Mathematics and Algorithms in Tomography

This was the ninth Oberwolfach conference on the mathematics of tomography. Modalities represented at the workshop included X-ray tomography, radar, seismic imaging, ultrasound, electron microscopy, impedance imaging, photoacoustic tomography, elastography, emission tomography, X-ray CT, and vector tomography along with a wide range of mathematical analysis

Mathematical Methods in Tomography

This is the seventh Oberwolfach conference on the mathematics of tomography, the first one taking place in 1980. Tomography is the most popular of a series of medical and scientific imaging techniques that have been developed since the mid seventies of the last century

Coupling of Light\u27s Orbital Angular Momentum to a Quantum Dot Ensemble

We theoretically and experimentally investigate the transfer of orbital angular momentum from light to an ensemble of semiconductor-based nanostructures composed of lead sulfide quantum dots. Using an ensemble of quantum dots offers a higher cross-section and more absorption of twisted light fields compared to experimentally challenging single-nanostructure measurements. However, each quantum dot (except for on-center) sees a displaced light beam parallel to its own axis of symmetry. The transition matrix elements for the light-matter interaction are calculated by expressing the displaced light beam in terms of the appropriate light field centered on the nanoparticles. The resulting transition rate induced by light\u27s orbital angular momentum depends on the nanostructure size, the displacement between the beam center and nanostructure axis, and the ratio of the nanostructure size to the beam waist. In addition, while the strength of the transitions induced by twisted light is much weaker than those induced by plane waves for the center case, they are almost identical when conceding illuminating an ensemble of nanostructures. Although we attempted to measure this transfer of orbital angular momentum, due to experimental limitations the transfer remained undetectable

Control of Spontanous Emission from Quantum Emitters Using Hyperbolic Metamaterial Substrates

Hyperbolic metamaterials (HMMs) are so named for possessing a hyperboloid-shaped dispersion which gives rise to a large photonic density of states. Quantum emitters placed inside or in the near-field of a HMM have been shown to exhibit strong enhancement of spontaneous emission due to the increase in available states. This thesis focuses on enhancing spontaneous emission of quantum emitters in optical frequencies by utilizing multilayered metal/dielectric composites that form these highly anisotropic metamaterials. In conjunction with the enhanced decay rate we experimentally demonstrate two methods for shaping and directing radiation trapped in the HMM into free space by employing a new class of artificial photonic media which we term a photonic hypercrystal. The ability to significantly enhance the spontaneous emission rate and control the directionality paves the way to practical applications using hyperbolic metamaterials such as sub-wavelength lasers, single-photon sources, and ultrafast light emitting diodes

Dispersion of Single-Walled Carbon Nanotubes in Organic Solvents

This thesis contains a systematic study of the dispersion of pristine HiPco Single Walled Carbon Nanotubes (SWNTs) in a series of organic solvents. A double beamed UV-Vis-NIR absorption spectrometer coupled with an integrating sphere was employed to demonstrate the dispersibility of SWNTs in different solvents. Raman Spectroscopy and Atomic Force Microscopy (AFM) were used to confirm the debundling and exfoliation of SWNTs aggregates. An investigation of the solubility of SWNTs in four chlorinated aromatic solvents demonstrated that the similarity in structure between solvent molecules and nanotube sidewall is not a dominant factor to obtain stable SWNT solutions. A comparative study of the solubility of SWNTs between the aromatic solvents and other reported solvents was then conducted, in terms of the solvent solubility parameters, including Hildebrand and Hansen solubility parameters. Although the established correlation between extinction/absorption coefficients as a function of Hildebrand/Hansen solubility parameters indicated there may be a selective debundling of metallic and semiconducting SWNTs in different solvents, this was not confirmed by a detailed Raman investigation. A further study of the dispersion limit of SWNTs in different solvents as a function of the solvent solubility parameters was carried out. Good agreement with literature is demonstrated here in terms of Hildebrand parameters, but not in terms of the Hansen solubility parameters. It has been demonstrated that the degree of dispersion is critically dependent on sample preparation conditions, in particular sonication. Finally, the effect of sonication parameters and solvent properties during the dispersion of SWNTs was investigated. The results indicated that the sonication process is closely dependent on many of the physical parameters of the solvent, including vapour pressure, viscosity, surface tension, density and molecular weight. Longer sonication time and higher sonication power help debundling SWNTs in organic solvents but significantly damage the nanotubes. The choice of solvent should be guided by minimisation of sonication requirements

Engineering photonic and plasmonic light emission enhancement

Thesis (Ph.D.)--Boston UniversitySemiconductor photonic devices are a rapidly maturing technology which currently occupy multi-billion dollar markets in the areas of LED lighting and optical data communication. LEDs currently demonstrate the highest luminous efficiency of any light source for general lighting. Long-haul optical data communication currently forms the backbone of the global communication network. Proper design of light management is required for photonic devices, which can increase the overall efficiency or add new device functionality. In this thesis, novel methods for the control of light propagation and confinement are developed for the use in integrated photonic devices. The first part of this work focuses on the engineering of field confinement within deep subwavelength plasmonic resonators for the enhancement of light-matter interaction. In this section, plasmonic ring nanocavities are shown to form gap plasmon modes confined to the dielectric region between two metal layers. The scattering properties, near-field enhancement and photonic density of states of nanocavity devices are studied using analytic theory and 3D finite difference time domain simulations. Plasmonic ring nanocavities are fabricated and characterized using photoluminescence intensity and decay rate measurements. A 25 times increase in the radiative decay rate of Er:Si02 is demonstrated in nanocavities where light is confined to volumes as small as 0.01(λ/n)^3 . The potential to achieve lasing, due to the enhancement of stimulated emission rate in ring nanocavities, is studied as a route to Si-compatible plasmon-enhanced nanolasers. The second part of this work focuses on the manipulation of light generated in planar semiconductor devices using arrays of dielectric nanopillars. In particular, aperiodic arrays of nanopillars are engineered for omnidirectional light extraction enhancement. Arrays of Er:SiNx nanopillars are fabricated and a ten times increase in light extraction is experimentally demonstrated, while simultaneously controlling far-field radiation patterns in ways not possible with periodic arrays. Additionally, analytical scalar diffraction theory is used to study light propagation from Vogel spiral arrays and demonstrate generation of OAM. Using phase shifting interferometry, the presence of OAM is experimentally verified. The use of Vogel spirals presents a new method for the generation of OAM with applications for secure optical communications

CHEMICAL FUNCTIONALIZATION OF CARBON NANOTUBES FOR CONTROLLED OPTICAL, ELECTRICAL AND DISPERSION PROPERTIES

A carbon nanotube is a graphitic sheet, rolled into a one-dimensional, hollow tube. This structure provides certain individual nanotubes with high conductivity and near-infrared optical activity. These properties are not necessarily translated at the macroscale, however, due to strong van der Waals attractive forces that determine the behavior at the bulk level - exemplified by aggregation of nanotubes into bundles with significantly attenuated functionality. Different methods of carbon nanotube covalent functionalization are studied to improve dispersion while simultaneously maintaining intrinsic electrical and optical properties. In addition to retention of known behavior, new carbon nanotube photoluminescence pathways are also revealed as a result of this same covalent functionalization strategy. With various wet chemistries, including super-acid oxidation, the Billups-Birch reaction, and various diazonium based reactions, that utilize strong reducing or oxidizing conditions to spontaneously exfoliate aggregated carbon nanotubes, we are able to covalently functionalize individually dispersed nanotubes in a highly scalable manner. Covalent addition to the nanotube sidewalls converts the native sp2 hybridized carbon atoms to sp3 hybridization, which helps disrupt inter-tube van der Waals forces. However, this change in hybridization also perturbs the carbon nanotube electronic structure, resulting in an undesired loss of electrical conductivity and optical activity. We observe that controlling the location of functionalization, such as to the outer-walls of double-walled carbon nanotubes or as discrete functional "bands," we avert the loss of desirable properties by leaving significant tracts of sp2 carbon atoms unperturbed. We also demonstrate that such functional groups can act as electron and hole traps through the creation of a potential well deviation in the carbon nanotube electronic structure. This defect-activated carrier trapping primes the formation of charged excitons (trions) which are observed as redshifted photoluminescence in the near-infrared region. Implications and impacts of these covalent functionalization strategies will be discussed

Transfer of tilted sample information in transmission electron microscopy

When a transmission electron microscope is used in imaging mode, information carried by the sample function is transformed by the optics of the instrument during the imaging process. A mathematical description of this physical process (the so-called imaging function) is a requirement for an accurate analysis and the interpretation of electron microscopy experimental data. When the sample is not imaged in tilted geometry (no defocus gradient is present across its extent), the imaging function has a well-known and extensively studied form : the Contrast Transfer Function (CTF) (Reimer, 1997). Several electron microscopy techniques, however, require the sample to be tilted to fully explore its 3-dimensional structure. Only recently a rigorous mathematical description for the imaging process under these conditions, derived from physical first principles, has been made available: the Tilted Contrast Imaging Function (TCIF) (Philippsen et al., 2006). The present work discusses in depth the nature and the characteristics of the TCIF model, expanding it to include astigmatism. A robust and efficient software implementation is presented, developed with the context of the IPLT software development framework (Philippsen et al., 2007). Computer simulations of images of tilted samples are then used to qualitatively and quantitatively analyze features of experimental images. No computationally-feasible analytical method for the inversion of the TCIF model is currently available, and its effects on experimental images are usually corrected using a number of heuristic methods that involve some approximations of the imaging parameters. Using computer simulations of tilted images, this work estimates the errors introduced by these approximations, and suggests optimal correction strategies for electron tomography and crystallography imaging conditions. Furthermore, this work describes possible approaches for the determination of the imaging parameters through the analysis of the experimental images, and for a non-analytical inversion of the effects of the TCIF model, showing preliminary results of their implementation applied to computer simulated-images. References: Reimer, L. (1997). Transmission Electron Microscopy. Physics of Image Formation and Microanalysis. Springer-Verlag GmbH, 4. A. edition. Philippsen, A., Engel, H. and Engel, A. (2006). The contrast-imaging function for tilted specimens. Ultramicroscopy, 107(2-3):202–12. Philippsen, A., Schenk, A. D., Signorell, G. A., Mariani, V. and Berneche, S.et al. (2007). Collaborative EM image processing with the IPLT image processing library and toolbox. Journal of Structural Biology, 157(1):28–37