Due to the current public demand of faster, more powerful, and more reliable electronic devices, research is prolific these days in the area of high electron mobility transistor (HEMT) devices. This is because of their usefulness in RF (radio frequency) and microwave power amplifier applications including microwave vacuum tubes, cellular and personal communications services, and widespread broadband access. Although electrical transistor research has been ongoing since its inception in 1947, the transistor itself continues to evolve and improve much in part because of the many driven researchers and scientists throughout the world who are pushing the limits of what modern electronic devices can do. The purpose of the research outlined in this paper was to better understand the mechanical stresses and strains that are present in a hybrid AlGaN (Aluminum Gallium Nitride) / GaN (Gallium Nitride) HEMT, while under electrically-active conditions. One of the main issues currently being researched in these devices is their reliability, or their consistent ability to function properly, when subjected to high-power conditions. The researchers of this mechanical study have performed a static (i.e. frequency-independent) reliability analysis using powerful multiphysics computer modeling/simulation to get a better idea of what can cause failure in these devices. Because HEMT transistors are so small (micro/nano-sized), obtaining experimental measurements of stresses and strains during the active operation of these devices is extremely challenging. Physical mechanisms that cause stress/strain in these structures include thermo-structural phenomena due to mismatch in both coefficient of thermal expansion (CTE) and mechanical stiffness between different materials, as well as stress/strain caused by "piezoelectric" effects (i.e. mechanical deformation caused by an electric field, and conversely voltage induced by mechanical stress) in the AlGaN and GaN device portions (both piezoelectric materials). This piezoelectric effect can be triggered by voltage applied to the device's gate contact and the existence of an HEMT-unique "two-dimensional electron gas" (2DEG) at the GaN-AlGaN interface. COMSOL Multiphysics computer software has been utilized to create a finite element (i.e. piece-by-piece) simulation to visualize both temperature and stress/strain distributions that can occur in the device, by coupling together (i.e. solving simultaneously) the thermal, electrical, structural, and piezoelectric effects inherent in the device. The 2DEG has been modeled not with the typically-used self-consistent quantum physics analytical equations, rather as a combined localized heat source* (thermal) and surface charge density* (electrical) boundary condition. Critical values of stress/strain and their respective locations in the device have been identified. Failure locations have been estimated based on the critical values of stress and strain, and compared with reports in literature. The knowledge of the overall stress/strain distribution has assisted in determining the likely device failure mechanisms and possible mitigation approaches. The contribution and interaction of individual stress mechanisms including piezoelectric effects and thermal expansion caused by device self-heating (i.e. fast-moving electrons causing heat) have been quantified. * Values taken from results of experimental studies in literature

<p>In this work, we proposed a spectral integral method (SIM)-spectral element method (SEM)- finite element method (FEM) domain decomposition method (DDM) for solving inhomogeneous multi-scale problems. The proposed SIM-SEM-FEM domain decomposition algorithm can efficiently handle problems with multi-scale structures, </p><p>by using FEM to model electrically small sub-domains and using SEM to model electrically large and smooth sub-domains. The SIM is utilized as an efficient boundary condition. This combination can reduce the total number of elements used in solving multi-scale problems, thus it is more efficient than conventional FEM or conventional FEM domain decomposition method. Another merit of the proposed method is that it is capable of handling arbitrary non-conforming elements. Both geometry modeling and mesh generation are totally independent for different sub-domains, thus the geometry modeling and mesh generation are highly flexible for the proposed SEM-FEM domain decomposition method. As a result, the proposed SIM-SEM-FEM DDM algorithm is very suitable for solving inhomogeneous multi-scale problems.</p> / Dissertation

The phenomenon of polarization interaction in certain nonlinear materials is presented, and the design of an all-optical logic device based on this concept is described. An efficient two-dimensional finite-difference time-domain code for studying third-order nonlinear optical phenomena is discussed, in which both the slowly varying and the rapidly varying components of the electromagnetic fields are considered. The algorithm solves the vector form Maxwell s equations for all field components and uses the nonlinear constitutive relation in matrix form as the equations required to describe the nonlinear system. The stability of the code is discussed and its accuracy demonstrated through the simulation of the self-phase modulation effect observed in Kerr media. Finally, the code is used to simulate polarization mixing in photonic crystal-based line defect and coupled resonator optical waveguides.

In the thesis, we propose a newly-developed method called the method of Connected Local Fields (CLF) to analyze opto-electromagnetic passive devices. The method of CLF somewhat resembles a hybrid between the finite difference and pseudo-spectral methods. For opto-electromagnetic passive devices, our primary concern is their steady state behavior, or narrow-band characteristics, so we use a frequency-domain method, in which the system is governed by the Helmholtz equation. The essence of CLF is to use the intrinsic general solution of the Helmholtz equation to expand the local fields on the compact stencil. The original equation can then be transformed into the discretized form called LFE-9 (in 2-D case), and the intrinsic reconstruction formulae describing each overlapping local region can be obtained. Further, we present rigorous analysis of the numerical dispersion equation of LFE-9, by means of first-order approximation, and acquire the closed-form formula of the relative numerical dispersion error. We are thereby able to grasp the tangible influences brought both by the sampling density as well as the propagation direction of plane wave on dispersion error. In our dispersion analysis, we find that the LFE-9 formulation achieves the sixth-order accuracy: the theoretical highest order for discretizing elliptic partial differential equations on a compact nine-point stencil. Additionally, the relative dispersion error of LFE-9 is less than 1%, given that sampling density greater than 2.1 points per wavelength. At this point, the sampling density is nearing that of the Nyquist-Shannon sampling limit, and therefore computational efforts can be significantly reduced.

Presence of cultural refuse has long posed a serious challenge to meaningful geological interpretation of near surface controlled–source electromagnetic data (CSEM). Cultural refuse, such as buried pipes, underground storage tanks, unexploded ordnance, is often highly conductive and magnetically permeable. Interpretation of the CSEM response in the presence of cultural noise requires an understanding of electromagnetic field diffusion and the effects of anomalous highly conductive and permeable structures embedded in geologic media. While many numerical techniques have been used to evaluate the response of three dimensional subsurface conductivity distributions, there is a lack of approaches for modeling the EM response incorporating variations in both subsurface conductivity σ and relative permeability μr. In this dissertation, I present a new three dimensional edge–based finite element (FE) algorithm capable of modeling the CSEM response of buried conductive and permeable targets. A coupled potential formulation for variable μ using the vector magnetic potential A and scalar electric potential V gives rise to an ungauged curl–curl equation. Using reluctivity (v=1/mu ), a new term in geophysical applications instead of traditional magnetic susceptibility, facilitates a separation of primary and secondary potentials. The resulting differential equation is solved using the finite element method (FEM) on a tetrahedral mesh with local refinement capabilities. The secondary A and V potentials are expressed in terms of the vector edge basis vectors and the scalar nodal basis functions respectively. The finite element matrix is solved using a Jacobi preconditioned QMR solver. Post processing steps to interpolate the vector potentials on the nodes of the mesh are described. The algorithm is validated against a number of analytic and multi dimensional numeric solutions. The code has been deployed to estimate the influence of magnetic permeability on the mutual coupling between multiple geological and cultural targets. Some limitations of the code with regards to speed and performance at high frequency, conductivity and permeability values have been noted. Directions for further improvement and expanding the range of applicability have been proposed.

Predicting performance metrics for the next-generation of multi-mode and multi-antenna wireless communication systems demands site-specific knowledge of the wireless channel's underlying radio wave propagation mechanisms. This thesis describes the first measurement system capable of characterizing individual propagation mechanisms in situ. The measurement system merges a high-resolution spatio-temporal wireless channel sounder with a new field reconstruction technique to provide complete knowledge of the wireless channel's impulse response throughout a 2-dimensional region. This wealth of data may be combined with space-time filtering techniques to isolate and characterize individual propagation mechanisms. The utility of the spatio-temporal measurement system is demonstrated through a measurement-based investigation of diffraction around building corners. These measurements are combined with space-time filtering techniques and a new linear wedge diffraction model to extract the first semi-mpirical diffraction coefficient. Specific contributions of this thesis are: * The first ultra-wideband single-input multiple-output (SIMO) channel sounder based upon the sliding correlator architecture. * A quasi 2-dimensional field reconstruction technique based upon a conjoint cylindrical wave expansion of coherent perimeter measurements. * A wireless channel ``filming' technique that records the time-domain evolution of the wireless channel throughout a 2-dimensional region. * High-resolution measurements of the space-time wireless channel near a right-angled brick building corner. * The application of space-time filtering techniques to isolate the edge diffraction problem from the overall wireless channel. * An approximate uniform geometrical theory of diffraction (UTD)-style linear model describing diffraction by an impedance wedge. * The first-ever semi-empirical diffraction coefficient extracted from in situ measurement data. This thesis paves the way for several new avenues of research. The comprehensive measurement data provided by channel "filming" will enable researchers to develop and implement powerful space-time filtering techniques that facilitate measurement-based investigations of radio wave propagation. The measurement procedure described in this thesis may be adapted to extract realistic reflection and rough-surface scattering coefficients. Finally, exhaustive measurements of individual propagation mechanisms will enable the first semi-empirical propagation model that integrates empirical descriptions of propagation mechanisms into a UTD-style mechanistic framework.

This thesis concentrates on the algorithmic aspects of Method of Moments (MoM) and Locally Corrected Nyström (LCN) numerical methods in electromagnetics. The data dependency in each step of the algorithm is analyzed to implement a parallel version that can harness the powerful processing power of a General Purpose Graphics Processing Unit (GPGPU). The GPGPU programming model provided by NVIDIA's Compute Unified Device Architecture (CUDA) is described to learn the software tools at hand enabling us to implement C code on the GPGPU. Various optimizations such as the partial update at every iteration, inter-block synchronization and using shared memory enable us to achieve an overall speedup of approximately 10. The study also brings out the strengths and weaknesses in implementing different methods such as Crout's LU decomposition and triangular matrix inversion on a GPGPU architecture. The results suggest future directions of study in different algorithms and their effectiveness on a parallel processor environment. The performance data collected show how different features of the GPGPU architecture can be enhanced to yield higher speedup.

Microstrip patch antennas are attractive for numerous military and commercial applications due to their advantages in terms of low-profile, broadside radiation, low-cost, low-weight and conformability. However, the inherent narrowband performance of patch antennas prohibits their use in systems that demand wideband radiation. To alleviate the issue, an existing approach is to combine multiple patch antennas within a log-periodic array configuration. These log-periodic patch antennas (LPMAs) are capable of providing large bandwidths (>50%) with stable broadside radiation patterns. However, they suffer from electrically large sizes. Therefore, their miniaturization without degrading the bandwidth performance holds promise for extending their use in applications that demand conformal and wideband installations. In recent years, electromagnetic band gap structures have been proposed to enhance the radiation performances of printed antennas. These engineered surfaces consist of a periodic arrangement of unit cells having specific metallization patterns. At particular frequencies, they provide a zero-degree phase shift for reflected plane waves and effectively act as high impedance surfaces. Since, their band-limited electromagnetic field behavior is quite similar to a hypothetical magnetic conductor; they are also referred to as artificial magnetic conductors (AMCs). AMC structures were shown to allow lower antenna profile, larger bandwidth, higher gain, and good unidirectional radiation by alleviating the field cancellation effects observed in ground plane backed antenna configurations. Previous research studies have already demonstrated that microstrip patch antennas can enjoy significant size reductions when placed above the AMC surfaces. This project, for the first time, investigates the application of AMCs to LPMA configurations. Specifically, the goal is to reduce the LPMA size while retaining its highly desired large bandwidth performance. To accomplish this, we employ various AMC surface configurations (e.g. uniform, log-periodic) under traditional LPMAs and investigate their performance in terms of miniaturization, bandwidth, gain, and radiation patterns.

This thesis explores two ways of developing a fracture diagnostics tool capable of estimating hydraulic fracture propped length and orientation. Both approaches make use of an electrically conductive proppant. The fabrication of an electrically conductive proppant is believed to be possible and an option currently on the market is calcined petroleum coke. The first approach for tool development was based on principles of antenna resonance whereas the second approach was based on low frequency magnetic induction. The former approach had limited success due to the lack of resonant features at the stipulated operating conditions. Low frequency induction is a more promising approach as electromagnetic fields showed measurable changes that were dependent on fracture length in simulations. The operation of a logging tool was simulated and the data showed differences in the magnetic field magnitude ranging from 2% to 107% between fracture sizes of 20m, 50m, 80m, and 100m. Continuing research of the topic should focus not only on simulating more diverse fracture scenarios but also on developing an inversion scheme necessary for interpreting field data. / text

Optical whispering-gallery mode (WGM) cavities, which exhibit extraordinary spatial and temporal confinement of light, are one of the leading transducers for examining molecular recognition at low particle counts. With the advent of hybrid photonic-plasmonic and increasingly sophisticated forms of these resonators, the importance of supporting numerical methods has correspondingly become evident. In response, we adopt a full-vector finite difference approximation in order to solve for WGM's in terms of their field distributions, resonant wavelengths, and quality factors in the context of naturally discontinuous permittivity structure. A segmented Taylor series and alignment/rotation operator are utilized at such singularities in conjunction with arbitrarily spaced grid points. Simulations for microtoroids, with and without dielectric nanobeads, and plasmonic microdisks are demonstrated for short computation times and shown to be in agreement with data in the literature. Constricted surface plasmon polariton (SPP) WGM's are also featured within this document. The module of this thesis is devised as a keystone for composite WGM models that may guide experiments in the field. / Graduate