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.

Chirality is a nuclear symmetry which is suggested to occur in nuclei when the total angular momentum of the system has an aplanar orientation [Fra97, Fra01]. It can occur for nuclei with triaxial shape, which have valence protons and neutrons with predominantly particle and hole nature. It is expected that the angular momenta of an odd particle and an odd hole (both occupying high-j orbitals) are aligned predominantly along the short and the long axes of the nucleus respectively, whereas the collective rotation occurs predominantly around the intermediate axis of a triaxially deformed nucleus in order to minimize the total energy of the system. Such symmetry is expected to be exhibited by a pair of degenerate DI = 1 rotational bands, i.e. all properties of the partner bands should be identical. The results suggested that spin independence of the energy staggering parameter S(I ) within two-quasiparticle chiral bands (previously suggested a fingerprint of chirality) is found only if the Coriolis interaction can be completely neglected. However, if the configuration is nonrestricted, the Coriolis interaction is often strong enough to create considerable energy staggering. It was also found that staggering in the intra- and inter-band B(M1) reduced transition probabilities (proposed as another fingerprint of chirality) may be a result of effects other than strongly broken chirality. Therefore, the use of the B(M1) staggering as a fingerprint of strongly broken chiral symmetry seems rather risky, in particular if the phase of the staggering is not checked.

Nearfield Acoustical Holography (NAH) is an acoustic field visualization technique that can be used to reconstruct three-dimensional (3-D) acoustic fields by projecting two-dimensional (2-D) data measured on a hologram surface. However, linear NAH algorithms developed and improved by many researchers can result in significant reconstruction errors when they are applied to reconstruct 3-D acoustic fields that are radiated from a high-level noise source and include significant nonlinear components. Here, planar, nonlinear acoustical holography procedures are developed that can be used to reconstruct 3-D, nonlinear acoustic fields radiated from a high-level noise source based on 2-D acoustic pressure data measured on a hologram surface. The first nonlinear acoustic holography procedure is derived for reconstructing steady-state acoustic pressure fields by applying perturbation and renormalization methods to nonlinear, dissipative, pressure-based Westervelt Wave Equation (WWE). The nonlinear acoustic pressure fields radiated from a high-level pulsating sphere and an infinite-size, vibrating panel are used to validate this procedure. Although the WWE-based algorithm is successfully validated by those two numerical simulations, it still has several limitations: (1) Only the fundamental frequency and its second harmonic nonlinear components can be reconstructed; (2) the application of this algorithm is limited to mono-frequency source cases; (3) the effects of bent wave rays caused by transverse particle velocities are not included; (4) only acoustic pressure fields can be reconstructed. In order to address the limitations of the steady-state, WWE-based procedure, a transient, planar, nonlinear acoustic holography algorithm is developed that can be used to reconstruct 3-D nonlinear acoustic pressure and particle velocity fields. This procedure is based on Kuznetsov Wave Equation (KWE) that is directly solved by using temporal and spatial Fourier Transforms. When compared to the WWE-based procedure, the KWE-based procedure can be applied to multi-frequency source cases where each frequency component can contain both linear and nonlinear components. The effects of nonlinear bent wave rays can be also considered by using this algorithm. The KWE-based procedure is validated by conducting an experiment with a compression driver and four numerical simulations. The numerical and experimental results show that holographically-projected acoustic fields match well with directly-calculated and directly-measured fields.

Magnetic resonance imaging (MRI) has long become one of the most powerful and accurate tools of medical diagnostic imaging. Central to the diagnostic capabilities of MRI is the notion of contrast, which is determined by the biochemical composition of examined tissue as well as by its morphology. Despite the importance of the prevalent T₁, T₂, and proton density contrast mechanisms to clinical diagnosis, none of them has demonstrated effectiveness in delineating the morphological structure of the white matter - the information which is known to be related to a wide spectrum of brain-related disorders. It is only with the recent advent of diffusion-weighted MRI that scientists have been able to perform quantitative measurements of the diffusivity of white matter, making possible the structural delineation of neural fibre tracts in the human brain. One diffusion imaging technique in particular, namely high angular resolution diffusion imaging (HARDI), has inspired a substantial number of processing methods capable of obtaining the orientational information of multiple fibres within a single voxel while boasting minimal acquisition requirements. HARDI characterization of fibre morphology can be enhanced by increasing spatial and angular resolutions. However, doing so drastically reduces the signal-to-noise ratio. Since pronounced measurement noise tends to obscure and distort diagnostically relevant details of diffusion-weighted MR signals, increasing spatial or angular resolution necessitates application of the efficient and reliable tools of image denoising. The aim of this work is to develop an effective framework for the filtering of HARDI measurement noise which takes into account both the manifold to which the HARDI signal belongs and the statistical nature of MRI noise. These goals are accomplished using an approach rooted in non-local means (NLM) weighted averaging. The average includes samples, and therefore dependencies, from the entire manifold and the result of the average is used to deduce an estimate of the original signal value in accordance with MRI statistics. NLM averaging weights are determined adaptively based on a neighbourhood similarity measure. The novel neighbourhood comparison proposed in this thesis is one of spherical neighbourhoods, which assigns large weights to samples with similar local orientational diffusion characteristics. Moreover, the weights are designed to be invariant to both spatial rotations as well as to the particular sampling scheme in use. This thesis provides a detailed description of the proposed filtering procedure as well as experimental results with synthetic and real-life data. It is demonstrated that the proposed filter has substantially better denoising capabilities as compared to a number of alternative methods.

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.

Thesis; Thesis information not provided; 1 Feb 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-39" "DOE/ER/40150-2763" Silvia Niccolai. 02/01/2003. Report is also available in paper and microfiche from NTIS.

Thesis (Ph.D.); Submitted to the Massachusetts Inst. of Tech., Cambridge, MA (US); 1 Oct 2003. / Published through the Information Bridge: DOE Scientific and Technical Information. "JLAB-PHY-03-174" "DOE/ER/40150-2571" Zhengwei Chai. 10/01/2003. Report is also available in paper and microfiche from NTIS.

Thesis (M.S.)--Miami University, Dept. of Physics, 2005. / Title from first page of PDF document. Document formatted into pages; contains [1], vii, 55 p. : ill. Includes bibliographical references (p. 53-55).

Made available in DSpace on 2014-10-09T12:43:31Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:05Z (GMT). No. of bitstreams: 1 06635.pdf: 4560564 bytes, checksum: 677cab6b14a66c0989ef5859a83679e3 (MD5) / Dissertacao (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP

Made available in DSpace on 2014-10-09T12:37:09Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T13:56:46Z (GMT). No. of bitstreams: 1 01909.pdf: 4337748 bytes, checksum: 86acf59a272732a64c336ea3408816ec (MD5) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN/CNEN-SP