Browsing by Subject "Electromagnetics"

In this thesis, a 3D microwave imaging method is developed for a microwave imaging system with an arbitrary background medium. In the previous study on the breast cancer detection of our research group, a full wave inverse method, the Diagonal Tensor approximation combined with Born Iterative Method (DTA-BIM), was proposed to reconstruct the electrical profile of the inversion domain in a homogenous background medium and a layered background medium. In order to evaluate the performance of the DTA-BIM method in a realistic microwave imaging system, an experimental prototype of an active 3D microwave imaging system with movable antennas is constructed. For the objects immersed in a homogenous background medium or a layered background medium, the inversion results based on the experimental data show that the resolution of the DTA-BIM method can reach finely to a quarter of wavelength of the background medium, and the system's signal-noise-ratio (SNR) requirement is 10 dB. Moreover, the defects of this system make it difficult to be implemented in a realistic application. Thus, another active 3D microwave imaging system is proposed to overcome the problems in the previous system. The new system employs a fix patch antenna array with electric switch to record the data. However, the antenna array makes the inversion system become a non-canonical inhomogeneous background. The analytical Greens' functions used in the original DTA-BIM method become unavailable. Thus, a modified DTA-BIM method, which use the numerical Green's functions combined with measured voltage, is proposed. This modified DTA-BIM method can be used to the inversion in a non-canonical inhomogeneous background with the measured voltages (or $S_{21}$ parameters). In order to verify the performance of this proposed inversion method, we investigate a prototype 3D microwave imaging system with a fix antenna array. The inversion results from the synthetic data show that this method works well with a fix antenna array, and the resolution of reconstructed images can reach to a quarter wavelength even in the presence of a strongly inhomogeneous background medium and antenna couplings. A time-reversal method is introduced as a pre-processing step to reduce the region of interest (ROI) in our inversion. In addition, a Multi-Domain DTA-BIM method is proposed to fit the discontinue inversion regions. With these improvements, the size of the inversion domain and the computational cost can be significantly reduced, and make the DTA-BIM method more feasible for rapid response applications.

This dissertation focuses on a FFT based forward EM solver and its application in inverse problems. The main contributions of this work are two folded. On the one hand, it presents the first scaled lab experiment system in the oil and gas industry for through casing hydraulic fracture evaluation. This system is established to validate the feasibility of contrasts enhanced fractures evaluation. On the other hand, this work proposes a FFT based VIE solver for hydraulic fracture evaluation. This efficient solver is needed for numerical analysis of such problem. The solver is then generalized to accommodate scattering simulations for anisotropic inhomogeneous magnetodielectric objects. The inverse problem on anisotropic objects are also studied.

Before going into details of specific applications, some background knowledge is presented. This dissertation starts with an introduction to inverse problems. Then algorithms for forward and inverse problems are discussed. The discussion on forward problem focuses on the VIE formulation and a frequency domain solver. Discussion on inverse problems focuses on iterative methods.

The rest of the dissertation is organized by the two categories of inverse problems, namely the inverse source problem and the inverse scattering problem.

The inverse source problem is studied via an application in microelectronics. In this application, a FFT based inverse source solver is applied to process near field data obtained by near field scanners. Examples show that, with the help of this inverse source solver, the resolution of unknown current source images on a device under test is greatly improved. Due to the improvement in resolution, more flexibility is given to the near field scan system.

Both the forward and inverse solver for inverse scattering problems are studied in detail. As a forward solver for inverse scattering problems, a fast FFT based method for solving VIE of magnetodielectric objects with large electromagnetic contrasts are presented due to the increasing interest in contrasts enhanced full wave EM imaging. This newly developed VIE solver assigns different basis functions of different orders to expand flux densities and vector potentials. Thus, it is called the mixed ordered BCGS-FFT method. The mixed order BCGS-FFT method maintains benefits of high order basis functions for VIE while keeping correct boundary conditions for flux densities and vector potentials. Examples show that this method has an excellent performance on both isotropic and anisotropic objects with high contrasts. Examples also verify that this method is valid in both high and low frequencies. Based on the mixed order BCGS-FFT method, an inverse scattering solver for anisotropic objects is studied. The inverse solver is formulated and solved by the variational born iterative method. An example given in this section shows a successful inversion on an anisotropic magnetodielectric object.

Finally, a lab scale hydraulic fractures evaluation system for oil/gas reservoir based on previous discussed inverse solver is presented. This system has been setup to verify the numerical results obtained from previously described inverse solvers. These scaled experiments verify the accuracy of the forward solver as well as the performance of the inverse solver. Examples show that the inverse scattering model is able to evaluate contrasts enhanced hydraulic fractures in a shale formation. Furthermore, this system, for the first time in the oil and gas industry, verifies that hydraulic fractures can be imaged through a metallic casing.

In this study we propose a fast hybrid spectral-element time-domain (SETD) / finite-element time-domain (FETD) method for transient analysis of multiscale electromagnetic problems, where electrically fine structures with details much smaller than a typical wavelength and electrically coarse structures comparable to or larger than a typical wavelength coexist.

Simulations of multiscale electromagnetic problems, such as electromagnetic interference (EMI), electromagnetic compatibility (EMC), and electronic packaging, can be very challenging for conventional numerical methods. In terms of spatial discretization, conventional methods use a single mesh for the whole structure, thus a high discretization density required to capture the geometric characteristics of electrically fine structures will inevitably lead to a large number of wasted unknowns in the electrically coarse parts. This issue will become especially severe for orthogonal grids used by the popular finite-difference time-domain (FDTD) method. In terms of temporal integration, dense meshes in electrically fine domains will make the time step size extremely small for numerical methods with explicit time-stepping schemes. Implicit schemes can surpass stability criterion limited by the Courant-Friedrichs-Levy (CFL) condition. However, due to the large system matrices generated by conventional methods, it is almost impossible to employ implicit schemes to the whole structure for time-stepping.

To address these challenges, we propose an efficient hybrid SETD/FETD method for transient electromagnetic simulations by taking advantages of the strengths of these two methods while avoiding their weaknesses in multiscale problems. More specifically, a multiscale structure is divided into several subdomains based on the electrical size of each part, and a hybrid spectral-element / finite-element scheme is proposed for spatial discretization. The hexahedron-based spectral elements with higher interpolation degrees are efficient in modeling electrically coarse structures, and the tetrahedron-based finite elements with lower interpolation degrees are flexible in discretizing electrically fine structures with complex shapes. A non-spurious finite element method (FEM) as well as a non-spurious spectral element method (SEM) is proposed to make the hybrid SEM/FEM discretization work. For time integration we employ hybrid implicit / explicit (IMEX) time-stepping schemes, where explicit schemes are used for electrically coarse subdomains discretized by coarse spectral element meshes, and implicit schemes are used to overcome the CFL limit for electrically fine subdomains discretized by dense finite element meshes. Numerical examples show that the proposed hybrid SETD/FETD method is free of spurious modes, is flexible in discretizing sophisticated structure, and is more efficient than conventional methods for multiscale electromagnetic simulations.

Electromagnetic scattering in a layered medium (LM) is important for many engineering applications, including the hydrocarbon exploration. Various computational methods for tackling well logging simulations are summarized. Given their advantages and limitations, main attention is devoted to the surface integral equation (SIE) and its hybridization with the finite element method (FEM).

The thin dielectric sheet (TDS) based SIE, i.e., TDS-SIE, is introduced to the simulation of fractures. Its accuracy and efficiency are extensively demonstrated by simulating both conductive and resistive fractures. Fractures of variant apertures, conductivities, dipping angles, and extensions are also simulated and analyzed. With the aid of layered medium Green's functions (LMGFs), TDS-SIE is extended into the LM, which results in the solver entitled LM-TDS-SIE.

In order to consider the borehole effect, the well-known loop and tree basis functions are utilized to overcome low-frequency breakdown of the Poggio, Miller, Chang, Harrington, Wu, and Tsai (PMCHWT) formulation. This leads to the loop-tree (LT) enhanced PMCHWT, which can be hybridized with TDS-SIE to simulate borehole and fracture together. The resultant solver referred to as LT-TDS is further extended into the LM, which leads to the solver entitled LM-LT-TDS.

For inhomogeneous or complex structures, SIE is not suitable for their scattering simulations. It becomes advantageous to hybridize FEM with SIE in the framework of domain decomposition method (DDM), which allows independent treatment of each subdomain and nonconformal meshes between them. This hybridization can be substantially enhanced by the adoption of LMGFs and loop-tree bases, leading to the solver entitled LM-LT-DDM. In comparison with LM-LT-TDS, this solver is more powerful and able to handle more general low-frequency scattering problems in layered media.

Active plasmonic nanostructures with tunable resonances promise to enable smart materials with multiple functionalities, on-chip spectral-based imaging and low-power optoelectronic devices. A variety of tunable materials have been integrated with plasmonic structures, however, the tuning range in the visible regime has been limited and small on/off ratios are typical for dynamically switchable devices. An all optical tuning mechanism is desirable for on-chip optical computing applications. Furthermore, plasmonic structures are traditionally fabricated on rigid substrates, restricting their application in novel environments such as in wearable technology.

In this dissertation, I explore the mechanisms behind dynamic tuning of plasmon resonances, as well as demonstrate all-optical tuning through multiple cycles by incorporating photochromic molecules into plasmonic nanopatch antennas. Exposure to ultraviolet (UV) light switches the molecules into a photoactive state enabling dynamic control with on/off ratios up to 9.2 dB and a tuning figure of merit up to 1.43, defined as the ratio between the spectral shift and the initial line width of the plasmonic resonance. Moreover, the physical mechanisms underlying the large spectral shifts are elucidated by studying over 40 individual nanoantennas with fundamental resonances from 550 to 720 nm revealing good agreement with finite-element simulations.

To fully explore the tuning capabilities, the molecules are incorporated into plasmonic metasurface absorbers based on the same geometry as the single nanoantennas. The increased interaction between film-coupled nanocubes and resonant dipoles in the photochromic molecules gives rise to strong coupling. The coupling strength can be quantified by the Rabi-splitting of the plasmon resonance at ~300 meV, well into the ultrastrong coupling regime.

Additionally, fluorescent emitters are incorporated into the tunable absorber platform to give dynamic control over their emission intensity. I use optical spectroscopy to investigate the capabilities of tunable plasmonic nanocavities coupled to dipolar photochromic molecules. By incorporating emission sources, active control over the peak photoluminescence (PL) wavelength and emission intensity is demonstrated with PL spectroscopy.

Beyond wavelength tuning of the plasmon resonance, design and characterization is performed towards the development of a pyroelectric photodetector that can be implemented on a flexible substrate, giving it the ability to be conformed to new shapes on demand. Photodetection in the NIR with responsivities up to 500 mV/W is demonstrated. A detailed plan is given for the next steps required to fully realize visible to short-wave infrared (SWIR) pyroelectric photodetection with a cost-effective, scalable fabrication process. This, in addition to real-time control over the plasmon resonance, opens new application spaces for photonic devices that integrate plasmonic nanoparticles and actively tunable materials.

Advanced numerical algorithms should be amenable to the scalability in the increasingly powerful supercomputer architectures, the adaptivity in the intricately multi-scale engineering problems, the efficiency in the extremely large-scale wave simulations, and the stability in the dynamically multi-phase coupling interfaces.

In this study, I will present a multi-scale \& multi-physics 3D wave propagation simulator to tackle these grand scientific challenges. This simulator is based on a unified high-order discontinuous Galerkin (DG) method, with adaptive nonconformal meshes, for efficient wave propagation modeling. This algorithm is compatible with a diverse portfolio of real-world geophysical/biomedical applications, ranging from longstanding tough problems: such as arbitrary anisotropic elastic/electromagnetic materials, viscoelastic materials, poroelastic materials, piezoelectric materials, and fluid-solid coupling, to recent challenging topics: such as fracture-wave interactions.

Meanwhile, I will also present some important theoretical improvements. Especially, I will show innovative Riemann solvers, inspired by physical meanings, in a unified mathematical framework, which are the key to guaranteeing the stability and accuracy of the DG methods and domain decomposition methods.

The design and characterization of electromagnetic metamaterial structures and their constituent subwavelength metamaterial elements are presented. The proposed structures can be employed in beamforming and physical layer processing applications. The common approach for designing such structures involves extracting the effective medium properties of the elements, a methodology inspired by early metamaterial research. The modeling and simulation method is made computationally feasible by assuming a periodic arrangement of the elements. In the case of aperiodic structures, the periodic assumption is no longer valid, and the electromagnetic behavior cannot be predicted accurately. To get a more accurate picture, the electromagnetic properties of individual elements must be evaluated to design a metamaterial structure. In this dissertation, I outline robust steps to realize electromagnetic metamaterial structures by characterizing metamaterial elements without any periodicity assumptions. The subwavelength elements are modeled as electric and magnetic dipoles, and I use dipole-based optimization techniques to design the structures. The dipolar elements are described by their electric and magnetic polarizabilities. Polarizability extraction methods to characterize the different metamaterial elements using numerical simulations are discussed in detail.

In recent years, the coupled dipole model (CDM) has been fully developed to predict the electromagnetic behavior of metamaterial given the element polarizabilities. However, the inverse problem to arrive at the desired medium given some desired behavior is a non-linear problem and can be computationally expensive to solve. Traditionally, holographic methods are used to linearize the problem in the perturbative limits limit to make it computationally tractable. The recently introduced symphotic method solves the non-linear electromagnetic inverse problem efficiently by iteratively solving two linear systems without making any assumptions. This allows one to encode multiple operations in a volume which is not possible with standard computer-generated holography design methods. Here, the two inverse design tools- holography and symphotic are investigated under the dipole framework and validated both numerically and experimentally using different metamaterial structures and corresponding elements.

Electroporation is a biological cell's natural reaction to strong electric fields, where transient pores are created in the cell membrane. While electroporation holds promise of being a safe and effective tool for enhancing molecular delivery in numerous medical applications, it remains largely confined to preclinical research and clinical trials due to an incomplete understanding of the exact mechanisms involved. Muscle fibers are an important delivery target, but traditional theoretical studies of electroporation ignore the individual fiber geometry, making it impossible to study the unique transverse and longitudinal effects from the pulse stimulus. In these long, thin muscle fibers, the total reaction of the fiber to the electric field is due to fundamentally different effects from the constituent longitudinal and transverse components of the electric field generated by the pulse stimulus. While effects from the transverse component have been studied to some degree, the effects from the longitudinal component have not been considered.

This study develops a model of electroporation and delivery of small molecules in muscle tissue that includes effects from both the transverse and longitudinal components of the electric field. First, an asymptotic model of electric potential in an individual muscle fiber is derived that separates the full 3D boundary value problem into transverse and a longitudinal problems. The transverse and longitudinal problems each have their own respective source functions: the new "transverse activating function" and the well known longitudinal activating function (AF). This separation enhances analysis of the different effects from these two AFs and drastically reduces computational intensity. Electroporation is added to the asymptotic fiber model, and simplified two-compartment mass transport equations are derived from the full 3D conservation of mass equations to allow simulation of molecular uptake due to diffusion and the electric field. Special emphasis is placed on choosing model geometry, electrical, and pulsing parameters that are in accordance with experiments that study electroporation-mediated delivery of small molecules in the skeletal muscle of small mammals.

Simulations reveal that for fibers close to the electrodes the transverse AF dominates, but for fibers far from the electrodes the longitudinal AF enhances uptake by as much as 2000%. However, on the macroscopic tissue level, the increase in uptake from the longitudinal AF is no more than 10%, given that fibers far from the electrodes contribute so little to the total uptake in the tissue. The mechanism underlying the smaller effect from the longitudinal AF is found to be unique to the process of electroporation itself. Electroporation occurs on the short time scale of polarization via the transverse AF, drastically increases membrane conductance, and effectively precludes further creation of pores from charging of the membrane via the longitudinal AF. The exact value of enhancement in uptake from the longitudinal AF is shown to depend on pulsing, membrane, and tissue parameters. Finally, simulation results reproduce qualitative, and in some cases quantitative, behavior of uptake observed in experiments.

Overall, percent increase in total tissue uptake from the longitudinal AF is on the order of experimental variability, and this study corroborates previous theoretical models that neglect the effects from the longitudinal AF. However, previous models neglect the longitudinal AF without explanation, while the asymptotic fiber model is able to detail the mechanisms involved. Mechanisms revealed by the model offer insight into interpreting experimental results and increasing efficiency of delivery protocols. The model also rigorously derives a new transverse AF based on individual fiber geometry, which affects the spatial distribution of uptake in tissue differently than predicting uptake based on the magnitude of the electric field, as used in many published models. Results of this study are strictly valid for transport of small molecules through small non-growing pores. For gene therapy applications the model must be extended to transport of large DNA molecules through large pores, which may alter the importance of the longitudinal AF. In broader terms, the asymptotic model also provides a new, computationally efficient tool that may be used in studying the effect of transverse and longitudinal components of the field for other types of membrane dynamics in muscle and nerves.

This dissertation focuses on the analytic model and design of waveguide-fed meta- surface antennas using the coupled-dipole method. In particular, it is demonstrated that the coupled-dipole method can be combined with models of waveguide feeds via network theory such that the self-consistency of the model of waveguide-fed metasurfaces is maintained. Thus, the proposed approach of modeling the meta- surface antennas allows the computation of key antenna parameters for practical design and considerations. It is also demonstrated that the proposed method allows direct implementation of optimization techniques to accelerate the design process of waveguide-fed metasurfaces. Design examples with various metasurface configu- rations, including printed cavity-backed metasurface, shared aperture metasurface, cylindrical conformal metasurface, are provided to confirm the utility of the proposed approach as an efficient design tool. Given the studies on the models and physics of waveguide-fed metasurface antennas, their applications to MIMO wireless commu- nication systems are explored in later chapters. The benefits of using metasurface antennas in various propagation channels are studied, showing that MIMO systems using metasurface antennas can improve channel capacity by utilizing flexibility in pattern synthesis offered by the metasurfaces.

A waveguide-fed metasurface consists of an array of metamaterial elements excited by a guided mode. When the metamaterial elements are excited, they in turn leak out a portion of the energy traveling through the waveguide to free space. As such, a waveguide-fed metasurface acts as an antenna. These antennas possess a planar form factor that offers tremendous dexterity in forming prescribed radiation patterns; a capability that has led to revolutionary advances in antenna engineering, microwave imaging, flat optics, among others.

Yet, the common approach to model and design such metasurfaces relies on effective surface properties, a methodology that is inspired by initial metamaterial designs. This methodology is only applicable to periodic arrangements of elements, and the assumption that the neighboring elements are identical. In the scenarios where the metasurface consists of an aperiodic array, or the neighboring elements are significantly different, or the coupling to the waveguide structure changes; the aforementioned approaches cannot predict the electromagnetic response of the waveguide-fed metasurface. In this thesis, I have implemented a robust technique to model waveguide-fed metasurfaces without any assumption on the metamaterial elements' geometry or arrangement. The only assumption is that the metamaterial elements can be modeled as effective dipoles, which is usually the case given the subwavelength size of metamaterial elements.

Throughout this document, the simulation tool will be referred to Dipole Model. In this framework, the total response of each dipole, representing a metamaterial element, depends on the mutual interaction between elements, as well as the perturbation of the guided mode. Both effects are taken into account and, by using full-wave simulations, I have confirmed the validity of the model and the ability to predict radiation patterns that can be used for beamforming as well as for microwave imaging.

Once the capabilities of the dipole model are compared with full wave simulations of both traditional antenna designs as well as more elaborated waveguide-fed metasurfaces, I develop an analysis on the use of these metasurfaces for microwave imaging systems. These systems are used to form images of buried objects, which is crucial in security screening and synthetic aperture radar (SAR). Traditionally, the hardware needed for many imaging techniques is cumbersome, including large arrays of antennas or bulky, moving parts. However, one attractive alternative to overcome these problems is to use dynamic metasurface antennas. By quickly varying the radiation patterns generated by these antennas, enough diverse measurements can be made in order to produce high quality images in a fraction of the time.

The compact size and speed come with a trade-off: a computationally intensive optical inverse problem has to be solved, which has so far prohibited these antennas from enjoying widespread use. I address this problem by reformulating the problem to make it similar to a SAR scenario, for which fast image reconstruction algorithms already exist. By adapting an algorithm known as the Range Migration to be compatible with these metasurfaces, I can cut down on real-time computation significantly. The computer simulations performed are highly promising for the field of microwave imaging, since it is demonstrated that diffraction-limited images can be acquired in a fraction of the time, in comparison with other imaging techniques.

Mass spectrometry is widely considered to be the gold standard of elemental analysis techniques due to its ability to resolve atomic and molecular and biological species. Expanding the application space of mass spectrometry often requires the need for portable or hand-held systems for use in field work or harsh environments. While only requiring “sufficient” mass resolution to meet the needs of their application space, these miniaturized systems suffer from poor signal to background ratio which limits their sensitivity as well as their usefulness in field applications.

Spatial aperture coding techniques have been used in optical spectroscopy to achieve large increases in signal intensity without compromising system resolution. In this work similar computational methods are used in the application of these techniques to the field of magnetic sector mass spectrometry. Gains in signal intensity of 10x and 4x were achieved for 1D and 2D coding techniques (respectively) using a simple 90 degree magnetic sector test setup. Initial compatibility with a higher mass resolution double focusing Mattauch-Herzog mass spectrograph is demonstrated experimentally and with high fidelity particle tracing simulations. A novel electric sector lens system was designed to stigmate high order coded aperture patterned beam which shows simulated gains in signal intensity of 50x are achievable using these techniques.

Domain decomposition method provides a solution for the very large electromagnetic

system which are impossible for single domain methods. Discontinuous Galerkin

(DG) method can be viewed as an extreme version of the domain decomposition,

i.e., each element is regarded as one subdomain. The whole system is solved element

by element, thus the inversion of the large global system matrix is no longer necessary,

and much larger system can be solved with the DG method compared to the

continuous Galerkin (CG) method.

In this work, the DG method is implemented on a subdomain level, that is, each subdomain contains multiple elements. The numerical flux only applies on the

interfaces between adjacent subdomains. The subodmain level DG method divides

the original large global system into a few smaller ones, which are easier to solve,

and it also provides the possibility of parallelization. Compared to the conventional

element level DG method, the subdomain level DG has the advantage of less total

DoFs and fexibility in interface choice. In addition, the implicit time stepping is

relatively much easier for the subdomain level DG, and the total CPU time can be

much less for the electrically small or multiscale problems.

The hybrid of elements are employed to reduce the total DoF of the system.

Low-order tetrahedrons are used to catch the geometry ne parts and high-order

hexahedrons are used to discretize the homogeneous and/or geometry coarse parts.

In addition, the non-conformal mesh not only allow dierent kinds of elements but

also sharp change of the element size, therefore the DoF can be further decreased.

The DGTD method in this research is based on the EB scheme to replace the

previous EH scheme. Dierent from the requirement of mixed order basis functions

for the led variables E and H in the EH scheme, the EB scheme can suppress the

spurious modes with same order of basis functions for E and B. One order lower in

the basis functions in B brings great benets because the DoFs can be signicantly

reduced, especially for the tetrahedrons parts.

With the basis functions for both E and B, the EB scheme upwind

ux and

EB scheme Maxwellian PML, the eigen-analysis and numerical results shows the

eectiveness of the proposed DGTD method, and multiscale problems are solved

eciently combined with the implicit-explicit hybrid time stepping scheme and multiple

kinds of elements.

The EB scheme DGTD method is further developed to allow arbitrary anisotropic

media via new anisotropic EB scheme upwind

ux and anisotropic EB scheme

Maxwellian PML. The anisotropic M-PML is long time stable and absorb the outgoing

wave eectively. A new TF/SF boundary condition is brought forward to

simulate the half space case. The negative refraction in YVO4 bicrystal is simulated

with the anisotropic DGTD and half space TF/SF condition for the rst time with

numerical methods.

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.

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.

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.

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.

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.

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.

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.

As research in electromagnetics has expanded, it has given rise to the examination of metamaterials, which possess nontrivial electromagnetic material properties such as engineered permittivity and permeability. Aside from their application in the microwave industry, metamaterials have been associated with novel phenomena since their invention, including sub-wavelength focusing in negative refractive index slabs, evanescent wave amplification in negative index media, and invisibility cloaking and its demonstration at microwave frequency with controlled material properties in space.

Effective medium theory plays a key role in the development and application of metamaterials, simplifying the electromagnetic analysis of complex engineered metamaterial composites. Any metamaterial composite can be treated as a homogeneous or inhomogeneous medium, while every unit structure in the composite is represented by its permittivity and permeability tensor. Hence, studying an electromagnetic wave's interaction with complex composites is equivalent to studying the interaction between the wave and an artificial material.

This dissertation first examines the application of a magnetic metamaterial lens in wireless power transfer (WPT) technology, which is proposed to enhance the mutual coupling between two magnetic dipoles in the system. I examine and investigate the boundary effect in the finite sized magnetic metamaterial lens using a numerical simulator. I propose to implement an anisotropic and indefinite lens in a WPT system to simplify the lens design and relax the lens dimension requirements. The numerical results agree with the analytical model proposed by Smith et al. in 2011, where lenses are assumed to be infinitely large.

By manipulating the microwave properties of a magnetic metamaterial, the nonlinear properties come into the scope of this research. I chose split-ring resonators (SRR) loaded with varactors to develop nonlinear metamaterials. Analogous to linear metamaterials, I developed a nonlinear effective medium model to characterize nonlinear processes in microwave nonlinear metamaterials. I proposed both experimental and numerical methods here for the first time to quantify nonlinear metamaterials' effective properties. I experimentally studied three nonlinear processes: power-dependent frequency tuning, second harmonic generation, and three-wave mixing. Analytical results based on the effective medium model agree with the experimental results under the low power excitation assumption and non-depleted pump approximation. To overcome the low power assumption in the effective medium model for nonlinear metamaterials, I introduced general circuit oscillation models for varactor/diode-loaded microwave metamaterial structures, which provides a qualitative prediction of microwave nonlinear metamaterials' responses at relatively high power levels when the effective medium model no longer fits.

In addition to 1D nonlinear processes, this dissertation also introduces the first 2D microwave nonlinear field mapping apparatus, which is capable of simultaneously capturing both the magnitude and phase of generated harmonic signals from nonlinear metamaterial mediums. I designed a C-band varactor loaded SRR that is matched to the frequency and space limitation of the 2D mapper. The nonlinear field generation and scattering properties from both a single nonlinear element and a nonlinear metamaterial medium composite are experimentally captured in this 2D mapper, and the results qualitatively agree with numerical results based on the effective medium model.

Microwave imaging platforms conventionally take the form of antenna arrays or synthetic apertures. Inspired by methods in the optical regime, computational microwave imaging has recently taken hold as an alternative approach that uses spatially-diverse waveforms to multiplex scene information. In this dissertation, we use dynamic metasurface apertures to demonstrate improved hardware characteristics and capabilities in computational microwave imaging systems. In particular, we demonstrate waveguide-fed and cavity-backed dynamic metasurface apertures. A waveguide-fed dynamic metasurface aperture consists of a waveguide device loaded with numerous independently tunable metamaterial elements, each of which couples energy from the guided mode into a reconfigurable radiation pattern. We explicate design considerations for a waveguide-fed dynamic metasurface aperture, optimize its usage, and utilize it in computational imaging. In addition, we leverage the dynamic aperture's agility to demonstrate through-wall imaging and beamforming for synthetic aperture radar. Significant attention is also devoted to imaging with a single frequency, an approach which can ease the complexity and improve the performance of the required RF components.

Expanding on the waveguide-fed instantiation, we investigate cavity-backed dynamic apertures. These apertures employ disordered cavity modes to feed a multitude of radiating elements. We investigate this approach with two structures: a volumetric cavity, where we tune the boundary condition, and a planar PCB-based cavity, where the radiating elements are tuned. Capable of generating diverse radiation patterns, we use these structures to assess the utility of dynamic tuning in computational imaging systems. Many of the architectures studied in this dissertation chart a path toward a low-cost dynamic aperture with a favorable form factor, a platform which provides immense control over its emitted fields for a variety of microwave applications.

In this study, we developed and improved the numerical mode matching (NMM) method which has previously been shown to be a fast and robust semi-analytical solver to investigate the propagation of electromagnetic (EM) waves in an isotropic layered medium. The applicable models, such as cylindrical waveguide, optical fiber, and borehole with earth geological formation, are generally modeled as an axisymmetric structure which is an orthogonal-plano-cylindrically layered (OPCL) medium consisting of materials stratified planarly and layered concentrically in the orthogonal directions.

In this report, several important improvements have been made to extend applications of this efficient solver to the anisotropic OCPL medium. The formulas for anisotropic media with three different diagonal elements in the cylindrical coordinate system are deduced to expand its application to more general materials. The perfectly matched layer (PML) is incorporated along the radial direction as an absorbing boundary condition (ABC) to make the NMM method more accurate and efficient for wave diffusion problems in unbounded media and applicable to scattering problems with lossless media. We manipulate the weak form of Maxwell's equations and impose the correct boundary conditions at the cylindrical axis to solve the singularity problem which is ignored by all previous researchers. The spectral element method (SEM) is introduced to more efficiently compute the eigenmodes of higher accuracy with less unknowns, achieving a faster mode matching procedure between different horizontal layers. We also prove the relationship of the field between opposite mode indices for different types of excitations, which can reduce the computational time by half. The formulas for computing EM fields excited by an electric or magnetic dipole located at any position with an arbitrary orientation are deduced. And the excitation are generalized to line and surface current sources which can extend the application of NMM to the simulations of controlled source electromagnetic techniques. Numerical simulations have demonstrated the efficiency and accuracy of this method.

Finally, the improved numerical mode matching (NMM) method is introduced to efficiently compute the electromagnetic response of the induction tool from orthogonal transverse hydraulic fractures in open or cased boreholes in hydrocarbon exploration. The hydraulic fracture is modeled as a slim circular disk which is symmetric with respect to the borehole axis and filled with electrically conductive or magnetic proppant. The NMM solver is first validated by comparing the normalized secondary field with experimental measurements and a commercial software. Then we analyze quantitatively the induction response sensitivity of the fracture with different parameters, such as length, conductivity and permeability of the filled proppant, to evaluate the effectiveness of the induction logging tool for fracture detection and mapping. Casings with different thicknesses, conductivities and permeabilities are modeled together with the fractures in boreholes to investigate their effects for fracture detection. It reveals that the normalized secondary field will not be weakened at low frequencies, ensuring the induction tool is still applicable for fracture detection, though the attenuation of electromagnetic field through the casing is significant. A hybrid approach combining the NMM method and BCGS-FFT solver based integral equation has been proposed to efficiently simulate the open or cased borehole with tilted fractures which is a non-axisymmetric model.

Hydraulic fracturing is an essential way to improve the production of unconventional oil and gas, especially shale gas. Therefore, it is important to characterize the produced fractures using either acoustic or electromagnetic (EM) methods, and evaluation of hydraulic fractures has been under intensive study since last decade. Electromagnetic techniques, including induction logging and galvanic techniques, have the advantages of nondestructive measurements and high sensitivity to the formation and fracture resistivity. They are widely used for produced fracture evaluation.

However, conventional forward and inverse methods in low frequency range face significant challenges by such multiscale problems where the fracture width (<1cm) is orders of magnitude smaller than its diameters (>100 m). The problem becomes much more complicated when the effects of borehole, casing, and planar stratified medium need to be considered for realistic oil field application.

This dissertation focuses on three aspects. First of all, the application of newly developed efficient forward electromagnetic solvers, hybrid distorted Born approximation and mixed ordered stabilized bi-conjugate gradient FFT (DBA-BCGS-FFT) method, and hybrid numerical mode matching with the stabilized bi-conjugate gradient FFT (NMM-BCGS-FFT) method, are illustrated. For the DBA-BCGS-FFT method, the two components of the solver, distorted Born approximation (DBA) and mixed ordered stabilized bi-conjugate gradient FFT (BCGS-FFT), are separately discussed with their advantages and disadvantages. Then the hybrid DBA-BCGS-FFT will be introduced and explained, including how the combination of the advantages of the two solvers and overcome their disadvantages. For the second forward method, the numerical mode matching (NMM) method is introduced with the procedures of the NMM-BCGS-FFT method for analyzing the effects of the complex cased borehole and planar stratified medium.

Second, the inverse solver, variational Born iterative method (VBIM), is introduced for hydraulic fracture reconstruction. The box constraints in the inversion process is introduced to enhance the fracture reconstruction resolution and avoid unrealistic parameter in the inversion. In the procedures of the inverse solver, the forward solvers are applied to construct the system matrix. In this application, the inverse solvers are applied to process the secondary field data obtained by field scanners and laboratory detectors.

The results will be separate into three sections. First, the validation of the forward and inverse solvers is demonstrated. The commercial software, COMSOL, is used for the validation. Then, induction logging detection and galvanic detection model results show the capability of the forward and inverse solvers. Last, two established experiment systems will be described with details. The laboratory scaled experimental system is established for feasibility study of the electromagnetic induction detection, and the field test control source electromagnetic system is designed and built for hydraulic fracture evaluation. In induction logging detection model, experimental results show that the inverse scattering algorithm is effective for electromagnetic contrast enhanced through-casing hydraulic fracture evaluation. In galvanic detection model, the impact of different hydraulic fracturing material and choices of transmitter/receiver locations on signal response will be discussed to show the application of the forward solvers in field configuration design. Both fracture reconstruction results by the inverse solvers with the experimental data will be discussed in these two chapters.

For the petroleum industry, layered medium subsurface detection plays an important role in discovering reservoirs and drilling wells. In geophysics, resistivity is an essential property for distinguishing formation layers or even small fractures. Well logging with electromagnetic induction tools can measure the subsurface resistivity. This measurement includes two steps: 1) directly measure the low-frequency response signals using the tool and 2) determine the subsurface geometric model and resistivity. The problem is that no formula can directly calculate the resistivity from the measured tool responses. A systematic solution is to combine forward electromagnetic simulations and inversion of the subsurface model. In this dissertation, two categories of inversion are investigated: Determine the proper subsurface model by 1) optimizing the objective function, such as data misfit, and 2) training a surrogate model for the inverse mapping. Many forward simulations are demanded for either estimating the data misfit of new candidate models or collecting data for training. Therefore, efficient electromagnetic simulation is critical for resistivity logging. From complex to simple, three types of simulation are discussed: 1) borehole simulation with real tool configuration, 2) borehole simulation with point sources as the virtual tool, and 3) simplified layered medium simulation with virtual tool. Three optimal methods are implemented, respectively: the domain decomposition method, the finite element boundary integral method, and the analytical method. The tool calibration and the borehole effects are studied in the comparison of these simulations. Ideally, the simplest forward simulation should be used in the inversion, and the additional effects can be extracted as correction terms. The optimization-based inversion of the formation model uses simulations of a virtual tool in the layered medium. The Occam inversion or Monte Carlo Markov chain can minimize the data misfit. Another special simulation for small fractures using the thin dielectric sheet approximate method collects the dataset of fracture models. Fracture parameters such as resistivity, extension, and tilt angle are accurately determined by machine learning methods. The surrogate model also tends to predict fracture properties correctly, even for the complete simulation result.

Electromagnetic forward modeling and inversion methods have extensive applications in geophysical exploration, and large-scale controlled-source electromagnetic method has recently drawed lots of attention. However, to obtain a rigorous and efficient forward solver for this large-scale three-dimensional problem is difficult, since it usually requires to solve for a large number of unknowns from a system of equations describing the complicate scattering behavior of electromagnetic waves that happened within inhomogeneous media. As for the development of an efficient inversion solver, because of the nonlinear, non-unique and ill-posed properties of the problem, it is also a very challenging task.

In the first part of this dissertation, a fast three-dimensional nonlinear reconstruction method is proposed for controlled-source electromagnetic method. The borehole-to-surface and airborne electromagnetic survey methods are investigated using synthetic data. In this work, it is assumed that there is only electric contrast between the inhomogeneous object and the layered background medium, for the reason that the electric contrast is much more dominant than magnetic contrast in most cases of the earth formation. Therefore, only the EFIE is needed to solve. While the forward scattering problem is solved by the stabilized bi-conjugate gradient FFT (BCGS-FFT) method to give a rigorous and efficient modeling, the Bore iterative method along with the multiplicative regularization technique is used in the inversion through frequency hopping. In the inversion, to speed up the expensive computation of the sensitivity matrix relating every receiver station to every unknown element, a fast field evaluation (FFE) technique is proposed using the symmetry property of the layered medium Green's function combined with a database strategy. The conjugate-gradient method is then applied to minimize the cost function after each iteration. Due to the benefits of using 3D FFT acceleration, the proposed FFE technique as well as the recursive matrix method combined with an interpolation technique to evaluate the LMGF, the developed inversion solver is highly efficient, and requires very low computation time and memory. Numerical experiments for both 3D forward modeling and conductivity inversion are presented to show the accuracy and efficiency of the method.

Some recent research on artificial nanoparticles have demonstrated the improved performance in geophysical imaging using magnetodielectric materials with enhanced electric and magnetic contrasts. This gives a promising perspective to the future geophysical exploration by infusing well-designed artificial magnetodielectric materials into the subsurface objects, so that a significantly improved imaging can be achieved. As a preparation for this promising application, the second part of the dissertation presents an efficient method to solve the scattering problem of magnetodielectric materials with general anisotropy that are embedded in layered media. In this work, the volume integral equation is chosen as the target equation to solve, since it solves for fields in inhomogeneous media with less number of unknowns than the finite element method. However, for complicated materials as magnetodielectric materials with general anisotropy, it is a very challenging task, because it requires to simultaneously solve the electric field integral equation (EFIE) and magnetic field integral equation (MFIE). Besides that, the numerous evaluation of the layered medium Green's function (LMGF) for the stratified background formation adds on the difficulty and complexity of the problem. To my knowledge, there is no existing fast solver for the similar problem. In this dissertation, using the mixed order stabilized biconjugate-gradient fast Fourier transform (mixed-order BCGS-FFT) method, a fast forward modeling method is developed to solve this challenging problem. Several numerical examples are performed to validate the accuracy and efficiency of the proposed method.

Besides the above mentioned two topics, one-dimensional inversion method is presented in the third part to determine the tilted triaxial conductivity tensor in a dipping layered formation using triaxial induction measurements. The tilted triaxial conductivity tensor is described by three conductivity components and three Euler angles. Based on my knowledge, due to the highly nonlinear and ill-posed nature of the inverse problem, this study serves as the first work that investigates on the subject. There are six principal coordinate systems that can give the same conductivity tensor. Permutation is performed to eliminate the ambiguity of inversion results caused by the ambiguity of the principal coordinate system. Three new Euler angles after permutation for each layer can be found by solving a nonlinear equation. Numerical experiments are conducted on synthetic models to study the feasibility of determining triaxially anisotropic conductivity tensor from triaxial induction data. This project is accomplished during my internship in the Houston Formation Evaluation Integration Center (HFE) at Schlumberger, a world-leading oilfield service company.

This thesis examines the bandwidth shortcomings of conventional inductive coupling biotelemetry systems for implantable devices, and presents two approaches toward an end-to-end biotelemetry system for reducing the power consumption of implanted devices at increased levels of bandwidth. By leveraging the transition zone between the near and far field, scattering in the near field at UHF frequencies for increased bandwidth at low power budgets can be employed. Additionally, taking advantage of surface wave propagation permits the use of single-wire RF transmission lines in biological tissue, offering more efficient signal routing over near field coupling resulting in controlled implant depth at low power budgets.

Due to the dielectric properties of biological tissue, and the necessity to operate in the radiating near field to communicate via scattered fields, the implant depth drives the carrier frequency. The information bandwidth supplied by each sensing electrode in conventional implants also drives the operating frequency and regime. At typical implant depths, frequencies in the UHF range permit operation in the radiating near field as well as sufficient bandwidth.

Backscatter modulation provides a low-power, high-bandwidth alternative to conventional low frequency inductive coupling. A prototype active implantable device presented in this thesis is capable of transmitting data at 30 Mbps over a 915 MHz link while immersed in saline, at a communication efficiency of 16.4 pJ/bit. A prototype passive device presented in this thesis is capable of operating battery-free, fully immersed in saline, while transmitting data at 5 Mbps and consuming 1.23 mW. This prototype accurately demodulates neural data while immersed in saline at a distance of 2 cm. This communication distance is extended at similar power budgets by exploiting surface wave propagation along a single-wire transmission line. Theoretical models of single-wire RF transmission lines embedded in high permittivity and conductivity dielectrics are validated by measurements. A single-wire transmission line of radius 152.4 um exhibits a loss of 1 dB/cm at 915 MHz in saline, and extends the implant depth to 6 cm while staying within SAR limits.

This work opens the door for implantable biotelemetry systems to handle the vast amount of data generated by modern sensing devices, potentially offering new insight into neurological diseases, and may aid in the development of BMI's.