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Pages
- Title
- Electrical Conductivity Imaging via Boundary Value Problems for the 1-Laplacian.
- Creator
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Veras, Johann, Tamasan, Alexandru, Mohapatra, Ram, Nashed, M, Dogariu, Aristide, University of Central Florida
- Abstract / Description
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We study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity...
Show moreWe study an inverse problem which seeks to image the internal conductivity map of a body by one measurement of boundary and interior data. In our study the interior data is the magnitude of the current density induced by electrodes. Access to interior measurements has been made possible since the work of M. Joy et al. in early 1990s and couples two physical principles: electromagnetics and magnetic resonance. In 2007 Nachman et al. has shown that it is possible to recover the conductivity from the magnitude of one current density field inside. The method now known as Current Density Impedance Imaging is based on solving boundary value problems for the 1-Laplacian in an appropriate Riemann metric space. We consider two types of methods: the ones based on level sets and a variational approach, which aim to solve specific boundary value problem associated with the 1-Laplacian. We will address the Cauchy and Dirichlet problems with full and partial data, and also the Complete Electrode Model (CEM). The latter model is known to describe most accurately the voltage potential distribution in a conductive body, while taking into account the transition of current from the electrode to the body. For the CEM the problem is non-unique. We characterize the non-uniqueness, and explain which additional measurements fix the solution. Multiple numerical schemes for each of the methods are implemented to demonstrate the computational feasibility.
Show less - Date Issued
- 2014
- Identifier
- CFE0005437, ucf:50388
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005437
- Title
- Inverse Problems in Multiple Light Scattering.
- Creator
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Broky, John, Dogariu, Aristide, Christodoulides, Demetrios, Wu, Shintson, Tamasan, Alexandru, University of Central Florida
- Abstract / Description
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The interaction between coherent waves and material systems with complex optical properties is a complicated, deterministic process. Light that scatters from such media gives rise to random fields with intricate properties. It is common perception that the randomness of these complex fields is undesired and therefore is to be removed, usually through a process of ensemble averaging. However, random fields emerging from light matter interaction contain information about the properties of the...
Show moreThe interaction between coherent waves and material systems with complex optical properties is a complicated, deterministic process. Light that scatters from such media gives rise to random fields with intricate properties. It is common perception that the randomness of these complex fields is undesired and therefore is to be removed, usually through a process of ensemble averaging. However, random fields emerging from light matter interaction contain information about the properties of the medium and a thorough analysis of the scattered light allows solving specific inverse problems. Traditional attempts to solve these kinds of inverse problems tend to rely on statistical average quantities and ignore the deterministic interaction between the optical field and the scattering structure. Thus, because ensemble averaging inherently destroys specific characteristics of random processes, one can only recover limited information about the medium. This dissertation discusses practical means that go beyond ensemble averaging to probe complex media and extract additional information about a random scattering system. The dissertation discusses cases in which media with similar average properties can be differentiated by detailed examination of fluctuations between different realizations of the random process of multiple scattering. As a different approach to this type of inverse problems, the dissertation also includes a description of how higher-order field and polarization correlations can be used to extract features of random media and complex systems from one single realization of the light-matter interaction. Examples include (i) determining the level of multiple scattering, (ii) identifying non-stationarities in random fields, and (iii) extracting underlying correlation lengths of random electromagnetic fields that result from basic interferences. The new approaches introduced and the demonstrations described in this dissertation represent practical means to extract important material properties or to discriminate between media with similar characteristics even in situations when experimental constraints limit the number of realizations of the complex light-matter interaction.
Show less - Date Issued
- 2012
- Identifier
- CFE0004656, ucf:49888
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0004656
- Title
- Multimaterial Fibers and Tapers A Platform for Nonlinear Photonics and Nanotechnology.
- Creator
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Shabahang, Soroush, Abouraddy, Ayman, Vanstryland, Eric, Dogariu, Aristide, Belfield, Kevin, University of Central Florida
- Abstract / Description
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The development of optical sources and components suitable for the mid-infrared is crucial for applications in this spectral range to reach the maturity level of their counterparts in the visible and near-infrared spectral regimes. The recent commercialization of quantum cascade lasers is leading to further interest in this spectral range. Wideband mid-infrared coherent sources, such as supercontinuum generation, have yet to be fully developed. A mid-infrared supercontinuum source would allow...
Show moreThe development of optical sources and components suitable for the mid-infrared is crucial for applications in this spectral range to reach the maturity level of their counterparts in the visible and near-infrared spectral regimes. The recent commercialization of quantum cascade lasers is leading to further interest in this spectral range. Wideband mid-infrared coherent sources, such as supercontinuum generation, have yet to be fully developed. A mid-infrared supercontinuum source would allow for unique applications in spectroscopy and sensing.Over the last decade, it has been shown that high-index confinement in highly nonlinear fibers pumped with high-peak-power pulses is an excellent approach to supercontinuum generation in the visible and near-infrared. Nonlinear waveguides such as fibers offer an obvious advantage in increasing the nonlinear interaction length maintained with a small cross section. In addition, fiber systems do not require optical alignment and are mechanically stable and robust with respect to the environmental changes. These properties have made fiber systems unique in applications where they are implemented in a harsh and unstable environment.In extending this approach into the mid-infrared, I have used chalcogenide glass fibers. Chalcogenide glasses have several attractive features for this application: they have high refractive indices for high optical-confinement, have a wide transparency window in the mid-infrared, and have a few orders-of-magnitude higher nonlinearity than silica glass and other mid-IR glasses. Producing chalcogenide glass fiber tapers offer, furthermore, the possibility of dispersion control and stronger field confinement and hence higher nonlinearity, desired for supercontinuum generation.
Show less - Date Issued
- 2014
- Identifier
- CFE0005252, ucf:50594
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005252
- Title
- Hole selective tunneling oxide applications with insight into sophisticated characterization techniques.
- Creator
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Ogutman, Nizamettin Kortan, Schoenfeld, Winston, Sundaram, Kalpathy, Batarseh, Issa, Davis, Kristopher, Dogariu, Aristide, University of Central Florida
- Abstract / Description
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Tunneling metal oxide layers combined with industrially applicable novel cleaning methods can boost the current efficiency limit, which corresponds to approximately %22 in production, of crystalline silicon (c-Si) solar cells. Within the scope of this dissertation, extremely thin tunneling layers (1-3nm) of aluminum oxide is studied in conjunction with the development of wet cleaning procedures that are feasible in production lines currently exist today. These tunneling stacks are deployed to...
Show moreTunneling metal oxide layers combined with industrially applicable novel cleaning methods can boost the current efficiency limit, which corresponds to approximately %22 in production, of crystalline silicon (c-Si) solar cells. Within the scope of this dissertation, extremely thin tunneling layers (1-3nm) of aluminum oxide is studied in conjunction with the development of wet cleaning procedures that are feasible in production lines currently exist today. These tunneling stacks are deployed to serve as exceptional surface passivation layers due to the inherent built-in charge provided by aluminum oxide. This capability is further strengthened by the introduction of extremely well controlled wet chemical oxide which not only saturates the dangling bonds at the interface but also enables conformal growth of the aforementioned tunneling oxide layers. Therefore, the interplay between aluminum oxide thickness, which effects the passivation quality tremendously, and carrier extraction capability (contact resistance) is also taken into account by the choice of ultimate boron doping profile and the optimization of the cleaning procedure. The resulting hole collecting surface passivation stack applied on doped surfaces provided record values of recombination current densities, with highly applicable contact resistivity values, enabling one-dimensional carrier transport. This dissertation is also concerned with spatially resolved characterization methods of such industrial c-Si solar cells given the importance of defects that can exist in these large area devices. Analytical image processing algorithms pertaining to biased-photoluminescence (PL) measurements are conducted to portray 2D maps of physical significant devices parameters such as dark saturation current density and efficiency. Finally, Fourier analysis is added into the analysis of raw PL images to pick up only the defected regions of the cells.
Show less - Date Issued
- 2018
- Identifier
- CFE0007069, ucf:51980
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0007069
- Title
- Random Transformations of Optical Fields and Applications.
- Creator
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Kohlgraf-Owens, Thomas, Dogariu, Aristide, Saleh, Bahaa, Schulzgen, Axel, Tamasan, Alexandru, University of Central Florida
- Abstract / Description
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The interaction of optical waves with material systems often results in complex, seemingly random fields. In many cases, the interaction, while complicated, is both linear and deterministic.This dissertation focuses on the possible inverse problems associated with the determination of either the excitation field or the scattering system. The scattered field can be thought of as a massive sampling and mixing of the excitation field. This dissertation will show how such complicated sampling...
Show moreThe interaction of optical waves with material systems often results in complex, seemingly random fields. In many cases, the interaction, while complicated, is both linear and deterministic.This dissertation focuses on the possible inverse problems associated with the determination of either the excitation field or the scattering system. The scattered field can be thought of as a massive sampling and mixing of the excitation field. This dissertation will show how such complicated sampling functions can be characterized and how the corresponding scattering medium can then be used as an optical device such as a lens, polarimeter, or spectrometer.Another class of inverse problems deals with extracting information about the material system from changes in the scattered field. This dissertation includes a novel technique, based on dynamic light scattering, that allows for a full polarimetric measurement of the scattered light using a reference field with controllable polarization. Another technique relates to imaging the reflectivity of a target that is being randomly illuminated. We demonstrate that a method based on the correlation between the integrated scattered intensity and the corresponding illumination intensity distribution can prove superior to standard imaging microscopy at low-light levels.
Show less - Date Issued
- 2012
- Identifier
- CFE0004786, ucf:49746
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0004786
- Title
- Volume Phase Masks in Photo-Thermo-Refractive Glass.
- Creator
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Segall, Marc, Glebov, Leonid, Zeldovich, Boris, Dogariu, Aristide, Rahman, Talat, Bass, Michael, University of Central Florida
- Abstract / Description
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In many applications such as beam shaping, mode conversion, and phase encoding it is necessary to alter the spatial phase profile of a beam via a phase mask. Conventional techniques to accomplish this either involve surface relief profiling in thin films such as PMMA or refractive index modulation in bulk photorefractive crystals such as lithium niobate. These materials have been used extensively for the past several decades and perform admirably in low power conditions. However, in high...
Show moreIn many applications such as beam shaping, mode conversion, and phase encoding it is necessary to alter the spatial phase profile of a beam via a phase mask. Conventional techniques to accomplish this either involve surface relief profiling in thin films such as PMMA or refractive index modulation in bulk photorefractive crystals such as lithium niobate. These materials have been used extensively for the past several decades and perform admirably in low power conditions. However, in high power systems these materials will be destroyed, requiring a new means of producing phase masks. In this dissertation a method for producing robust phase masks in the bulk of photo-thermo-refractive glass is developed and successfully demonstrated. Three main applications of phase masks were studied in detail. The first is mode conversion, where binary phase masks convert a Gaussian beam to higher order modes. The second is beam shaping, where phase masks are used as focusing elements and for optical vortex generation. Near-theoretical conversion efficiency was achieved for all elements in these cases. The third application is aberration analysis and correction. Here the degradation of volume Bragg gratings recorded in an aberrated holographic system was modeled, with the simulations indicating that correcting elements are generally necessary for high-quality production of gratings. Corrective phase masks are designed which can selectively correct one or multiple aberrations of varying magnitudes are shown. A new type of optical element is also developed in which a phase mask is encoded into a transmitting Bragg grating. This technique combines the local phase modulation of a phase mask with the multiplexing ability of transmitting Bragg gratings, allowing for multiple phase masks to be recorded in a single element. These masks may be used at any wavelength satisfying the Bragg condition, increasing the useful wavelength regime of a single element by orders of magnitude.
Show less - Date Issued
- 2013
- Identifier
- CFE0005414, ucf:50431
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005414
- Title
- Optically Induced Forces in Scanning Probe Microscopy.
- Creator
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Kohlgraf-Owens, Dana, Dogariu, Aristide, Christodoulides, Demetrios, Kik, Pieter, DeWilde, Yannick, University of Central Florida
- Abstract / Description
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The focus of this dissertation is the study of measuring light not by energy transfer as is done with a standard photodetector such as a photographic film or charged coupled device, but rather by the forces which the light exerts on matter. In this manner we are able to replace or complement standard photodetector-based light detection techniques. One key attribute of force detection is that it permits the measurement of light over a very large range of frequencies including those which are...
Show moreThe focus of this dissertation is the study of measuring light not by energy transfer as is done with a standard photodetector such as a photographic film or charged coupled device, but rather by the forces which the light exerts on matter. In this manner we are able to replace or complement standard photodetector-based light detection techniques. One key attribute of force detection is that it permits the measurement of light over a very large range of frequencies including those which are difficult to access with standard photodetectors, such as the far IR and THz. The dissertation addresses the specific phenomena associated with optically induced force (OIF) detection in the near-field where light can be detected with high spatial resolution close to material interfaces. This is accomplished using a scanning probe microscope (SPM), which has the advantage of already having a sensitive force detector integrated into the system. The two microscopies we focus on here are atomic force microscopy (AFM) and near-field scanning optical microscopy (NSOM). By detecting surface-induced forces or force gradients applied to a very small size probe ( diameter), AFM measures the force acting on the probe as a function of the tip-sample separation or extracts topography information. Typical NSOM utilizes either a small aperture ( diameter) to collect and/or radiate light in a small volume or a small scatterer ( diameter) in order to scatter light in a very small volume. This light is then measured with an avalanche photodiode or a photomultiplier tube.These two modalities may be combined in order to simultaneously map the local intensity distribution and topography of a sample of interest. A critical assumption made when performing such a measurement is that the distance regulation, which is based on surface induced forces, and the intensity distribution are independent. In other words, it is assumed that the presence of optical fields does not influence the AFM operation. However, it is well known that light exerts forces on the matter with which it interacts. This light-induced force may affect the atomic force microscope tip-sample distance regulation mechanism or, by modifying the tip, it may also indirectly influence the distance between the probe and the surface. This dissertation will present evidence that the effect of optically induced forces is strong enough to be observed when performing typical NSOM measurements. This effect is first studied on common experimental situations to show where and how these forces manifest themselves. Afterward, several new measurement approaches are demonstrated, which take advantage of this additional information to either complement or replace standard NSOM detection. For example, the force acting on the probe can be detected while simultaneously extracting the tip-sample separation, a measurement characteristic which is typically difficult to obtain. Moreover, the standard field collection with an aperture NSOM and the measurement of optically induced forces can be operated simultaneously. Thus, complementary information about the field intensity and its gradient can be, for the first time, collected with a single probe. Finally, a new scanning probe modality, multi-frequency NSOM (MF-NSOM), will be demonstrated. In this approach, the tuning fork is driven electrically at one frequency to perform a standard tip-sample distance regulation to follow the sample topography and optically driven at another frequency to measure the optically induced force. This novel technique provides a viable alternative to standard NSOM scanning and should be of particular interest in the long wavelength regime, e.g. far IR and THz.
Show less - Date Issued
- 2013
- Identifier
- CFE0004705, ucf:49829
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0004705
- Title
- Tiling properties of spectra of measures.
- Creator
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Haussermann, John, Dutkay, Dorin, Han, Deguang, Sun, Qiyu, Dogariu, Aristide, University of Central Florida
- Abstract / Description
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We investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and...
Show moreWe investigate tiling properties of spectra of measures, i.e., sets ? in R with an orthogonal basis in L2 with respect to some finite Borel measure on R. Such measures include Lebesgue measure on bounded Borel subsets, finite atomic measures and some fractal Hausdorff measures. We show that various classes of such spectra of measures have translational tiling properties. This lead to some surprising tiling properties for spectra of fractal measures, the existence of complementing sets and spectra for finite sets with the Coven-Meyerowitz property, the existence of complementing Hadamard pairs in the case ofHadamard pairs of size 2,3,4 or 5. In the context of the Fuglede conjecture, we prove that any spectral set is a tile, if the period of the spectrum is 2,3,4 or 5.
Show less - Date Issued
- 2014
- Identifier
- CFE0005182, ucf:50656
- Format
- Document (PDF)
- PURL
- http://purl.flvc.org/ucf/fd/CFE0005182
