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.

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.

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.

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.

No description available.

The widespread adoption of photonic circuits requires the economics of volume manufacturing offered by integration technology. A Complementary Metal-Oxide Semiconductor compatible silicon material platform is particularly attractive because it leverages the huge investment that has been made in silicon electronics and its high index contrast enables tight confinement of light which decreases component footprint and energy consumption. Nevertheless, there remain challenges to the development of photonic integrated circuits. Although the density of integration is advancing steady and the integration of the principal components – waveguides, optical sources and amplifiers, modulators, and photodetectors – have all been demonstrated, the integration density is low and the device library far from complete. The integration density is low primarily because of the difficulty of confining light in structures small compared to the wavelength which measured in micrometers. The device library is incomplete because of the immaturity of hybridisation on silicon of other materials required by active devices such as III-V semiconductor alloys and ferroelectric oxides and the difficulty of controlling the coupling of light between disparate material platforms. Metamaterials are nanocomposite materials which have optical properties not readily found in Nature that are defined as much by their geometry as their constituent materials. This offers the prospect of the engineering of materials to achieve integrated components with enhanced functionality. Metamaterials are a class of photonic crystals includes subwavelength grating waveguides, which have already provided breakthroughs in component performance yet require a simpler fabrication process compatible with current minimum feature size limitations. The research reported in this PhD thesis advances our understanding of the structure-property relations of key planar light circuit components and the metamaterial engineering of these properties. The analysis and simulation of components featuring structures that are only just subwavelength is complicated and consumes large computer resources especially when a three dimensional analysis of components structured over a scale larger than the wavelength is desired. This obstructs the iterative design-simulate cycle. An abstraction is required that summarises the properties of the metamaterial pertinent to the larger scale while neglecting the microscopic detail. That abstraction is known as homogenisation. It is possible to extend homogenisation from the long-wavelength limit up to the Bragg resonance (band edge). It is found that a metamaterial waveguide is accurately modeled as a continuous medium waveguide provided proper account is taken of the emergent properties of the homogenised metamaterial. A homogenised subwavelength grating waveguide structure behaves as a strongly anisotropic and spatially dispersive material with a c-axis normal to the layers of a one dimensional multi-layer structure (Kronig-Penney) or along the axis of uniformity for a two dimensional photonic crystal in three dimensional structure. Issues with boundary effects in the near Bragg resonance subwavelength are avoided either by ensuring the averaging is over an extensive path parallel to boundary or the sharp boundary is removed by graded structures. A procedure is described that enables the local homogenised index of a graded structure to be determined. These finding are confirmed by simulations and experiments on test circuits composed of Mach-Zehnder interferometers and individual components composed of regular nanostructured waveguide segments with different lengths and widths; and graded adiabatic waveguide tapers. The test chip included Lüneburg micro-lenses, which have application to Fourier optics on a chip. The measured loss of each lens is 0.72 dB. Photonic integrated circuits featuring a network of waveguides, modulators and couplers are important to applications in RF photonics, optical communications and quantum optics. Modal phase error is one of the significant limitations to the scaling of multimode interference coupler port dimension. Multimode interference couplers rely on the Talbot effect and offer the best in-class performance. Anisotropy helps reduce the Talbot length but temporal and spatial dispersion is necessary to control the modal phase error and wavelength dependence of the Talbot length. The Talbot effect in a Kronig-Penny metamaterial is analysed. It is shown that the metamaterial may be engineered to provide a close approximation to the parabolic dispersion relation required by the Talbot effect for perfect imaging. These findings are then applied to the multimode region and access waveguide tapers of a multi-slotted waveguide multimode interference coupler with slots either in the transverse direction or longitudinal direction. A novel polarisation beam splitter exploiting the anisotropy provided by a longitudinally slotted structure is demonstrated by simulation. The thesis describes the design, verification by simulation and layout of a photonic integrated circuit containing metamaterial waveguide test structures. The test and measurement of the fabricated chip and the analysis of the data is described in detail. The experimental results show good agreement with the theory, with the expected errors due to fabrication process limitations. From the Scanning Electron Microscope images and the measurements, it is clear that at the boundary of the minimum feature size limit, the error increases but still the devices can function.