Дисертації з теми "Light angular momentum"

The idea is now well established that light possesses angular momentum and that this comes in two distinct forms, namely spin and orbital angular momentum which are associated with circular polarisation and helical phase fronts respectively. In this thesis, we explain that this is, in fact, a mere glimpse of a much larger picture: light possesses an infinite number of distinct angular momenta, the conservation of which in the strict absence of charge reflects the myriad rotational symmetries then inherent to Maxwell's equations. We recognise, moreover, that many of these angular momenta can be identified explicitly in light-matter interactions, which leads us in particular to identify new possibilities for the use of light to probe and manipulate chiral molecules.

We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons.

Dans une première partie introductive, nous rappelons la description théorique de la propagation de faisceaux optiques en terme des modes solutions de l'équation de propagation dans l'approximation paraxialle. Dans ce cadre, nous présentons les notions de moment cinétique transporté par les faisceaux lumineux, et de sa décomposition en moment cinétique intrinsèque (ou spin) et en moment angulaire.La seconde partie est consacrée au codage de l'information dans les degrés de libertés de polarisation et de modes transverses des faisceaux optiques. Les modes spin-orbites sont définis et un dispositif expérimental optique pour produire ces modes est présenté. Les modes spin-orbites sont alors exploités pour implémenter un protocole de distribution de clés BB84 ne nécessitant pas le partage à priori d'une base de référence.Dans une troisième partie, nous proposons un critère de type inégalité de Bell, qui constitue une condition suffisante pour caractériser la non-séparabilité en spin-orbite d'un faisceau optique classique. Nous montrons ensuite que la notion de modes spin-orbite séparable ou non-séparable constitue une analogie pertinente avec la notion d'intrication d'états quantiques et permet l'étude de certaines de ses propriétés fondamentales. Enfin, une implémentation expérimentale de cette simulation de tests de Bell avec des faisceaux optiques classiques est présentée, ainsi que sa description détaillée dans le cadre de l'optique quantique.Dans une dernière partie, nous nous intéressons à des inégalités de Bell, pour des états quantiques de systèmes quantiques à deux parties, qui sont caractérisées chacune par une variable continue de type angulaire (périodique). Nous montrons comment détecter la non-localité sur ce type de système, avec des inégalités qui sont similaires aux inégalités CHSH; inégalités qui avaient été développées originellement pour des systèmes de type spin 1/2. Nos inégalités, sont construites à partir de la mesure de la corrélation de fonctions angulaires. Nous montrons qu'elles sont en fait la superposition continue d'inégalités CHSH de type spin 1/2. Nous envisageons une possible implémentation expérimentale, où les corrélations mesurées sont les corrélations angulaires du profil transverse des photons intriqués
We shall present a theoretical description of paraxial beams, showing the propagation modes that arise from the solution of the paraxial equation in free space. We then discuss the angular momentum carried by light beams, with its decomposition in spin and orbital angular momentum and its quantization. We present the polarization and transverse modes of a beam as potential degrees of freedom to encode information. We define the Spin-Orbit modes and explain the experimental methods to produce such modes. We then apply the Spin-Orbit modes to perform a BB84 quantum key distribution protocol without a shared reference frame.We propose a Bell-like inequality criterion as a sufficient condition for the spin-orbit non-separability of a classical laser beam. We show that the notion of separable and non-separable spin-orbit modes in classical optics builds a useful analogy with entangled quantum states, allowing for the study of some of their important mathematical properties. We present a detailed quantum optical description of the experiment in which a comprehensive range of quantum states are considered.Following the study of Bell's inequalities we consider bipartite quantum systems characterized by a continuous angular variable θ. We show how to reveal non-locality on this type of system using inequalities similar to CHSH ones, originally derived for bipartite spin 1/2 like systems. Such inequalities involve correlated measurement of continuous angular functions and are equivalent to the continuous superposition of CHSH inequalities acting on two-dimensional subspaces of the infinite dimensional Hilbert space. As an example, we discuss in detail one application of our results, which consists in measuring orientation correlations on the transverse profile of entangled photons

Orbital angular momentum of light is a new field of research which is concerned with the mechanical and optical effects of light with a helical phase structure. In this thesis we ask fundamental questions on the properties of light carrying orbital angular momentum. We discuss the uncertainty relation for angle and angular momentum on the example of orbital angular momentum of light. The lower bound in the angular uncertainty relation is state dependent, which requires a distinction between states satisfying the equality in the uncertainty relation and states giving a minimum in the uncertainty product. We examine these special states and their uncertainty product. We show that for both kinds of states, the uncertainty product can be surprisingly large. We propose an experimentally testable criterion for an EPR paradox for orbital angular momentum and azimuthal angle. The criterion is designed for an experimental demonstration using orbital angular momentum of light. For the interpretation of future experimental results from the proposed setup, we include a model for the indeterminacies inherent to the angular position measurement. We show how angular apertures can be used to determine the angle, and we discuss the effects of this measurement on the proposed criterion. We show that for a class of aperture functions a demonstration of an angular EPR paradox, according to our criterion, is to be expected. The quantum theory of rotation angles is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the orientation of a phase discontinuity associated with fractional values of the orbital angular momentum. We apply our formalism to the propagation of light modes with fractional orbital angular momentum in the paraxial and non-paraxial regime.

While the story of optical orbital angular momentum (OAM) dates back to the development of Maxwell's equations, the study of photon OAM by the physics community begins in earnest in the 1990s, led in part by a paper by Allen et al. describing the independent control of spin and orbital angular momentum in paraxial modes of light. The recognition of the orbital angular momentum of light in astronomy is a much more recent affair. This thesis explores the role of the OAM of light in astronomy and attempts to make the case for the measurement of photon OAM as a new tool in astronomy. Two contributions are made in order to prepare the groundwork for future endeavours: a laboratory assessment of the effectiveness of adaptive optics (AO) systems on atmospheric turbulence when measuring optical OAM, and an initial field test of an instrument measuring the optical OAM spectrum of the sun. Regarding the first study, the author finds that realistic atmospheric turbulence (1'' seeing) severely corrupts any incoming OAM signal at visible wavelengths, in spite of AO correction (<10% power recovered), however results suggest adequate correction at IR wavelengths. In the second study, an instrument to measure the OAM spectrum of a source is constructed and employed to measure the OAM spectrum of local regions of the sun. It represents the first measurement of its kind, distinguishing sunspots by analyzing their OAM spectrum and in addition, demonstrates the improvement of OAM measurements by implementing a lucky imaging routine. Finally, this thesis highlights a new avenue for further study into the measurement of OAM for observational astronomy. A new type of OAM measurement is proposed, capable of measuring rotations in the plane orthogonal to the line of sight. This measurement takes advantage of the rotational Doppler shift, an analogue of the translational Doppler shift, and an OAM interferometer designed to measure the associated phase shift is outlined. A future instrument is also proposed by combining the OAM interferometer with a high resolution spectrograph. This would allow for measurements of both the rotational and translational Doppler shifts, providing information about the three dimensional motion of an object.

New dynamical applications of quantum beat spectroscopy (QBS) to molecular dynamics are employed to probe the angular momentum polarization effects in photodissociation and molecular collisions. The magnitude and the dynamical behaviour of angular momentum alignment and orientation, two types of polarization, can be measured via QBS technique on a shot-by-shot basis. The first part of this thesis describes the experimental studies of collisional angular momentum depolarization for the electronically excited state radicals in the presence of the collider partners. Depolarization accompanies both inelastic collisions, giving rise to rotational energy transfer (RET), and elastic collisions. Experimental results also have a fairly good agreement with the results of quasi-classical trajectory scattering calculations. Chapter 1 provides the brief theories about the application of the QBS technique and collisional depolarization. Chapter 2 describes the method and instrumentation employed in the experiments of this work. In Chapter 3, the QBS technique is used to measure the total elastic plus elastic depolarization rate constants under thermal conditions for NO(A,v=0) in the presence of He, Ar, N2, and O2. In the case of NO(A) with Ar, and particularly with He, collisional depolarization is significantly smaller than RET, reflecting the weak long-range forces in these systems. In the case of NO(A)+N2/O2, collisional depolarization and RET are comparable, reflecting the relatively strong long-range forces in these systems. In Chapter 4, the QBS technique is used to measure the elastic and inelastic depolarization and total RET rate constants for OH(A,v=0) under thermal conditions in the presence of He and Ar, as well as the total depolarization rate constants under superthermal conditions. In the case of OH(A)+He, elastic depolarization is sensitive to the N rotational state, and inelastic depolarization is strongly dependent on the collision energy. In the case of OH(A)+Ar, elastic depolarization is insensitive to N, and inelastic depolarization is less sensitive to the collision energy, reflecting that the relatively strong long-range force in OH(A)+Ar system. The second part of this thesis describes the experimental studies of photodissociation under thermal conditions. Chapter 5 provides a brief introduction about several polarization parameter formalisms used for photodissociation, and the incorporation of the QBS technique to measure these polarization parameters. In this thesis, most polarization parameters of the molecular photofragments are measured using the LIF method, and the QBS technique is used as a complementary tool to probe these polarization parameters. In Chapter 6, rotational orientation in the OH(X,v=0) photofragments from H2O2 photodissociation using circularly polarized light at 193 nm is observed. Although H2O2 can be excited to both the A and B electronic states by 193 nm, the observed orientation is only related to the A state dynamics. A proposed mechanism about the coupling between a polarized photon and the H2O2 parent rotation is simulated, and the good agreement between the experimental and simulation results further confirms the validity of this mechanism. In Chapter 7, rotational orientation in the NO(X,v) photofragments from NO2 photodissociation using circularly polarized light at 306 nm (v=0,1,2) and at 355 nm (v=0,1) is observed. Two possible mechanisms, the parent molecular rotation and the coherent effect between multiple electronic states, are discussed. NOCl is photodissociated using circularly polarized light at 306 nm, and NO(X,v) rotational distributions (v=0,1) and rotational orientation (v=0) are measured. For the case of NOCl, the generation of orientation is attributed to the coherent effect.

Thesis (PhD)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: High-dimensional quantum entanglement offers an increase in information capacity per photon; a highly desirable property for quantum information processes such as quantum communication, computation and teleportation. As the orbital angular momentum (OAM) modes of light span an infinite-dimensional Hilbert space, they have become frontrunners in achieving entanglement in higher dimensions. In light of this, we investigate the potential of OAM entanglement of photons by controlling the parameters in both the generation and measurement systems. We show the experimental procedures and apparatus involved in generating and measuring entangled photons in two-dimensions. We verify important quantum tests such as the Einstein, Podolsky and Rosen (EPR) paradox using OAM and angle correlations, as well as a violation of a Bell-type inequality. By performing a full state tomography, we characterise our quantum state and show we have a pure, highly entangled quantum state. We demonstrate that this method can be extended to higher dimensions. The experimental techniques used to generate and measure OAM entanglement place an upper bound on the number of accessible OAM modes. As such, we investigate new methods in which to increase the spiral bandwidth of our generated quantum state. We alter the shape of the pump beam in spontaneous parametric down-conversion and demonstrate an effect on both OAM and angle correlations. We also made changes to the measurement scheme by projecting the photon pairs into the Bessel-Gaussian (BG) basis and demonstrate entanglement in this basis. We show that this method allows the measured spiral bandwidth to be optimised by simply varying the continuous radial parameter of the BG modes. We demonstrate that BG modes can be entangled in higher dimensions compared with the commonly used helical modes by calculating and comparing the linear entropy and fidelity for both modes. We also show that quantum entanglement can be accurately simulated using classical light using back-projection, which allows the study of projective measurements and predicts the strength of the coincidence correlations in an entanglement experiment. Finally, we make use of each of the techniques to demonstrate the effect of a perturbation on OAM entanglement measured in the BG basis. We investigate the self-healing property of BG beams and show that the classical property is translated to the quantum regime. By calculating the concurrence, we see that measured entanglement recovers after encountering an obstruction.
AFRIKAANSE OPSOMMING: Hoë-dimensionele kwantumverstrengeldheid bied ’n toename in inligtingskapasiteit per foton. Hierdie is ’n hoogs wenslike eienskap vir kwantum inligting prosesse soos kwantum kommunikasie, berekening en teleportasie. Omdat die orbitale hoekmomentum (OAM) modusse van lig ’n oneindig dimensionele Hilbertruimte beslaan, het dit voorlopers geword in die verkryging van verstrengeling in hoër dimensies. In die lig hiervan, ondersoek ons die potensiaal van OAM verstrengeling van fotone deur die parameters in beide die generering en meting stelsels te beheer. Ons toon die eksperimentele prosedures en apparaat wat betrokke is by die generering en die meet van verstrengelde fotone in twee dimensies. Ons verifieer kwantumtoetse, soos die Einstein, Podolsky en Rosen (EPR) paradoks vir OAM en die hoekkorrelasies, sowel as ’n skending van ’n Bell-tipe ongelykheid. Deur middel van ’n volledige toestand tomografie, karakteriseer ons die kwantum toestand en wys ons dat dit ’n suiwer, hoogs verstrengel kwantum toestand is. Ons toon ook dat hierdie metode uitgebrei kan word na hoër dimensies. Die eksperimentele tegnieke wat tydens die generasie en meet van OAM verstrengeling gebruik is, plaas ’n bogrens op die aantal toeganklik OAM modusse. Dus ondersoek ons nuwe metodes om die spiraal bandwydte van ons gegenereerde kwantum toestand te verhoog. Ons verander die vorm van die pomp bundel in spontane parametriese af-omskakeling en demonstreer die uitwerking daarvan op beide OAM en die hoekkorrelasies. Ons het ook veranderinge aan die meting skema gemaak deur die foton pare op die Bessel-Gauss (BG) basis te projekteer. Ons wys dat hierdie metode die gemeetde spiraal bandwydte kan optimeer deur eenvoudig die kontinue radiale parameter van die BG modes te verander. Ons demonstreer dat BG modusse verstrengel kan word in hoër dimensies as die heliese modusse, wat algemeen gebruik word, deur berekeninge te maak en te vergelyk met lineêre entropie en vir beide modusse. Ons wys ook dat kwantumverstrengling akkuraat nageboots kan word, met behulp van die klassieke lig terug-projeksie, wat die studie van projeksie metings toelaat en voorspel die krag van die saamval korrelasies in ’n verstrengeling eksperiment. Ten slotte, gebruik ons elk van die tegnieke om die effek van ’n storing op OAM verstrengling wat in die BG basis gemeet is, te demonstreer. Ons ondersoek die self-genesingseienskap van BG bundels en wys dat die klassieke eienskap vertaal na die kwantum-gebied. Deur die berekening van die konkurrensie (concurrence), sien ons dat die gemeetde verstrengeling herstel word nadat ’n obstruksie ondervind is.

The classical field theory approach to the angular momentum of light, specifically how it represents the spin angular momentum of light, has been a matter of controversy for some time. This thesis analyses the aforementioned approach from the point of view of the Exterior Calculus and de Rham Cohomology. It is found purely mathematically that the spin angular momentum of a circularly polarized plane wave of light must be identically zero. It is concluded that the classical formulation of the angular momentum of a plane wave of light is, on some level, incomplete.

The torque exerted by a beam of polarized light on a half-wave plate which alters its state of polarization is calculated for several laser wavelengths and intensities using electromagnetic theory. The second-order torque that arises through the nonlinear interaction is formulated and the numerical values are calculated for the 42m crystal class. The experiment used to detect the existence of the torque is reviewed and a demonstration experiment is suggested.

Beams of light can carry spin and orbital angular momentum. Spin angular momentum describes how the direction of the electric field rotates about the propagation axis, while orbital angular momentum describes the rotation of the field amplitude pattern. These concepts are well understood for monochromatic beams, but previous theoretical studies have constructed polychromatic superpositions where the connection between angular momentum and rotation of the electric field becomes much less clear. These states are superpositions of two states of light carrying opposite signs of angular momentum and slightly detuned frequencies. They rotate at the typically small detuning frequency and thus we call them slowly rotating modes of light. Strangely, some of these modes appear to rotate in the direction opposing the sign of their angular momentum, while others exhibit overall rotation with no angular momentum at all! These findings have been the subject of some controversy, and in 2012, Susanna Todaro (HMC ’12) and I began work on trying to shed light on this “angular momentum paradox." In this thesis, I extend previous work in theory, simulation, and experiment. Via theory and modeling in Mathematica, I present a possible intuitive explanation for the angular momentum paradox. I also present experimental realization of slowly rotating spin superpositions, and outline the steps necessary to generate slowly rotating orbital angular momentum superpositions.

Three-dimensional (3D) displays project 3D images that give 3D perceptions and mimic real-world objects. Among the rich varieties of 3D displays, multiview displays take advantage of light’s various degrees of freedom and provide some of the 3D perceptions by projecting 2D subsampling of a 3D object. More 2D subsampling is required to project images with smoother parallax and more realistic sensation. As an additional degree of freedom with theoretically unlimited state space, orbital angular momentum (OAM) modes may be an alternative to the conventional multiview approaches and potentially project more images. This research involves exploring the possibility of encoding/decoding off-axis points in 2D images with OAM modes, development of the optical system, and design and development of a multiview colour display architecture. The first part of the research is exploring encoding/decoding off-axis points with OAM modes. Conventionally OAM modes are used to encode/decode the on-axis information only. Analysis of on-axis OAM beams referenced to off-axis points suggests representation of off-axis displacements as a set of expanded OAM components. At current stage off-axis points within an effective coding area are possible to be encoded/decoded with chosen OAM modes for multiplexing. Experimentally a 2D image is encoded/decoded with an OAM modes. When the encoding/decoding OAM modes match, the image is reconstructed. On the other hand, a dark region with zero intensity is shown. The dark region suggests the effective coding area for multiplexing. The final part of the research develops a multiview colour display. Based on understandings of off-axis representation of a set of different OAM components and experimental test of the optical system, three 1 mm monochromatic images are encoded, multiplexed and projected. Having studied wavelength effects on OAM coding, the initial architecture is updated to a scalable colour display consisting of four wavelengths.

Des interactions entre la matière et la lumière sont à l'origine de phénomènes opto-mécaniques. L'une des caractéristiques distinctives de l'interaction lumière-matière est l'interaction spin-orbite de la lumière. Cette dernière s'étudie au sein d'un domaine de recherche émergent consacré à l'étude des effets opto-mécaniques en présence de l'interaction entre la polarisation et des degrés de liberté spatiaux de la lumière. En particulier, ce travail vise à observer directement la manifestation (i) des forces latérales et (ii) des couples optiques gauches qui sont des effets opto-mécaniques contre-intuitifs. On utilise pour cela des milieux non homogènes et anisotropes comme ingrédients essentiels à la fabrication d’éléments optiques spin-orbite. Nous rapportons tout d'abord, les tentatives d’observations expérimentales directes, à partir des résultats préliminaires obtenus préalablement dans notre groupe de recherche. Nous présentons ensuite de nouvelles propositions d'expérimentations ainsi qu'une généralisation adaptée au cas des forces latérales. Par conséquent, nous rapportons d’une observation directe à l’échelle du millimètre des forces latérales optiques et des couples optiques gauches dépendantes du spin en effectuant une étude complète. Il ressort de l'analyse des deux phénomènes que leurs vitesses peuvent être augmentées en réduisant l'inertie ou la taille des éléments optiques spin-orbite au point de rendre les phénomènes significatifs à l'échelle microscopique et intéressants pour les applications technologiques. Nous faisons un rapport chronologique de notre travail expérimental consistant à observer le moment de force orienté à gauche à l'échelle du micromètre en utilisant des versions miniaturisées des échantillons précédents. Comme la dernière tentative n’était pas concluante, nous finissons par proposer de nouvelles stratégies prometteuses pour manipuler de tels micro-objets
Interactions between light and matter cause optomechanical phenomena, where a distinctive feature of light-matter interaction, namely, the spin-orbit interaction of light, takes place within an emerging research area dedicated to the study of optomechanical effects in the presence of the interplay between polarization and spatial degrees of freedom of light. In particular, this work aims to directly observe the manifestation of (i) lateral forces and (ii) left-handed torques, which are counterintuitive optomechanical effects, by using inhomogeneous and anisotropic media as a critical ingredient for the manufacture of spin-orbit optical elements. Hence, we report on their direct experimental observations attempts, starting from the preliminary results obtained in our group before this work, and then present our new proposals and further generalization to the case of lateral forces. Consequently, we report on a millimeter-scale direct observation of optical spin-dependent lateral forces and left-handed torques with a full study. From the analysis of both phenomena, it turns out that their speed can be increased by reducing the spin-orbit optical elements inertia or size, making the phenomena relevant at microscopic-scale and interesting for technological applications. Thus, we account for our experimental journey chronologically, to observe the left-handed torque at micrometer-scale with samples that correspond to miniaturized versions of previous ones. Since the last results were inconclusive, we finish by proposing new strategies of manipulation of such micro-elements with promising implementation

The aim of this work is to study the propagation of orbital angular momentum (OAM) of light for astrophysical applications and a method for OAM detection with optical telescopes. The thesis deals with the study of the orbital angular momentum (OAM) as a new observable for astronomers, which could give additional information with respect to those already inferred from the analysis of the intensity, frequency and polarization of light. Indeed, the main purpose of this work is to highlight that light can have a much more complex structure, and therefore can transport much more information. In particular, firstly we show that OAM can be imparted to light from interstellar media with a perturbed electron density function in the plane perpendicular to the propagation direction, revealing that the study of OAM could give information about the spatial structures of the traversed inhomogeneous media. The second part of the thesis deals with an experimental verification of the preservation of orbital angular momentum even for uncorrelated non-monochromatic wave beams, showing that this observable of light is preserved, thus we can aim at detecting it. Finally, if OAM can transport information, and if it is preserved in propagation, the obvious consequence is the study of its detection, in particular by an OAM mode sorter fitted to optical telescopes.
Lo scopo di questo lavoro è analizzare la propagazione del momento angolare orbitale (OAM) della luce per applicazioni astrofisiche e studiarne un metodo per la rilevazione con telescopi ottici. La tesi si occupa dello studio del momento angolare orbitale come un nuovo osservabile per gli astronomi, che potrebbe dare informazioni aggiuntive rispetto a quelle già deducibili dall'analisi della intensità, frequenza e polarizzazione della luce. Infatti, lo scopo principale di questo lavoro è di evidenziare come la luce possa avere una struttura molto più complessa, e quindi trasportare molte più informazioni. Inizialmente si dimostra che mezzi interstellari con una funzione di densità elettronica inomogenea nel piano perpendicolare alla direzione di propagazione della luce che li attraversa, possono conferire OAM. Ciò indica che lo studio dell' OAM può fornire informazioni sulle strutture spaziali dei mezzi attraversati non omogenei. Nella seconda parte della tesi viene esposta una verifica sperimentale della conservazione del momento angolare orbitale, anche per fasci d'onda non monocromatici e non coerenti . Viene così dimostrando che questo osservabile della luce si conserva, consentendone la rilevazione. Infine, osservato che l'OAM può trasportare informazioni, e che si conserva nella propagazione, si propone lo studio di un metodo per rivelarlo, in particolare di un uno spettrografo OAM per telescopi ottici.

Les besoins toujours croissants en terme de transfert de données numériques poussent au développement de nouvelles technologies pour accroître la capacité des réseaux, notamment en ce qui concerne les réseaux de fibre optique. Parmi ces nouvelles technologies, le multiplexage spatial permet de multiplier la capacité des liens optiques actuels. Nous nous intéressons particulièrement à une forme de multiplexage spatial utilisant le moment cinétique orbital de la lumière comme base orthogonale pour séparer un certain nombre de canaux. Nous présentons d’abord les notions d’électromagnétisme et de physique nécessaires à la compréhension des développements ultérieurs. Les équations de Maxwell sont dérivées afin d’expliquer les modes scalaires et vectoriels de la fibre optique. Nous présentons également d’autres propriétés modales, soit la coupure des modes, et les indices de groupe et de dispersion. La notion de moment cinétique orbital est ensuite introduite, avec plus particulièrement ses applications dans le domaine des télécommunications. Dans une seconde partie, nous proposons la carte modale comme un outil pour aider au design des fibres optiques à quelques modes. Nous développons la solution vectorielle des équations de coupure des modes pour les fibres en anneau, puis nous généralisons ces équations pour tous les profils de fibres à trois couches. Enfin, nous donnons quelques exemples d’application de la carte modale. Dans la troisième partie, nous présentons des designs de fibres pour la transmission des modes avec un moment cinétique orbital. Les outils développés dans la seconde partie sont utilisés pour effectuer ces designs. Un premier design de fibre, caractérisé par un centre creux, est étudié et démontré. Puis un second design, une famille de fibres avec un profil en anneau, est étudié. Des mesures d’indice effectif et d’indice de groupe sont effectuées sur ces fibres. Les outils et les fibres développés auront permis une meilleure compréhension de la transmission dans la fibre optique des modes ayant un moment cinétique orbital. Nous espérons que ces avancements aideront à développer prochainement des systèmes de communications performants utilisant le multiplexage spatial.
The always increasing need for digital data bandwidth pushes the development of emerging technologies to increase network capacity, especially for optical fiber infrastructures. Among those technologies, spatial multiplexing is a promising way to multiply the capacity of current optical links. In this thesis, we are particularly interested in current spatial multiplexing using the orbital angular momentum of light as an orthogonal basis to distinguish between a few optical channels. We first introduce notions from electromagnetism and physic needed for the understanding of the later developments. We derive Maxwell’s equations describing scalar and vector modes of optical fiber. We also present other modal properties like mode cutoff, group index, and dispersion. Orbital angular momentum is briefly explained, with emphasis on its applications to optical communications. In the second part, we propose the modal map as a tool that can help in the design of few mode fibers. We develop the vectorial solution of the ring-core fiber cutoff equation, then we extend those equations to all varieties of three-layer fiber profiles. Finally, we give some examples of the use of the modal map. In the third part of this thesis, we propose few fiber designs for the transmission of modes with an orbital angular momentum. The tools that were developed in the second part of this thesis are now used in the design process of those fibers. A first fiber design, characterized by a hollow center, is studied and demonstrated. Then a second design, a family of ring-core fibers, is studied. Effective indexes and group indexes are measured on the fabricated fibers, and compared to numerical simulations. The tools and the fibers developed in this thesis allowed a deeper comprehension of the transmission of orbital angular momentum modes in fiber. We hope that those achievements will help in the development of next generation optical communication systems using spatial multiplexing.

Magneto-optical materials such as permalloy can be used to create artificial spin- ice (ASI) lattices with antiferromagnetic ordering. Magneto-optical materials used to create diffraction lattices are known to exhibit magnetic scattering at the half- order Bragg peak while in the ground state. The significant drawbacks of studying the magneto-optical generation of OAM using x-rays are cost, time, and access to proper equipment. In this work, it is shown that the possibility of studying OAM and magneto-optical materials in the spectrum of visible light at or around 2 eV is viable. Using spectroscopic ellipsometry it is possible to detect a change in the magnetization of thin permalloy films with thicknesses between 5 and 20 nm. Patterns consistent with OAM were found at 1.95 eV using a square lattice with a 4𝜋 radial phase shift in the antiferromagnetic ground state. Evidence of magnetic scattering at the half-order Bragg peak using 1.95 eV was also found.

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In this thesis we discuss some fundamental aspects of the quantum theory from a contemporaneous point of view, where we could develop three works. In the first we analyze theoretically an atomic double-slit interferometer. It has been shown that if the energy eigenstates of the atom are correlated with its particle and wave behaviors, complementary phenomena can be measured simultaneously, indicating a reinterpretation of the complementarity principle. We also demonstrate that this experiment possesses quantum erasure properties. In the second we present a two-particle interferometer in order to analyze the way in which decoherence affects quantum interference. It has been shown how the environmental constituents, here considered as photons, can destroy the oscillations in the coincidence detection rate of the particles. Due to the temporal characteristic of this kind of interference, we name this process as quantum temporal decoherence. In the last work we study the existence of a novel complete family of exact and orthogonal solutions of the paraxial wave equation. The complex amplitude of these beams is proportional to the confluent hypergeometric functions, which we name hypergeometric modes of type-II (HyG-II). It is formally demonstrated that a hyperbolic-index medium can generate and support the propagation of such a class of beams. Since these modes are eigenfunctions of the photon orbital angular momentum, we conclude that an optical fiber with hyperbolic-index profile could take advantage over other graded-index fibers by the capacity of data transmission.
Nesta tese discutimos alguns aspectos fundamentais da teoria quântica de um ponto de vista mais contemporâneo, onde também pudemos desenvolver três trabalhos. No primeiro analisamos teoricamente um interferômetro de fenda dupla para átomos. Mostramos que se os autoestados de energia do átomo estão correlacionados com os comportamentos de partícula e de onda do mesmo, fenômenos complementares podem ser medidos simultaneamente, indicando uma reinterpretação do princípio da complementaridade. O mesmo aparato também apresentou propriedades de apagador quântico. No segundo apresentamos um interferômetro de duas partículas e a maneira como a decoerência afeta o grau de interferência. Mostramos como os constituintes do ambiente, aqui considerados como fótons, podem destruir a oscilação na taxa de coincidência de detecção das partículas. Devido a sua característica temporal, chamamos este processo de decoerência temporal quântica. No último trabalho estudamos a existência de uma nova família de soluções ortogonais da equação paraxial da luz. A amplitude complexa desses feixes são proporcionais às funções hipergeométricas confluentes, que denominamos modos hipergeométricos do segundo tipo (HyG-II). Demonstramos formalmente que um meio com um perfil hiperbólico de índice de refração pode gerar e suportar essa classe de feixes. Uma vez que esses modos são autofunções do momento angular orbital do fóton, concluímos que uma fibra ótica com este perfil de índice, em certas situações, poderia levar vantagem em relação a outras fibras com índice variável na capacidade de transmissão de dados.

This thesis encompasses a body of experimental work on the use of structured light in quantum cryptographic protocols. In particular, we investigate the ability to perform quantum key distribution through various quantum channels (fibre, free-space, underwater) in laboratory and realistic conditions. We first demonstrate that a special type of optical fibre (vortex fibre) capable of coherently transmitting vector vortex modes is a viable quantum channel. Next, we describe the first demonstration of high-dimensional quantum cryptography using structured photons in an urban setting. In particular, the prevalence of atmospheric turbulence can introduce many errors to a transmitted key; however, we are still able to transmit more information per carrier using a 4-dimensional scheme in comparison to a 2-dimensional one. Lastly, we investigate the possibility of performing secure quantum communication with twisted photons in an uncontrolled underwater channel. We find that though it is possible for low-dimensional schemes, high-dimensional schemes suffer from underwater turbulence without the use of corrective wavefront techniques.

L'interaction spin-orbite pour la lumière permet le couplage entre les degrés de liberté associés à l'état de polarisation de la lumière et ceux associés à l'espace. Ce couplage est particulièrement important dans les milieux qui sont à la fois inhomogènes et anisotropes. Dans ce travail, nous exploitons la mise en forme des propriétés de biréfringence artificielle ou naturelles de matériaux optiques tels que la silice, le nitrure de silicium, le silicium ou les cristaux liquides pour façonner différentes propriétés d'un faisceau lumineux. En particulier, nous démontrons la réalisation d'éléments optiques originaux permettant la transformation d'un faisceau gaussien en un faisceau de Laguerre-Gauss. En exploitant la superposition de tels modes générés par le couplage spin-orbite optique, nous montrons qu'il est possible de façonner des textures de polarisation de type skyrmion. Enfin, en tirant parti de la dépendance en longueur d'onde du niveau d'interaction spin-orbite, des dispositifs électro-optiques à base de cristaux liquides sont proposés pour moduler spectralement la topologie de la distribution de phase spatiale du champ lumineux, ce qui ouvre un champ d'applications dans la mise en forme d'impulsions optiques ultra-brèves
The spin-orbit interaction for light allows coupling between the degrees of freedom associated with the polarization state of light and those associated with space. Such coupling is particularly important in media that are both inhomogeneous and anisotropic. In this work, we exploit the shaping of artificial or natural birefringence properties of optical materials such as silica, silicon nitride, silicon, or liquid crystals to shape different properties of a light beam. In particular, we demonstrate the realization of original optical elements that allow the transformation of a Gaussian beam into a Laguerre-Gauss beam. By exploiting the superposition of such modes generated by optical spin-orbit coupling, we show that it is possible to shape skyrmion-like polarization textures. Finally, by exploiting the wavelength dependence of the level of spin-orbit interaction, liquid crystal-based electro-optical devices are proposed to spectrally modulate the topology of the spatial phase distribution of the light field, opening a field of applications in the shaping of ultrashort optical pulses

Cette thèse porte sur la manipulation du moment angulaire de la lumière à l'échelle sub-micronique. Le moment angulaire total de la lumière est composé d'une partie de spin, relié au degré de liberté de polarisation circulaire de la lumière, et d'une partie orbitale, relié au degré de libertés spatiaux de la lumière que sont sa direction de propagation (locale et globale) et sa distribution spatiale d'intensité. Le couplage spin-orbite existant entre ces deux contributions permet alors de manipuler les degrés de libertés spatiaux de la lumière par un simple contrôle de son état de polarisation circulaire. Dans cette thèse, nous avons étudié et exploité ce couplage à l'échelle sub-micronique dans deux nouveaux phénomènes que nous avons mis en évidence. Le premier met à profit ce couplage pour permettre d'exciter de manière unidirectionnelle des modes plasmoniques guidés. Une étude complète (numérique, expérimentale et analytique) de ce phénomène nouveau, basé sur un couplage entre le moment de spin du photon incident et le moment orbital extrinsèque des modes plasmoniques guidés dans la courbure d'un guide, est présentée. La deuxième étude présente une voie pour tirer parti du transfert de moment orbital de la lumière à un gaz d'électrons libres dans un métal afin de générer et contrôler le sens et la géométries de boucles de courants sub-microniques dans des structures métalliques. Ce contrôle permettrait la génération d'optomaimants nanométriques, entièrement contrôlés par la lumière, pouvant être modulés aux fréquences optiques. Ce travail a été soutenu par le LABEX Action
This thesis focuses on the manipulation of the angular momentum of light at the nanoscale.The total angular momentum of light is composed of a spin component, connected to the polarization degree of freedom of light, and an orbital component, related to the spatial degrees of freedom of the light which are its propagation direction (local and global) and its intensity distribution. The spin-orbit coupling between these two contributions allows the control of the spatial degrees of freedom of light by a simple manipulation of its circular polarization state. In this thesis, we have studied and applied this coupling at the nanoscale anbd we have highlighted two new phenomenas. The first one takes part of this coupling to allows unidirectional excitation of plasmonic guided modes. A complete study (numerical, experimental and analytical) of this new phenomenon, based on a coupling between the spin of the incident photon and the extrinsic orbital momentum of the plasmonic guided modes within the curvature of a waveguide, is presented. The second study propose a way to benefit from the transfer of the angular momentum of light to the free electrons gas in a metal to generate and control the direction and the geometry of nanoscale current loops in metallic structures. this control would at optical frequencies. This work was supported by the LABEX Action

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CNPQ
In this thesis are presented various results regarding the transverse structure of light beams in the paraxial propagation regime, with a special concern with singularities in the transverse profile and in nonlinear optics applications. Theoretical and experimental tools were developed for the study of Optical Vortices (OV) and its most important characteristics, as the Orbital Angular Momentum (OAM) and the Topological Charge (TC). In a first step, we theoretically described and experimentally demonstrated that it is possible to shape the intensity profile of a beam containing OV by distributing TC over the plane transverse to the propagation direction [1]. The TC is associated with a phase singularity that implies in points of zero intensity. By distributing the TC on the transverse plane, it is possible to shape the beam dark region and also the OAM profile with the goal of optimizing the light beam for a given application. However, a problem identified in [1] was that most of the current available techniques to characterize OAM light implicitly assume that the beam has cylindrical symmetry, thus being inadequate to characterize fields resulting from more general TC distributions. These problems were approached in a second work [2], where it was shown that by measuring the field transverse amplitude and phase profiles it is possible to measure the OAM and the TC in TC distributions with arbitrary geometries. By combination of the results [1] and [2] it is possible to optimize and characterize the TC distributions for given applications, as for example by designing the transverse forces in an optical tweezer for microparticle manipulation. An important theoretical unfold during these works was the identification of an analogous relation between the field transverse phase in a TC distribution with the Coulomb potential in two-dimensional electrostatics. We then introduced in [3] the Topological Potential (TP) concept which allows the design of structured optical beams with complex spatial profiles inspired by two-dimensional electrostatics analogies. The TP can be used to describe a broad class of TC distributions, as those from [1,2] or the more sophisticate examples in [3]. In another set of results, it is discussed the possibility of using concepts and the formalism of quantum mechanics to solve light propagation problems in the classical approximation. Among the results obtained, it should be remarked that the formalism obtained has a simple and direct relation with ABCD matrices and ray optics [4]. These results were used to understand light propagation in systems containing nonlinear materials, as in SLIM [5] and D4σ [6] techniques. In [5, 6] the theoretical results were compared with experimental data obtained from standard samples, as carbon dissulfide (CS2), acetone and fused silica. It was obtained a very good agreement between the measured optical nonlinearities and the results established in literature for these materials.
Nesta tese são apresentados resultados relacionados com a estrutura transversal de feixes de luz no regime paraxial de propagação, com uma atenção especial em singularidades no perfil transversal e em aplicações para óptica não linear. Foram desenvolvidas ferramentas teóricas e experimentais para o estudo de vórtices ópticos (Optical Vortices - OVs), e suas características mais importantes, como o momento angular orbital (Orbital Angular Momentum - OAM) e a carga topológica (Topological Charge - TC). Inicialmente, foi teoricamente descrito e experimentalmente demonstrado como é possível moldar o perfil de intensidade de um feixe contendo OVs usando uma distribuição de TC sobre o plano transversal à direção de propagação [1]. A TC está associada a uma singularidade na fase, o que implica em um zero de intensidade. Ao se distribuir a TC sobre o plano transversal, é possível moldar o formato da região de intensidade nula e também o perfil de OAM no intuito de otimizar o feixe para uma dada aplicação. No entanto, um problema identificado neste trabalho é que a maior parte das técnicas de caracterização disponíveis para luz com OAM implicitamente supunham que o feixe possui simetria cilíndrica, e portanto não eram adequadas para caracterizar campos obtidos a partir de distribuições de TC com geometrias mais gerais. Tais problemas foram abordados em um segundo trabalho [2], onde foi mostrado que por meio de medições dos perfis transversais de amplitude e fase do campo elétrico é possível medir o OAM e a TC em distribuições de TC com formas geométricas arbitrárias. A união dos trabalhos [1] e [2] permite então que as distribuições de TC possam ser adequadamente otimizadas e caracterizadas para aplicações específicas, como por exemplo ao moldar as forças transversais numa pinça óptica para a manipulação de micropartículas. Um desdobramento teórico importante obtido foi identificar uma relação análoga entre o perfil de fase em uma distribuição de TC com o potencial de Coulomb em eletrostática bidimensional. Foi então introduzido em [3] o conceito de potencial topológico (Topological Potential - TP) que possibilita a construção de feixes ópticos estruturados com perfis espaciais complexos inspirados em analogias com eletrostática bidimensional. O TP pode ser usado na descrição de uma grande variedade de distribuições de TC, como nos feixes em [1, 2] ou nos exemplos mais sofisticados em [3]. Posteriormente, é discutida a possibilidade de se utilizar conceitos e o formalismo da mecânica quântica na solução de problemas de propagação da luz descrita na aproximação clássica. Dentre os resultados obtidos, destaca-se que o formalismo possui uma relação simples e direta com as matrizes ABCD e a óptica de raios [4]. Estes resultados foram utilizados na compreensão da propagação da luz em sistemas contendo materiais não lineares, como nas técnicas SLIM [5] e D4σ[6]. Nos trabalhos [5,6] os resultados teóricos foram comparados com dados experimentais obtidos em amostras padrão, como dissulfeto de carbono (CS2), acetona e sílica fundida. Foi obtida uma concordância muito boa entre os valores medidos para as não linearidades ópticas nestes materiais e os valores estabelecidos na literatura.

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 polaritons sont des quasi-particules bosoniques venant du couplage fort entre des photons de cavité et des excitons confinés dans une hétérostructure semiconductrice. De par leur temps de vie très court et leur très fortes interactions, les polaritons sont un système idéal pour étudier des problèmes fondamentaux d’hydrodynamique quantique hors équilibre ainsi que des aspects plus appliqués d’optique quantique, comme l’implémentation de transistors opto-electroniques ultra-rapides ou la génération d’états non-classiques de la lumière.Ces deux thèmes sont traités dans cette thèse. Dans la première partie j’y dépeins plusieurs méthodes par lesquelles on injecte optiquement un moment angulaire donné dans un superfluide de polaritons, afin d’observer sa nucléation en plusieurs vortex élémentaires. L’impact de la géometrie, du désordre et de l’interaction nonlinéaire de type "polaritonpolariton" sont étudiés. Nous démontrons la conservation du moment angulaire dans le régime stationnaire malgré la nature hors équilibre et ouverte du système. Dans le régime linéaire, un reseau d’interférences contenant des singularités de phase (vortex optiques) est visible. Dans le régime nonlinéaire (superfluide), les interférences disparaissent et des vortex du même signe se forment en conséquence de la conservation du moment angulaire injecté. Enfin, en ajoutant une contrainte sur la géométrie du système nous avons créé de manière controlée un anneau stable de vortex élémentaire du même signe, ce qui pourrait ouvrir la voie à l’étude des interactions inter-vortex dans les fluides quantiques de lumière.Un autre aspect des polaritons sont les propriétés quantiques de la lumière qu’ils émettent. Dans la seconde partie de cette thèse, je décris une source améliorée de lumière comprimée en régime de variables continues dans des micropiliers semiconducteurs en régime de couplage fort. En effet, la génération de lumière comprimée et intriquée est un ingrédient crucial pour l’implémentation de protocoles en information quantique. Dans ce contexte, les matériaux semiconducteurs ont un grand potentiel pour la realization d’éléments sur puce opérant au niveau quantique. Ici, un mélange à quatre ondes dégénérées est obtenu en excitant le micro-pilier à incidence normale. Nous observons un comportement bistable et démontrons la génération de lumière comprimée près du point tournant de la courbe de bistabilité. La nature confinée de la géométrie du piller permet d’atteindre un taux de compression bien supérieur que dans les microcavités planaires, grâce aux niveaux d’énergies discrets protégés des excès de bruits. En analysant le bruit dans la lumière émise par les micro-piliers, nous obtenons une réduction du bruit d’intensité mesurée à 20,3%, et estimée à 35,8% après correction des pertes de détection
Polaritons are bosonic quasiparticles coming from the strong coupling between photons and excitons in a solid-state semiconductor microcavity. Due to their short lifetime and their strong nonlinear interactions, polaritons are an ideal system to study fundamental problems of out-of-equilibrium quantum hydrodynamics as well as more applied problematic in quantum optics, such as the implementation of ultrafast opto-electronic switches or the generation of non-classical states of light.In this thesis the two themes are treated. In the first part of my thesis I will depict several schemes by which we optically inject a controlled angular momentum in a polartion superfluid, in order to observe its nucleation into elementary vortices. The impact of the geometry, disorder, and polariton-polariton nonlinear interactions is studied. We show the conservation of angular momentum in the steady state regime despite the open, out-of-equilibrium nature of the system. In the linear regime, an interference pattern containing phase defects is visible. In the nonlinear(superfluid) regime, the interference disappear and the vortices nucleate as a consequence of the angular momentum conservation. Finally, constraining the geometry we were able to create in a controlled way a stable ring of elementary vortices of the same sign, opening the way to the study of vortex-vortex interactions in quantum fluids of light.A second aspect of polaritons is the quantum properties of their emitted light. In the second part of the manuscript I describe a novel source of continuous-variable squeezed light in pillar-shaped semiconductor microcavities in the strong coupling regime. Indeed, the generation of squeezedand entangled light fields is a crucial ingredient for the implementation of quantum information protocols. In this context, semiconductor materials offer a strong potential for the implementation of on-chip devices operating at the quantum level. Here, degenerate polariton four-wave mixing is obtained by exciting the pillar at normal incidence. We observe a bistable behavior and we demonstrate the generation of squeezing near the turning point of the bistability curve. The confined pillar geometry allows for a larger amount of squeezing than planar microcavities due to the discrete energy levels protected from excess noise. By analyzing the noise of the emitted light we obtain a measured intensity squeezing of 20,3%, inferred to be 35,8% after corrections for losses in the detection setup

Optical microcavities (OMs) are receiving increasing attention owing to their potential applications ranging from cavity quantum electrodynamics, optical detection to photonic devices. Recently, rolled-up structures have been demonstrated as OMs which have gained considerable attention owing to their excellent customizability. To fully exploit this customizability, asymmetric and topological rolled-up OMs are proposed and investigated in addition to conventional rolled-up OMs in this thesis. By doing so, novel phenomena and applications are demonstrated in OMs. The fabrication of conventional rolled-up OMs is presented in details. Then, dynamic mode tuning by a near-field probe is performed on a conventional rolled-up OM. Next, mode splitting in rolled-up OMs is investigated. The effect of single nanoparticles on mode splitting in a rolled-up OM is studied. Because of a non-synchronized oscillating shift for different azimuthal split modes induced by a single nanoparticle at different positions, the position of the nanoparticle can be determined on the rolled-up OM. Moreover, asymmetric rolled-up OMs are fabricated for the purpose of introducing coupling between spin and orbital angular momenta (SOC) of light into OMs. Elliptically polarized modes are observed due to the SOC of light. Modes with an elliptical polarization can also be modeled as coupling between the linearly polarized TE and TM mode in asymmetric rolled-up OMs. Furthermore, by adding a helical geometry to rolled-up structures, Berry phase of light is introduced into OMs. A -π Berry phase is generated for light in topological rolled-up OMs so that modes have a half-integer number of wavelengths. In order to obtain a deeper understanding for existing rolled-up OMs and to develop the new type of rolled-up OMs, complete theoretical models are also presented in this thesis.

Light vehicle rollover accidents on soft surfaces can be modeled assuming constant drag with linear motion equations and other engineering principles. The concept of using segment average results to evaluate roll mechanics parameters throughout a roll sequence, and specifically, segment duration to evaluate vehicle trajectory between ground impacts is developed. The trajectory model is presented, explained and compared to values obtained by analyzing digital video of rollover crash tests. Detailed film analysis procedures are developed to obtain data from rollover crash tests that are not otherwise documented. Elevation of the center of gravity of vehicles is obtained where instrumentation does not explicitly yield this data. Instantaneous center of gravity elevation data throughout a roll sequence provides the opportunity to calculate descend distances as a vehicle travels from one ground contact to another. This data is used to quantify severity of ground impacts as a vehicle interact with the ground throughout a roll sequence. Segment average analysis is a reasonable method for determining general roll mechanics parameters. Because of the chaotic nature of rollover accidents, the range of effective drag factors for a given roll surface may be quite large. Choosing an average of typical drag factors is a reasonable approach for a first-order approximation although certain parameters may be predicted less accurately than if actual values were known. The trajectory results demonstrate the influence of drag factor descent height calculations. Typical constant drag factors tend to overestimate descent height early in a roll sequence and underestimate descent height later in the sequence. The trajectory model is a useful tool to aid in understanding rollover mechanics although a rolling vehicle may be in contact with the ground for a significant fraction of a roll segment. The model should not be used at locations in roll sequences where there are extremes in translational center of gravity decelerations. These extremes include the segments immediately following overturn where there are large angular accelerations and large differences between the tangential velocity of the vehicle perimeter and the translational velocity of the center of gravity, as well as segments that include vehicle impacts with irregular topography.

The work presented in this thesis is centred on the generation of superimposed optical fields which each carry orbital angular momentum (OAM) and the development of OAM measurement techniques. Optical fields which carry OAM have found applications ranging from optical tweezing to quantum cryptography. Due to the fact that they offer a potentially infinite-dimensional state space, much interest has been generated in the measurement of OAM in optical fields, in order for higher-dimensional quantum information processing to be realised. In this study we generate superpositions of higher-order Bessel beams and show that even though we can create a field which carries no overall OAM, we can still witness an angular rotation in the intensity profile of the beam. We also develop two new OAM measurement techniques: (1) a robust odd-even-OAM interferometer and (2) a method to measure the OAM density of an optical field by means of a single spatial light modulator (SLM). In the first chapter we give an overview of the literature regarding optical OAM, followed by the derivation of the Helmholtz wave equation from Maxwell’s equations. We illustrate that helically-phased beams, having a phase factor of exp(ilθ), possess a well-defined OAM. Definitions for the fundamental Gaussian mode, as well as two OAM-carrying modes: Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) modes are also given. Since a majority of this thesis involves generating superimposed OAM fields as well as the measurement of OAM, chapter 2 contains detailed discussions on the optical components used to generate and measure OAM. In section 2.9 we present one of our contributions to the field of OAM-measurement, which involves a stable Dove-prism embedded Mach-Zehnder interferometer, capable of sorting 41 OAM states into odd and even ports with a contrast ranging from 92% to 61%. We implement the Dove prism embedded Mach-Zehnder interferometer to mimic an amplitude damping channel for OAM states in chapter 3. Our device is useful in modelling a ‘lossy’ environment for OAM states. In chapter 4 we develop a new technique for the generation of superimposed Bessel beams through the use of a single digital hologram and theoretically and experimentally show that even though the superimposed Bessel beams can be constructed to produce no overall OAM, a rotation in the beam’s intensity profile is still present, as the field propagates. This rotation is due to the differing longitudinal wave-vectors present in the field and we make quantitative, experimental measurements of the angular rotation rates, which are in very good agreement with our theoretical predictions. We also show that the far-field of these superimposed Bessel beams, exhibit no rotation in their intensity profile and we offer a theoretical explanation for this occurrence. In chapter 5, we adapt our technique for generating superimposed Bessel beams to create non-diffracting speckle fields, which are known to possess optical vortices, and show that by controlling the standard deviation of the phase distribution within the digital hologram, we are able to control the evolution of the non-diffracting speckle field into a non-diffracting zero-order Bessel beam. Our final chapter contains a novel technique for the measurement of the OAM density of optical fields, by implementing two optical components: an SLM and a lens.
Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012.

A theoretical and experimental study of optical vortices and phase singularities has been performed, focusing on generation and control techniques. New devices capable of generating optical vortices have been proposed and manipulation and tuning of the orbital angular momentum of a light beam via linear and nolinear optical processes has been studied and experimentally demonstrated.

The angular momentum of light is a useful resource for many applications. In specific physical architectures it can be considered as the sum of two independent terms, the spin and the orbital components, in analogy to particle systems. The spin angular momentum is related to the polarization of the optical beam, that is the direction of the oscillating electric field, whereas the orbital angular momentum is associated with the spatial distribution of the field. Being independent, spin and orbital angular momenta have been discovered and explored in separate contexts for many years, while only recently it has been considered the possibility to address both quantities on the same beam (or individual photons). The interaction between these two quantities gives rise to complex structures of the electromagnetic field, or to the so called classical entanglement in the domain of single photons. The research presented in this work aimed to show that combining spin and orbital angular momenta in light beams or single photons may be a useful tool for a variety of applications, with particular interest to the case of architectures characterized by spin-orbit interaction. This concept was made concrete through the design and the realization of several experiments, in the framework of singular optics, foundations of quantum mechanics, quantum information theory and quantum simulation.

碩士
國立成功大學
光電科學與工程學系
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When the electron beam passes through the grating structure, the surface plasma is radiated, and changing the period of the grating changes the radiation angle. Using this mechanism, we designed periodic gratings to be arranged along a circle, with an electron beam with electron cyclotron motion passing under the structure to radiate an orbital angular momentum beam. By fixing the electron beam energy to change the number of gratings and the number of fixed gratings to change the energy of the electron beam, orbital angular momentum beams with different topological charges can be obtained, and the phase distribution can be observed. This paper mainly discusses a new method for generating orbital angular momentum. Due to its unique phase pattern and physical properties, it is widely used in optical tweezers, optical communication systems, and quantum communication.

Imaging at the nanoscale and/or at remote locations holds great promise for studies in fields as disparate as the life sciences and materials sciences. One such microscopy technique, stimulated emission depletion (STED) microscopy, is one of several fluorescence based imaging techniques that offers resolution beyond the diffraction-limit. All current implementations of STED microscopy, however, involve the use of free-space beam shaping devices to achieve the Gaussian- and donut-shaped Orbital Angular Momentum (OAM) carrying beams at the desired colors –-- a challenging prospect from the standpoint of device assembly and mechanical stability during operation. A fiber-based solution could address these engineering challenges, and perhaps more interestingly, it may facilitate endoscopic implementation of in vivo STED imaging, a prospect that has thus far not been realized because optical fibers were previously considered to be incapable of transmitting the OAM beams that are necessary for STED. In this thesis, we investigate fiber-based STED systems to enable endoscopic nanoscale imaging. We discuss the design and characteristics of a novel class of fibers supporting and stably propagating Gaussian and OAM modes. Optimization of the design parameters leads to stable excitation and depletion beams propagating in the same fiber in the visible spectral range, for the first time, with high efficiency (>99%) and mode purity (>98%). Using the fabricated vortex fiber, we demonstrate an all-fiber STED system with modes that are tolerant to perturbations, and we obtain naturally self-aligned PSFs for the excitation and depletion beams. Initial experiments of STED imaging using our device yields a 4-fold improvement in lateral resolution compared to confocal imaging. In an experiment in parallel, we show the means of using q-plates as free-space mode converters that yield alignment tolerant STED microscopy systems at wavelengths covering the entire visible spectrum, and hence dyes of interest in such imaging schematics. Our study indicates that the vortex fiber is capable of providing an all-fiber platform for STED systems, and for other imaging systems where the exploitation of spatio-spectral beam shaping is required.

Optical microcavities (OMs) are receiving increasing attention owing to their potential applications ranging from cavity quantum electrodynamics, optical detection to photonic devices. Recently, rolled-up structures have been demonstrated as OMs which have gained considerable attention owing to their excellent customizability. To fully exploit this customizability, asymmetric and topological rolled-up OMs are proposed and investigated in addition to conventional rolled-up OMs in this thesis. By doing so, novel phenomena and applications are demonstrated in OMs. The fabrication of conventional rolled-up OMs is presented in details. Then, dynamic mode tuning by a near-field probe is performed on a conventional rolled-up OM. Next, mode splitting in rolled-up OMs is investigated. The effect of single nanoparticles on mode splitting in a rolled-up OM is studied. Because of a non-synchronized oscillating shift for different azimuthal split modes induced by a single nanoparticle at different positions, the position of the nanoparticle can be determined on the rolled-up OM. Moreover, asymmetric rolled-up OMs are fabricated for the purpose of introducing coupling between spin and orbital angular momenta (SOC) of light into OMs. Elliptically polarized modes are observed due to the SOC of light. Modes with an elliptical polarization can also be modeled as coupling between the linearly polarized TE and TM mode in asymmetric rolled-up OMs. Furthermore, by adding a helical geometry to rolled-up structures, Berry phase of light is introduced into OMs. A -π Berry phase is generated for light in topological rolled-up OMs so that modes have a half-integer number of wavelengths. In order to obtain a deeper understanding for existing rolled-up OMs and to develop the new type of rolled-up OMs, complete theoretical models are also presented in this thesis.