The growth of data capacity in optical communications links, which form the critical backbone of the modern internet, is facing a slowdown due to fundamental nonlinear limitations, leading to an impending "capacity crunch" on the horizon. Current technology has already exhausted degrees of freedom such as wavelength, amplitude, phase and polarization, leaving spatial multiplexing as the last available dimension to be efficiently exploited. To minimize the significant energy requirements associated with digital signal processing, it is critical to explore the upper limit of unmixed spatial channels in an optical fiber, which necessitates ideally packing spatial channels either in real space or in momentum space. The former strategy is realized by uncoupled multi-core fibers whose channel count has already saturated due to reliability constraint limiting fiber sizes. The later strategy is realized by the unmixed multimode fiber whose high spatial efficiency suggest the possibility of high channel-count scalability but the right subset of mode ought to be selected in order to mitigate mode coupling that is ever-present due to the plethora of perturbations a fiber normally experiences. The azimuthal modes in ring-core fibers turn out to be one of the most spatially efficient in this regard, by exploiting light’s orbital angular momentum (OAM). Unmixed mode counts have reached 12 in a ~1km fiber and 24 in a ~10m fiber. However, there is a fundamental bottleneck for scalability of conventionally bound modes and their relatively high crosstalks restricts their utility to device length applications. In this thesis, we provide a fundamental solution to further fuel the unmixed-channel count in an MMF. We utilize the phenomenon of topological confinement, which is a regime of light guidance beyond conventional cutoff that has, to the best of our knowledge, never been demonstrated till publications based on the subject matter of this thesis. In this regime, light is guided by the centrifugal barrier created by light’s OAM itself rather than conventional total internal reflection arising from the index inhomogeneity of the fiber. The loss of these topologically confined modes (TCMs) decreases down to negligible levels by increasing the OAM of fiber modes, because the centrifugal barrier that keeps photons confined to a fiber core increases with the OAM value of the mode. This leads to low-loss transmission in a km-scale fiber of these cutoff modes. Crucially, the mode-dependent confinement loss of TCMs further lifts the degeneracy of wavevectors in the complex space, leading to frustration of phase-matched coupling. This thus allows further scaling the mode count that was previously hindered by degenerate mode coupling in conventionally bound fiber modes. The frustrated coupling of TCMs thus enables a record amount of unmixed OAM modes in any type of fiber that features a high index contrast, whether specially structured as a ring-core, or simply constructed as a step-index fiber. Using all these favorable attributes, we achieve up to 50 low-loss modes with record low crosstalk (approaching -45 dB/km) over a 130-nm bandwidth in a ~1km-long ring-core fiber. The TCM effect promises to be inherently scalable, suggesting that even higher modes counts can be obtained in the future using this design methodology. Hence, the use of TCMs promises breaking the record spectral efficiency, potentially making it the choice for transmission links in future Space-Division-Multiplexing systems. Apart from their chief attribute of significantly increasing the information content per photon for quantum or classical networks, we expect that this new light guidance may find other applications such as in nonlinear signal processing and light-matter interactions.

The physical-layer security of a line-of-sight (LOS) free-space optical (FSO) link using orbital angular momentum (OAM) multiplexing is studied. We discuss the effect of atmospheric turbulence to OAM-multiplexed FSO channels. We numerically simulate the propagation of OAM-multiplexed beam and study the secrecy capacity. We show that, under certain conditions, the OAM multiplexing technique provides higher security over a single-mode transmission channel in terms of the total secrecy capacity and the probability of achieving a secure communication. We also study the power cost effect at the transmitter side for both fixed system power and equal channel power scenarios.

Made available in DSpace on 2015-05-14T12:14:08Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1944924 bytes, checksum: e08f0978e6406af124c9fe4875d2aa1e (MD5) Previous issue date: 2013-06-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / 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.

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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.

To address key challenges for both quantum communication and quantum computing applications in a simultaneous manner, we propose to employ the photon angular momentum approach by invoking the well-known fact that photons carry both the spin angular momentum (SAM) and the orbital angular momentum (OAM). SAM is associated with polarization, while OAM is associated with azimuthal phase dependence of the complex electric field. Given that OAM eigenstates are mutually orthogonal, in principle, an arbitrary number of bits per single photon can be transmitted. The ability to generate/analyze states with different photon angular momentum, by using either holographic or interferometric methods, allows the realization of quantum states in multidimensional Hilbert space. Because OAM states provide an infinite basis state, while SAM states are 2-D only, the OAM can also be used to increase the security for quantum key distribution (QKD) applications and improve computational power for quantum computing applications. The goal of this paper is to describe photon angular momentum based deterministic universal quantum qudit gates, namely, {generalized-X, generalized-Z, generalized-CNOT} qudit gates, and different quantum modules of importance for various applications, including (fault-tolerant) quantum computing, teleportation, QKD, and quantum error correction. For instance, the basic quantum modules for quantum teleportation applications include the generalized-Bell-state generation module and the QFT-module. The basic quantum module for quantum error correction and fault-tolerant computing is the nonbinary syndrome calculator module. The basic module for entanglement assisted QKD is either the generalized-Bell-state generation module or the Weyl-operator-module. The possibility of implementing all these modules in integrated optics is discussed as well. Finally, we provide security analysis of entanglement assisted multidimensional QKD protocols, employing the proposed qudit modules, by taking into account the imperfect generation of OAM modes.

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.

In ground based high frequency (HF) radio pumping experiments, absorption of ordinary (O) mode pump waves energises the ionospheric plasma, producing optical emissions and other effects. Pump-induced or natural kilometre-scale field-aligned density depletions are believed to play a role in self-focussing phenomena such as the magnetic zenith (MZ) effect, i.e., the increased plasma response observed in the direction of Earth's magnetic field. Using ray tracing, we study the propagation of ordinary (O) mode HF radio waves in an ionosphere modified by density depletions, with special attention to transmission through the radio window (RW), where O mode waves convert into the extraordinary (X, or Z) mode. The depletions are shown to shift the position of the RW, or to introduce RWs at new locations. In a simplified model neglecting absorption, we estimate the wave electric field strength perpendicular to the magnetic field at altitudes normally inaccessible. This field could excite upper hybrid waves on small scale density perturbations. We also show how transmission and focussing combine to give stronger fields in some directions, notably at angles close to the MZ, with possible implications for the MZ effect. In a separate study, we consider electromagnetic (e-m) beams with helical wavefronts (i.e., twisted beams), which are associated with orbital angular momentum (OAM). By applying geometrical optics to each plane wave component of a twisted nonparaxial e-m Bessel beam, we calculate analytically the shift of the beam's centre of gravity during propagation perpendicularly and obliquely to a weak refractive index gradient in an isotropic medium. In addition to the so-called Hall shifts expected from paraxial theory, the nonparaxial treatment reveals new shifts in both the transverse and lateral directions. In some situations, the new shifts should be significant also for nearly paraxial beams.

We present the theory of orbital angular momentum of light (MAO), based on the basic concepts of electromagnetism, as well as some techniques from generation and characterization of light beams possessing MAO. We also present non-linear optical processes of parametric conversion spontaneous descendant (CPD) and stimulated (CPDE). We reviewed the problem of conservation of MAO in CPD in the scheme does not collinear, describing States of using Laguerre-Gauss beams MAO. We extend this study to the case in which Bessel beams are used to describe the States of MAO. Our results show that rape occurs on conservation law of MAO, which is attributed to deformation of the angular spectrum of beam pumping (pump) transferred to the twin photons. However, this violation can be advantageous because through breach of MAO have access to entangled States of dimension greater than those generated with collinear geometry. As an alternative to the note of the violation of the law of conservation in parametric down conversion process we proposed an experiment based on CPDE, where the experimental implementation is simpler. Using MAO as target and polarization qubit as qubit control, we experimentally a alternative to optical circuit proposal for Li-Ping et al. [16] for the implementation of the logic gate C-NOT. Also we present an application of logic gate C-NOT for the generation of entangled States of a single photon, which can be implemented with our optical circuit. The generation of entangled States, multidimensional, and the implementation quantum logic gates are important for the areas of information and quantum computation. / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresentamos a teoria do momento angular orbital da luz (MAO), baseada nos conceitos básicos do eletromagnetismo, bem como algumas técnicas de geração e caracterização de feixes de luz possuindo MAO. Apresentamos também os processos ópticos não lineares de conversão paramétrica descendente espontânea (CPD) e estimulada (CPDE). Revisamos o problema da conservação do MAO na CPD no regime não colinear, descrevendo os estados de MAO utilizando feixes Laguerre-Gauss. Extendemos este estudo para o caso em que feixes Bessel são usados para descrever os estados de MAO. Nossos resultados mostram que ocorre violação na lei de conservação do MAO, que é atribuída a deformação do espectro angular do feixe de bombeamento (pump) transferido para os fótons gêmeos. Entretanto, esta violação pode ser vantajosa, pois através da violação do MAO conseguimos ter acesso a estados emaranhados de dimensão maior do que aqueles gerados com geometria colinear. Como alternativa para a observação da violação da lei de conservação no processo de conversão paramétrica descendente, propusemos um experimento baseado na CPDE, onde a realização experimental é mais simples. Utilizando o MAO como qubit alvo e a polarização como qubit controle, realizamos experimentalmente um circuito ótico alternativo à proposta de Li-Ping e colaboradores [16] para a implementação da porta lógica C-NOT. Também apresentamos uma aplicação da porta lógica C-NOT para a geração de estados emaranhados de um único fóton, que pode ser implementada com nosso circuito ótico. A geração de estados emaranhados multidimensionais e a implementaçãode portas lógicas quânticas são importantes para as áreas de informação e computação quântica.