L’information quantique peut être traitée de deux manières fondamentalement différentes: à l’aide de variables discrètes ou continues. Dans cette thèse, nous étudions de manière théorique la réalisation de protocoles d’information quantique dans les systèmes caractérisés par des variables continues. Pour ce faire, nous utilisons les variables modulaires comme outil afin de révéler des structures discrètes dans les états, opérations et observables. Le présent travail est fortement motivé par l’applicabilité expérimentale de nos idées dans des expériences d’optique quantique. Le thème principal de cette thèse est la formulation d’un cadre pour le traitement quantique de l’information dans l’espace des phases grâce aux variables modulaires. L’usage des variables modulaires permet d’encoder des états logique dans des espaces de Hilbert de dimension infinie et de définir des opérations qui permettent de les manipuler. En particulier, nous considérons des protocoles qui impliquent des mesures de variables modulaires qui permettent la lecture d’information discrète codée dans des variables continues. Grâce à ce formalisme, nous montrons comment il est possible de réaliser des tests des propriétés fondamentales de la mécanique quantique comme l’intrication, la non-localité ou la contextualité dans des espaces de Hilbert de dimensions finie ou infinie. Ensuite, nous discutons pourquoi les degrés de liberté transverse des photons sont des candidats naturels pour l’implémentation expérimentale des variables modulaires. À cet effet, nous démontrons comment il est possible d’utiliser l’effet Talbot - un effet d’interférence de champ proche - afin d’encoder de l’information discrète dans la distribution spatiales des photons. Finalement, nous montrons pour la première fois comment produire des photons intriqués de dimension arbitraire de manière déterministe en utilisant la conversion paramétrique et des éléments d’optique linéaire. / Quantum information can be processed in two fundamentally different ways, using either discrete- or continuous-variable implementations. In this thesis we study theoretically how to implement discrete quantum information protocols in physical objects characterized by continuous variables. In order to do so we use modular variables as a helpful tool to reveal discrete structures in continuous-variable states, operations and observables. The present work is strongly guided by the experimental applicability of our ideas in quantum optics experiments, with a particular focus on the transverse degrees of freedom of single photons. One of the main themes of this thesis is the formulation of a framework for quantum information processing in phase-space based on the use of modular variables. The latter permit us to introduce logical states and operations allowing to manipulate discrete quantum information encoded in infinite dimensional Hilbert spaces. In particular, we consider protocols that involve measurements of judiciously chosen logical observables enabling the readout of the encoded discrete quantum information. Based on this framework we show how to perform tests of fundamental properties of quantum mechanics, such as entanglement, Bell nonlocality and contextuality, in Hilbert spaces of various dimensions. Further on, we discuss the transverse degrees of freedom of single photons as a natural platform to manipulate and measure modular variables. In particular, we demonstrate how to process discrete quantum information encoded in the spatial distribution of single photons via the optical Talbot effect - a near-field interference effect. Finally, we show for the first time how to produce deterministically d-dimensional entangled photon pairs using spontaneous parametric down-conversion and linear optical elements only.

Les techniques de génération et de traitement des signaux souffrent des limitations intrinsèques des systèmes électroniques : bande passante limitée, sensibilité aux interférences électromagnétiques, encombrement et coût. Au contraire, les systèmes optiques s’affranchissent naturellement de ces contraintes et sont potentiellement très attractifs pour la génération et le traitement des signaux. Au cours de cette thèse, nous avons étudié un système optique original utilisé pour la photonique micro-onde : les boucles à décalage de fréquence.Les propriétés temporelles de ces boucles présentent un parallèle frappant avec certaines propriétés de l’effet Talbot en optique spatiale. Cette dualité s’est révélée particulièrement riche au cours de ce travail, car elle nous a conduits à démontrer de nombreuses propriétés à la fois en optique temporelle dans les boucles à décalage de fréquence, mais aussi en optique spatiale dans des montages simples de diffraction.Nous avons ainsi mis en évidence la possibilité de calculer analogiquement la transformée de Fourier et la transformée de Fourier fractionnaire d’un signal arbitraire, avec une très bonne résolution spectrale. Ceci nous a permis de mesurer le taux de « chirp » d’un signal à modulation linéaire de fréquence, ou d’améliorer le rapport signal sur bruit de certains signaux. Nous avons également montré la possibilité de générer des trains d’impulsions avec un taux de répétition ajustable, et de faire de la mise en forme spectrale de haute résolution, en amplitude et en phase. Ce résultat permet de générer des signaux arbitraires optiques ou radiofréquences, avec des bandes passantes de plusieurs dizaines de GHz et des durées pouvant aller jusqu’à plusieurs dizaines de ns.La richesse de la dualité entre l’optique spatiale et les boucles à décalage de fréquence nous a conduits à réinterpréter un certain nombre de propriétés de l’effet Talbot (formation des images, auto-réparation des images de Talbot) et à proposer des concepts nouveaux, tels que le contrôle des images de Talbot (période et taille) ou l’amplification d’image. / Signal generation and processing techniques suffer from intrinsic limitations of electronic systems: limited bandwidth, sensitivity to electromagnetic interference, bulk and cost. On the contrary, optical systems naturally overcome these constraints and are potentially very attractive for the generation and processing of signals. During this thesis, we studied an original optical system used for microwave photonics: frequency shifting loops.The temporal properties of these loops have a strong link with some properties of the Talbot effect in spatial optics. This duality has been successful during this work, because it led us to demonstrate many properties both in time optics in the frequency shifting loops, and in spatial optics with simple diffraction setup.We have thus demonstrated the possibility of analogically calculating the Fourier transform and the fractional Fourier transform of an arbitrary signal, with a very good spectral resolution. This allowed us to measure the "chirp" rate of a linearly frequency modulated signal, or to improve the signal-to-noise ratio of some signals. We have also shown the possibility to generate pulse trains with an adjustable repetition rate, and to make spectral shaping of high resolution, in amplitude and phase. This result has been used to generate arbitrary optical or radiofrequency signals with bandwidths of several tens of GHz and durations of up to several tens of ns.The properties of the duality between spatial optics and frequency shifting loops led us to reinterpret a number of properties of the Talbot effect (image formation, self-healing of Talbot images) and to propose new concepts, such as control of Talbot images (period and size) or image amplification.

This thesis represents an important investigation into the much-neglected period of exile endured by many Royalists as a consequence of the violence and alienation of the Wars of the Three Kingdoms (1639-1651).Drawing from extensive archival research conducted in Britain, Ireland and Europe, this study expands upon existing literature on royalism, British and Irish interaction with Continental Europe and seventeenth-century mentalities more generally in order to illumine the unique issues faced by these exiles. Central to this study are the roles and experiences of the Irish element within Charles II’s exiled court. Recent studies focussed upon the place of Ireland within Europe and the North Atlantic are employed to assess such issues as confessional division, court culture, the impact of memory and the influence of conflicting European ideas upon the survival of the exiles and the course of the restoration cause. A thematic, rather than chronological structure is employed in order to develop these interpretations, allowing for an approach which emphasizes the place of individuals in relation to broader Royalist mentalities. Dominant figures include Murrough O’Brien, Lord Inchiquin (c. 1614-1674), Theobald, Lord Taaffe (d. 1677), John Bramhall (1594-1663), Church of Ireland bishop of Derry, Daniel O’Neill (c. 1612-1664), Father Peter Talbot (SJ) (c. 1618/20 – 1680) and James Butler, marquis of Ormond (1610-1688). Through investigation of Irish strands of royalism and the wider issues in which they were set in the course of civil war and exile, this thesis makes a powerful argument for the need to consider seventeenth-century ideas of allegiance and identity not only within a ‘Three Kingdoms’ approach, but Europe more generally. It also makes a compelling case for the centrality of Irish Royalists in the formation and implementation of policy during the exile period through their familiarity with and access to European centres of power and influence.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Les progrès en microtechnologie durant la dernière décennie ont abouti à la réalisation de plans focaux infrarouge (PFIR) de grand format, intégrant une importante densité de détecteurs (ou pixels) au centimètre carré. La caractérisation de ces composants sophistiqués devient alors un véritable défi, en particulier la mesure de la réponse spatiale des détecteurs, décrite par la fonction de transfert de modulation (FTM). Cette mesure nécessite la projection de mires parfaitement connues qui couvrent toute la surface du PFIR et contiennent des détails sub-pixels. Depuis plusieurs années, une technique originale de mesure de FTM est à l'étude à l'ONERA. L'idée initiale était d'utiliser la propriété d'auto-imagerie d'un réseau en transmission éclairé par une onde plane quasi-monochromatique, appelée effet Talbot. Un premier banc de test a été développé et a permis d'effectuer des mesures sur des PFIR fonctionnant dans la bande [1-2,5 µm] et [3-5µm]. Pour le test des composants fonctionnant dans la bande des hautes longueurs d'onde (8-12 µm), la technique se heurte à des limitations physiques (appelées effets non-paraxiaux) et des solutions alternatives ont été proposées, basées sur une classe particulière de faisceaux auto-imageants, appelés les tableaux nondiffractants. L'objet de la thèse est d'étudier de manière quantitative et rigoureuse ces effets non-paraxiaux et de développer les solutions proposées précédemment. En particulier, des techniques originales permettant de générer des tableaux nondiffractants haute-résolution (c'est-à-dire contenant des motifs de taille proche de la longueur d'onde) sont étudiées théoriquement et expérimentalement. Ces techniques exploitent l'éclairage panchromatique du réseau ainsi qu'un nouveau type de réseaux auto-imageants appelés réseaux continûment auto-imageants. Enfin, on montre que pour les mesures de FTM à différentes longueurs d'onde, une somme incohérente d'auto-images monochromatiques enregistrées à différentes distances permet de construire des motifs analogues à ceux obtenus avec un éclairage panchromatique.

Diffractive optical elements (DOEs) serve an important function in many dynamic and static optical systems. The theory and design of surface diffractive structures are well understood and practically applied at high spatial and phase resolution for a wide range of optical applications in science and industry. However, these structures normally only harness phase modulation of uniform fields for the beam diffraction and therefore limit their range of application, as well as being susceptible to surface damage. Multilayered volume diffractive elements offer a powerful opportunity to harness both phase and amplitude modulation for benefits in diffraction efficiency and beam shaping. However, multilayered combinations have been difficult to fabricate and provide only weak diffraction for phase gratings with low refractive index contrast. The advent of femtosecond laser writing inside transparent media has enabled the facile embedding of optical devices such as waveguides and diffractive optics into novel three-dimensional geometries that offer advanced functionality with compact design. In this work, femtosecond laser writing is pushed to the limits of forming high resolution phase elements with sufficiently strong refractive index contrast on which to develop volume phase gratings with the highest diffractive efficiency. The formation of both positive and negative zones of refractive index contrast together with rapid Talbot self imaging inside weakly contrasting phase gratings are major challenges here diminish the efficiency of assembled gratings. A method of strategic layering of otherwise weakly diffracting gratings onto Talbot planes is introduced to demonstrate, in FDTD models, the definitive enhancement of overall diffraction efficiency. A systematic optimization of laser writing in fused silica verify this enhancement or diminishment with weak volume gratings assembled on aligned or misaligned on Talbot planes. Advanced laser beam control methods were further demonstrated that underpin new direction for the facile assembly of highly functional DOEs that can exploit coherent light diffraction for opportunities in improving the performance of holographic devices and extend further to the powerful combination of phase and amplitude modulation control that is potentially available in a single optical device, thereby opening new directions for the design and fabrication of robust and strongly diffracting volume optical devices.

Diffractive optical elements (DOEs) serve an important function in many dynamic and static optical systems. The theory and design of surface diffractive structures are well understood and practically applied at high spatial and phase resolution for a wide range of optical applications in science and industry. However, these structures normally only harness phase modulation of uniform fields for the beam diffraction and therefore limit their range of application, as well as being susceptible to surface damage. Multilayered volume diffractive elements offer a powerful opportunity to harness both phase and amplitude modulation for benefits in diffraction efficiency and beam shaping. However, multilayered combinations have been difficult to fabricate and provide only weak diffraction for phase gratings with low refractive index contrast. The advent of femtosecond laser writing inside transparent media has enabled the facile embedding of optical devices such as waveguides and diffractive optics into novel three-dimensional geometries that offer advanced functionality with compact design. In this work, femtosecond laser writing is pushed to the limits of forming high resolution phase elements with sufficiently strong refractive index contrast on which to develop volume phase gratings with the highest diffractive efficiency. The formation of both positive and negative zones of refractive index contrast together with rapid Talbot self imaging inside weakly contrasting phase gratings are major challenges here diminish the efficiency of assembled gratings. A method of strategic layering of otherwise weakly diffracting gratings onto Talbot planes is introduced to demonstrate, in FDTD models, the definitive enhancement of overall diffraction efficiency. A systematic optimization of laser writing in fused silica verify this enhancement or diminishment with weak volume gratings assembled on aligned or misaligned on Talbot planes. Advanced laser beam control methods were further demonstrated that underpin new direction for the facile assembly of highly functional DOEs that can exploit coherent light diffraction for opportunities in improving the performance of holographic devices and extend further to the powerful combination of phase and amplitude modulation control that is potentially available in a single optical device, thereby opening new directions for the design and fabrication of robust and strongly diffracting volume optical devices.

Dynamic Cone Penetration Tests for LiquefactionEvaluation of Gravelly SoilsMichael H. TalbotDepartment of Civil and Environmental Engineering, BYUDoctor of PhilosophyIn North American practice, the Becker Penetration Test (BPT) has become the primary field test used to measure penetration resistance of gravelly soils. However, this test is expensive and uncertainties exist regarding correlations and corrections for rod friction. As an alternative, the dynamic penetration test (DPT) developed in China has recently been correlated with liquefaction resistance in gravelly soils. The DPT equipment consists of a 74 mm diameter cone tip driven by a 120 kg hammer with a free fall height of 100 cm using 60 mm drill rod to reduce friction. The DPT is a very rugged, economical device, capable of penetrating dense gravel layers. During DPT field investigations following the 2008 Wenchuan earthquake in China, liquefaction resistance was correlated with DPT blow count.Dynamic Cone Penetration tests (DPT) tests were also performed adjacent to Becker Penetration test (BPT) sites at Pence Ranch, Whiskey Springs, and Larter Ranch in Idaho where gravel liquefaction was observed during the 1983 Mw6.9 Borah Peak earthquake. Companion DPT tests were performed using an automatic hammer at two energy levels, namely the energy specified in the original Chinese standard and the energy typical of SPT testing which would be easier to use in practice. Companion testing was undertaken to determine if the cone could be driven in gravelly soil with more standard drilling equipment available to geo-professionals. The second energy level also offers the potential to provide more resolution on the soil layering. PDA measurements were made to determine the energy transferred to the cone rods and the statistical variation in the energy transferred.Additionally, companion DPT tests were undertaken at the downstream toe of Millsite Dam near Ferron, Utah, where gravelly soils are predicted to liquefy in an earthquake. Two energy levels were used, one using an automatic hammer and the other a manual donut hammer. The blow counts from the BPT and DPT correlated reasonably well for gravels using the automatic hammer, but poor correlation was obtained with the donut hammer. Liquefaction resistance for the BPT and DPT soundings were also in reasonable agreement for gravel layers suggesting that the DPT can provide liquefaction hazard evaluations more economically than the BPT using direct correlations with field performance.Correlations suggest that the standard energy corrections developed for the SPT can be used for the DPT. In general, the liquefaction resistance from the BPT and DPT correlated reasonably well when using the 30% probability of liquefaction resistance curve developed for the DPT.Keywords: Michael H Talbot, liquefaction, Chinese dynamic penetration test, gravelly soils.

No description available.

The goal of the research reported in this thesis is to establish the feasibility of a novel optical architecture for an optical route & select circuit switch suitable for implementation as a photonic integrated circuit. The proposed architecture combines Optical Phased Array (OPA) switch elements implemented as multimode interference coupler based Generalised Mach-Zehnder Interferometers (GMZI) with a planar Lüneburg lens-based optical transpose interconnection network implemented using graded metamaterial waveguide slabs. The proposed switch is transparent to signal format and, in principle, can have zero excess insertion loss and scale to large port counts. These switches will enable the low-energy consumption high capacity communications network infrastructure needed to provide environmentally-friendly broadband access to all. The thesis first explains the importance of switch structures in optical communications networks and the difficulties of scaling to a large number of switch ports. The thesis then introduces the Talbot effect, i.e. the self-imaging of periodic field distributions in free space. It elaborates on a new approach to finding the phase relations between pairs of Talbot image planes at carefully selected positions. The free space Talbot effect is mapped to the waveguide Talbot effect which is fundamental to the operation of multimode interference couplers (MMI). Knowledge of the phase relation between the MMI ports is necessary to achieve correct operation of the GMZI OPA switch elements. An outline of the design procedures is given that can be applied to optimise the performance of MMI couplers and, as a consequence, the GMZI OPA switch elements. The Lüneburg Optical Transpose Interconnection System (LOTIS) is introduced as a potential solution to the problem of excessive insertion loss and cross-talk caused by the large number of crossovers in a switch fabric. Finally, the thesis explains how a Lüneburg lens may be implemented in a graded ‘metamaterial’, i.e. a composite material consisting of ‘atoms’ arranged on a regular lattice suspended in a host by nano-structuring of silicon waveguide slabs using a single etch-step. Furthermore, the propagation of light in graded almost-periodic structures is discussed. Detailed consideration is given to the calibration of the local homogenised effective index; in terms of the local parameters of the metamaterial microstructure in the plane and the corrections necessary to accommodate slab waveguide confinement in the normal to the plane. The concept and designs were verified by FDTD simulation. A 4×4 LOTIS structure showed correct routing of light with a low insertion loss of -0.25 dB and crosstalk of -24.12 dB. An -0.45 dB excess loss for 2D analysis and an -0.83 dB insertion excess loss for 3D analysis of two side by side metamaterial Lüneburg lenses with diameter of 15 μm was measured, which suggests that the metamaterial implementation produces minimal additional impairments to the switch.