In the context of Schrödinger's equation, damping is absent and energy is conserved. In the damped setting, application of Bloch analysis is not straight-forward and requires additional considerations in order to obtain valid results. Results are presented in which the approach is applied to example structures. These results reveal that damping may introduce wavenumber band gaps and bending of dispersion curves such that two or more temporal frequencies exist for each dispersion curve and wavenumber. We close the thesis by deriving conditions which predict the number of wavevectors at each frequency in a dispersion relation. This has important implications for the number of nearest neighbor interactions that must be included in a model in order to obtain dispersion predictions which match experiment.

This thesis analyzes different light localization phenomena in waveguide arrays. We report on the observation of quasi-Bloch oscillations, a new type of dynamic localization in the spatial evolution of light in curved, coupled optical waveguides. The delocalization and final relocalization of an optical beam in a waveguide array is shown by spatially resolving the optical intensity at various propagation distances. Through comparison to different structures, quasi-Bloch oscillations are shown to be robust beyond the nearest-neighbor tight-binding approximation.

This thesis analyzes different light localization phenomena in waveguide arrays. We report on the observation of quasi-Bloch oscillations, a new type of dynamic localization in the spatial evolution of light in curved, coupled optical waveguides. The delocalization and final relocalization of an optical beam in a waveguide array is shown by spatially resolving the optical intensity at various propagation distances. Through comparison to different structures, quasi-Bloch oscillations are shown to be robust beyond the nearest-neighbor tight-binding approximation.

Made available in DSpace on 2014-06-11T19:23:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-12-18Bitstream added on 2014-06-13T19:50:17Z : No. of bitstreams: 1 nacbar_dr_me_bauru.pdf: 1169690 bytes, checksum: c7a661675601c87b8e63ac301a1c144c (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / São calculadas e analisadas as funções de Wannier de localização máxima para elétrons em cristais unidimensionais. Essas funções formam uma base apropriada para descrever estados eletrônicos em materiais sólidos. Para cristais com simetria de inversão é utilizado o método desenvolvido por Bruno-Alfonso e Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Cada banda de energia é classificada segundo a simetria das funções de Bloch nos pontos 'gama' e 'qui' da zona de Brillouin. Para cada classe de banda a fase das funções de Bloch é escolhida para que as funções de Wannier tenham localização máxima. A simetria da últimas é determinda pelo tipo de banda. São apresentados resultados analíticos e numéricos para o modelo de Kronig-Penney obtidos através da técnica da matriz de transferência e do método tight binding. Posteriormente, apresenta-se um novo procedimento para calcular funções de Wannier de localização máxima em cristais sem simetria de inversão. Para isso são utilizadas técnicas do Cálculo Variacional. A teoria é aplicada para obter e analisar funções de Wannier de elétrons de condução em duas superredes de materiais semicondutores. Uma dessas estruturas tem simetria de inversão e a outra, não. O comportamento assintótico das funções de Wannier é predito analiticamente e verificado através dos cálculos numéricos. As funções de Wannier de localização máxima mostram um decaimento exponencial multiplicado por um decaimento em lei de potência, ambos isotrópicos. O mesmo acontece com parte das funções que não tem localização máxima. Porém, há outras que que apresentam decaimento exponecial reduzido e anisotropia em seu decaimento em lei de potência. Esses resultados novos são explicados levando em conta pontos de ramificação da continuação analítica das funções de Bloch sobre o plano de vetor de onda complexo. / The maximally localized Wannier functions of electrons in one-dimensional crystals are calculated and analyzed. Those functions form a suitable basis to describe localized states in solid materials. For crystals with inversion symmetry we use the procedure of Bruno-Alfonso and Hai [J. Phys: Condensed Matter 15, 6701 (2003)]. Each energy band is classified according to the symmetry of the Bloch functions at the points 'gama' e 'qui' of the Brillouin zone. For each band class, the phase of the Bloch functions in chosen to give the maximally localized Wannier functions. The symmmetry of those functions depends on the band class. Analytical and numerical results are presented for the Kronig-Penney model. Those result are obtained through the tight-binding method or a transfer-matrix technique. A new procedure to calculate the maximally localized Wannier functions in crystals without inversion symmetry is established. This involves techniques of the Variational Calculus. The theory is applied to obtain the Wannier functions of conduction electrons in superlattices of semiconductor materials. One of the superlattices presents inversion symmetry, but the other does not. The asymptotic behavior of the Wannier functions is predicted analytically and verified through numerical calculations. The maximally localized Wannier functions display an isotropic exponetial decal times an isotropic power-law decay. The same applies to a class of non-optimal Wannier functions. However, there is another class of non-optimal Wannier functions with reduced exponential decay and anisotropic power-law decay. Such new results are explained by taking into account branch points in the analytical continuation of the Bloch functions into the plane of complex wave vector.

[pt] Esta tese tem como objetivo propor uma reflexão teórica sobre o discurso biográfico e sua aplicação na própria produção de uma biografia. Para isso, está dividida em duas partes. Na primeira, são expostos os referenciais teóricos que tentam mapear a complexidade da construção deste tipo de discurso, levando em conta que estamos lidando com múltiplas e flexíveis redes de interpretação e discussão. Na segunda parte,elaboramos uma biografia em fractais de Adolpho Bloch, com o propósito de abordar as múltiplas e complexas identidades do biografado. Nossa proposta busca fugir da ineficácia de explicações unilaterais e totalizadoras e defende que as interpretações tenham como referência a complexidade. / [en] This dissertation intends to propose a theorical reflection about de discourse of biographies and its aplication by producting a biography. In order to do this, the dissertation has two parts. In the first one, we expose the theorical references that try to map the complexy of this kind of discourse construction, taking the account that we are working with multiplies and flexives nets of interpretation and discussion. In the second part, we ve made a fractal biography of Adolph Bloch, with the intention of study the multiples and complex identities of him. Our porpouse wants to escape from the ineficience of the total and unilateral explanations, and bases its references in the complexity of the interpretations.