The high-density integrated circuit (IC) gives rise to geometrically complex multiscale chip-package structures whose electromagnetic performance is difficult to predict. This motivates this dissertation to work on an efficient full-wave transient solver that is capable of capturing all the electromagnetic behaviors of such structures with high accuracy and reduced computational complexity compared to the existing methods. In this work, the unconditionally stable Laguerre-FDTD method is adopted as the core algorithm for the transient full-wave solver. As part of this research, skin-effect is rigorously incorporated into the solver which avoids dense meshing inside conductor structures and significantly increases computational efficiency. Moreover, as an alternative to typical planar interconnects for next generation high-speed ICs, substrate integrated waveguide, is investigated. Conductor surface roughness is efficiently modeled to accurately capture its high-frequency loss behavior. To further improve the computational performance of chip-package co-simulation, a novel transient non-conformal domain decomposition method has been proposed. Large-scale chip-package structure can be efficiently simulated by decomposing the computational domain into subdomains with independent meshing strategy. Numerical results demonstrate the capability, accuracy and efficiency of the proposed methods.

This thesis investigates near-field wireless power transfer using multiple transmitters or multiple receivers. First, transmitter diversity is investigated in terms of the power transfer efficiency (PTE). It is found that an improvement in the PTE can be achieved by increasing the number of transmitters. Furthermore, a region of constant PTE can be created with the proper arrangement of transmitters. Next, receiver diversity is investigated in detail. An improvement in the PTE can be also achieved by increasing the number of receivers. However, it is shown that when two or more receivers are closely located, the PTE is reduced due to mutual coupling between receivers. This is termed a ‘sink’ phenomenon, and it is investigated through measurement and simulation. Finally, to account for more general situations of multiple transmitters and multiple receivers, Monte-Carlo simulation is applied. The cumulative distribution function (CDF) is used to interpret the results of the Monte-Carlo simulation. The transmitter and receiver diversity gain can be found based on the CDF. Moreover, the sink phenomenon can be observed by analyzing the CDF curve. Several strategies for positioning receivers are introduced to reduce the sink phenomenon. The results of the Monte-Carlo simulation also show that a saturation in the transmitter or receiver gain is reached when the number of transmitters or receivers is increased. Therefore, increasing the number of transmitters or receivers beyond a certain number does not help increase the PTE. / text

The Method of Moments (MoM) has been widely used for the full-wave electromagnetic analysis of planar multilayered media. However, the MoM is a computationally intensive process and requires considerable computer resources to perform the analysis. Thus, several efficient numerical techniques both in the spectral domain and spatial domain are investigated and further developed in this research. Two fitting procedures, i.e., the Rational Function Fitting Method (RFFM) and the Discrete Complex Image Method (DCIM), are investigated and developed in order to obtain closed-form spatial-domain Green's functions (GFs). Because the subtraction of the surface-wave pole contribution plays an important role for the accurate estimation of the spatial-domain GFs via DCIM, an efficient and accurate surface-wave pole location method is developed to find all the surface-wave poles for general multilayered media. The RFFM can be realized through either the Total Least Square Algorithm (TLSA) or the Vector Fitting (VECTFIT) method. Both the RFFM using VECTFIT and DCIM are detailed in step by step procedures. An efficient and low cost algorithm combining the advantages of DCIM and TLSA is also developed to evaluate the closed-form Green's functions for general multilayered media. A prototype version of the Full-Wave Layered-Interconnect Simulator (UA-FWLIS) was developed by analytically calculating the MoM reaction elements via Cauchy's residue theorem and the Complementary Incomplete Lipschitz-Hankel Integrals in stripline structures. After applying RFFM via VECTFIT to the G-functions, which are directly related to the spectral-domain GFs for microstrip structures, a procedure that is similar to the one used in the previously developed UA-FWLIS for stripline structures can be applied to calculate the MoM reaction elements analytically when the two reaction cells are close (< 0.1λ₀) in the spectral domain via the Electrical Field Integral Equation (EFIE). When the two reaction cells are far enough away (> 0.10.1λ₀), a simple expression for the reaction element can be obtained in the spatial domain via the Mixed Potential Integral Equation (MPIE) by a summation of a few complex image terms for the evaluation of the vector and scalar GFs. An efficient hybrid spectral-spatial method is thus developed to extend UA-FWLIS to microstrip structures. The method is validated by several numerical examples.

Technology trends toward lower power, higher speed and higher density devices have pushed the package performance to its limits. The high frequency effects e.g., crosstalk and signal distortion, may cause high bit error rates or malfunctioning of the circuit. Therefore, the successful release of a new product requires constant attention to the high frequency effects through the whole design process. Full-wave electromagnetic tools must be used for this purpose. Unfortunately, currently available full-wave tools require excessive computational resources to simulate large-scale interconnect structures.A prototype version of the Full-Wave Layered-Interconnect Simulator (UA-FWLIS), which employs the Method of Moments (MoM) technique, was developed in response to this design need. Instead of using standard numerical integration techniques, the MoM reaction elements were analytically evaluated, thereby greatly improving the computational efficiency of the simulator. However, the expansion and testing functions that are employed in the prototype simulator involve filamentary functions across the wire. Thus, many problems cannot be handled correctly. Therefore, a fundamental extension is made in this dissertation to incorporate rectangular-based, finite-width expansion and testing functions into the simulator. The critical mathematical issues and theoretical issues that were met during the extension are straightened out. The breakthroughs that were accomplished in this dissertation lay the foundation for future extensions. A new bend-cell expansion function is also introduced, thus allowing the simulator to handle bends on the interconnects with fewer unknowns. In addition, the Incomplete Lipschitz-Hankel integrals, which are used in the analytical solution, are studied. Two new series expansions were also developed to improve the computational efficiency and accuracy.

<p>Intense developments in optical metamaterials have led to a renaissance in several optics fields. Metamaterials, artificially structured media, provide several additional degrees of freedom that cannot be accessed with conventional materials. For example, metamaterials offer a convenient and precise way to explore a wide range of refractive indices, including negative values. </p><p>In this dissertation, I introduce the idea of metamaterial based diffractive optics. Merging diffractive optics with metamaterials has several benefits, including access to almost continuous phase profiles and a wide range of available controlled anisotropy. I demonstrate this concept with several examples. I begin with an example of metamaterial based blazed diffraction grating using gradient index metamaterials for <em>f</em>É = 10.6 <em>f</em>Êm. A series of non-resonant metamaterial elements were designed and fabricated to mimic a saw-tooth refractive index profile with a linear index variation of . The linear gradient profile is repeated periodically to form the equivalent of a blazed grating, with the gradient occurring across a spatial distance of 61 <em>f</em>Êm. The index gradient is confirmed by comparing the measured magnitudes of the -1, 0 and +1 diffracted orders to those obtained from full wave simulations. </p><p>In addition to a metamaterial grating, a metamaterial based computer-generated phase hologram was designed by implementing the Gerchberg-Saxton (GS) iterative algorithm to form a 2D phase panel. A three layer metamaterial hologram was fabricated, with the size of 750 <em>f</em>Êm ~ 750 <em>f</em>Êm. Each pixel is comprised of metamaterial elements. This simple demonstration shows the potential for practical applications of metamaterial based diffractive optics.</p><p>The demand for compact and integrated optoelectronic systems increases the urgency for optical components that can simultaneously perform various functions. This dissertation also presents an optical element capable of multiplexing two diffraction patterns for two orthogonal linear polarizations, based on the use of non-resonant metamaterial cross elements. The metamaterial cross elements provide unique building blocks for engineering arbitrary birefringence. As a proof-of-concept demonstration, I present the design and experimental characterization of a polarization multiplexed blazed diffraction grating and a polarization multiplexed computer-generated hologram, for the telecommunication wavelength of <em>f</em>É = 1.55 <em>f</em>Êm. A quantitative study of the polarization multiplexed grating reveals that this approach yields a very large polarization contrast ratio. The results show that metamaterials can form the basis for a versatile and compact platform useful in the design of multi-functional photonic devices. </p><p>The examples I have mentioned only provide a glimpse of the opportunities for metamaterials. I envision more compact optical devices, with greater functionality, being realized with metamaterials.</p> / Dissertation

Classically, researchers in Computational Physics and specifically in Computational Electromagnetics have sought to find numerical solutions to complex physical problems. Several techniques have been developed to accomplish such tasks, each of which having advantages over their counterparts. Typically, each solution method has been developed separately despite having numerous commonalities with other methods. This fact motivates a unified software tool to house each solution method to avoid duplicating previous efforts. Subsequently, these solution methods can be used alone or in conjunction with one another in a straightforward manner. The aforementioned goals can be accomplished by using an Object Oriented software approach. Thus, the goal of the presented research was to incorporate a specific solution technique, an Integral Equation Nystrm method, into a general, Object Oriented software framework.

Accurate modeling of current flow and network parameter extraction in 2-D and 3-D conductors has an important application in signal integrity of high-speed interconnects. In this thesis, we propose a new rigorous single-source Surface-Volume-Surface Electric Field Integral Equation (SVS-EFIE) for magnetostatic analysis of 2-D transmission lines and broadband resistance and inductance extraction in 3-D interconnects. Furthermore, the novel integral equation can be used for the solution of full-wave scattering problems on penetrable 2-D cylinders of arbitrary cross-section under transverse magnetic polarization. The new integral equation is derived from the classical Volume Electric Field Integral Equation (V-EFIE) by representing the electric field inside a conductor or a scatterer as a superposition of the cylindrical waves emanating from the conductor’s surface. This converts the V-EFIE into a surface integral equation involving only a single unknown function on the surface. The novel equation features a product of integral operators mapping the field from the conductor surface to its volume and back to its surface terming the new equation the Surface-Volume-Surface EFIE. The number of unknowns in the proposed SVS-EFIE is approximately the square root of the number of degrees of freedom in the traditional V-EFIE; therefore, it allows for substantially faster network parameter extraction and solutions to 2-D scattering problems without compromising the accuracy. The validation and benchmark of the numerical implementation of the Method of Moment discretization of the novel SVS-EFIE has been done via comparisons against numerical results obtained by using alternative integral equations, data found in literature, simulation results acquired from the CAD software, and analytic formulas.

<p>Since their introduction by Mercedes Benz in the late 1990s, W-band radars operating at 76-77 GHz have found their way into more and more passenger cars. These automotive radars are typically used in adaptive cruise control, pre-collision sensing, and other driver assistance systems. While these systems are usually only about the size of two stacked cigarette packs, system size, and weight remains a concern for many automotive manufacturers.</p><p>In this dissertation, I discuss how artificially structured metamaterials can be used to improve lens-based automotive radar systems. Metamaterials allow the fabrication of smaller and lighter systems, while still meeting the frequency, high gain, and cost requirements of this application. In particular, I focus on the development of planar artificial dielectric lenses suitable for use in place of the injection-molded lenses now used in many automotive radar systems.</p><p>I begin by using analytic and numerical ray-tracing to compare the performance of planar metamaterial GRIN lenses to equivalent aspheric refractive lenses. I do this to determine whether metamaterials are best employed in GRIN or refractive automotive radar lenses. Through this study I find that planar GRIN lenses with the large refractive index ranges enabled by metamaterials have approximately optically equivalent performance to equivalent refractive lenses for fields of view approaching ±20°. I also find that the uniaxial nature of most planar metamaterials does not negatively impact planar GRIN lens performance.</p><p>I then turn my attention to implementing these planar GRIN lenses at W-band automotive radar frequencies. I begin by designing uniform sheets of W-band electrically-coupled LC resonator-based metamaterials. These metamaterial samples were fabricated by the Jokerst research group on glass and liquid crystal polymer (LCP) substrates and tested at Toyota Research Institute- North America (TRI-NA). When characterized at W-band frequencies, these metamaterials show material properties closely matching those predicted by full-wave simulations.</p><p>Due to the high losses associated with resonant metamaterials, I shift my focus to non-resonant metamaterials. I discuss the design, fabrication, and testing of non-resonant metamaterials for fabrication on multilayer LCP printed circuit boards (PCBs). I then use these non-resonant metamaterials in a W-band planar metamaterial GRIN lens. Radiation pattern measurements show that this lens functions as a strong collimating element.</p><p>Using similar lens design methods, I design a metamaterial GRIN lens from polytetrafluoroethylene-based (PTFE-based) non-resonant metamaterials. This GRIN lens is designed to match a target dielectric lens's radiation characteristics across a ±6° field of view. Measurements at automotive radar frequencies show that this lens has approximately the same radiation characteristics as the target lens across the desired field of view.</p><p>Finally, I describe the development of electrically reconfigurable metamaterials using thin-film silicon semiconductors. These silicon-based reconfigurable metamaterials were developed in close collaboration with several other researchers. My major contribution to the development of these reconfigurable metamaterials consisted of the initial metamaterial design. The Jokerst research group fabricated this initial design while TRI-NA characterized the fabricated metamaterial experimentally. Measurements showed approximately 8% variation in transmission under a 5 Volt DC bias. This variation in transmission closely matched the variation in transmission predicted by coupled electronic-electromagnetic simulation run by Yaroslav Urzhumov, one of other contributors to the development of the reconfigurable metamaterial.</p> / Dissertation

This thesis examines the sensitivity of the marine controlled source electromagnetic (CSEM) method to sub-seafloor resistivity structure, with a focus on gas hydrate and free gas occurrences. Different analysis techniques are applied with progressive sophistication to a series of studies based on simulated and measured data sets. CSEM data are modelled in time domain for one-dimensional models with gas hydrate, free gas and/or permafrost occurrences. Linearized and non-linear inversion methods are considered to infer subsurface models from CSEM data. One study applies forward modelling and singular value decomposition to estimate uncertainties for permafrost models of the Beaufort Sea. This simulation study analyzes the resolution of the CSEM data for shallow water depth which is a challenging case because the electromagnetic signature of the air-water boundary may mask the sub-seafloor response. The results reveal a blind window as a function of water depth in which the CSEM data are insensitive to the sub-seafloor structure. However, the CSEM data are sensitive to the top and the bottom of the permafrost with increasing uncertainties with depth. The next study applies non-linear Bayesian inversion to CSEM data acquired in 2005/2006 on the Northern Cascadia margin to investigate sub-seafloor resistivity structure related to gas hydrate deposits and cold vents. Bayesian inversion provides a rigorous approach to estimate model parameters and uncertainties by probabilistically sampling of the parameter space. The resulting probability density function is interpreted here in terms of posterior median models, marginal and joint marginal probability densities for model parameters and credibility intervals. The Bayesian information criterion is applied to determine the amount of structure (number of layers) that can be resolved by the data. The parameter space is sampled with the Metropolis-Hastings algorithm in principal-component space. Non-linear, probabilistic inversion allows the analysis of unknown acquisition parameters such as time delays between receiver and transmitter clocks or unknown source amplitude. The estimated posterior median models and credibility intervals from Bayesian CSEM inversion are compared to reflection seismic data to provide a more complete geological interpretation. The CSEM data on the Northern Cascadia margin generally reveal a 1 to 3 layer sediment structure. Inversion results at the landward edge of the gas hydrate stability zone indicate a sediment unconformity as well as several potential cold vents which were previously unknown. The resistivities generally increase upslope due to sediment erosion along the slope. Inversion results on the middle slope infer several vent systems close to well-known Bullseye vent in agreement with ongoing interdisciplinary observations. Finally, a trans-dimensional (trans-D) Bayesian inversion is applied to CSEM data acquired in 2012 in the German North Sea to investigate possible free gas occurrences. Trans-D inversion treats the number of layers as an additional unknown sampled probabilistically in the inversion. %over the parameter space by evaluating probabilistically the transition to a higher or lower number of interfaces. Parallel tempering is applied to increase sampling efficiency and completeness. Inversion results for the German North Sea yield resistivities at the seafloor which are typical for marine deposits, while resistivities at greater depth increase slightly and can be correlated with a transition from fine-grained marine deposits (Holocene age) to coarse-grained, glacial sediments (Pleistocene age), which is observed in a sediment core. The depths of layer interfaces estimated from CSEM inversion match the seismic reflector related to the contrast between the two depositional environments. The CSEM survey targeted a strong, phase-reversed, inclined seismic reflector within the glacial sediments, potentially indicating free gas. While interface-depth estimates from CSEM inversion do not correlate closely with this reflector, resistivities are generally elevated above the strong seismic amplitudes and the thickness of the resistive layer follows the trend of the inclined reflector. However, the uncertainties of deeper interface depth estimates increase significantly and overlap with the targeted reflector at some of the measurement sites. Relatively low resistivities of a third layer correlate with sediments of late-Miocene origin with a high gamma-ray count indicating an increased amount of fine-grained sediments with organic material. The interface at the bottom of the third layer has wide uncertainties which relates to the penetration limit of the CSEM array. / Graduate

Gas hydrates are a solid, ice-like mixture of water and low molecular weight hydrocarbons. They are found under the permafrost and to a far greater extent under the ocean, usually at water depths greater than 300m. Hydrates are a potential energy resource, a possible factor in climate change, and a geohazard. For these reasons, it is critical that gas hydrate deposits are quantitatively assessed so that their concentrations, locations and distributions may be established. Due to their ice-like nature, hydrates are electrically insulating. Consequently, a method which remotely detects changes in seafloor electrical conductivity, such as marine controlled source electromagnetics (CSEM), is a useful geophysical tool for marine gas hydrate exploration. Hydrates are geometrically complex structures. Advanced electromagnetic modelling and imaging techniques are crucial for proper survey design and data interpretation. I develop a method to model thin resistive structures in conductive host media which may be useful in building approximate geological models of gas hydrate deposits using arrangements of multiple, bent sheets. I also investigate the possibility of interpreting diffusive electromagnetic data using seismic imaging techniques. To be processed in this way, such data must first be transformed into its non-diffusive, seismic-like counterpart. I examine such a transform from both an analytical and a numerical point of view, focusing on methods to overcome inherent numerical instabilities. This is the first step to applying seismic processing techniques to CSEM data to rapidly and efficiently image resistive gas hydrate structures. The University of Toronto marine electromagnetics group has deployed a permanent marine CSEM array offshore Vancouver Island, in the framework of the NEPTUNE Canada cabled observatory, for the purposes of monitoring gas hydrate deposits. In this thesis I also propose and examine a new CSEM survey technique for gas hydrate which would make use of the stationary seafloor transmitter already on the seafloor, along with a cabled receiver array, towed from a ship. I furthermore develop a modelling algorithm to examine the electromagnetic effects of conductive borehole casings which have been proposed to be placed in the vicinity of this permanent marine CSEM array, and make preliminary recommendations about their locations.