Browsing by Subject "Metamaterials"

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 In the case of aperiodic structures, the periodic assumption is no longer valid, and the electromagnetic behavior cannot be predicted accurately.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.

Complex artificial materials (metamaterials) strongly interact with light and can be used to fabricate structures which mimic a material response that has no natural equivalent. Classical tools for the design of optical or radio frequency devices are often ill-suited to utilize such media or have shortcomings in their ability to capture important physics in the device behavior. Recently it has been demonstrated that the structure of Maxwell's equations can be used to exploit this newly available freedom. By leveraging the `form-invariance' of Maxwell's equations under coordinate transforms, it is possible to develop material distributions in which light will behave as though flowing through warped coordinates. This design process is termed `transformation optics' and has inspired the creation of many novel electromagnetic structures such as the invisibility cloak.

In this dissertation the tools used in the field of transformation optics will be explored and expanded. Several new designs are discussed, each of which expands upon the ideas that have previously been employed in the field. To begin, I show that the explicit use of a transformation which extends throughout all space may be used to reduce the overall size of an optical device without changing its optical properties. A lens is chosen as a canonical device to demonstrate this behavior. For this work I provided the original idea for a compressing transformation as well as its dielectric-only implementation. I then mentored Dan Roberts as he confirmed the device properties through simulation. I further demonstrate that currents may be succesfully employed within the framework of transformation optics-resulting in novel antenna designs. For this work I suggested handling the sheet currents as the limit of a volumetric current density. I also demonstrated how an intermediate coordinate system could be used to easily handle the types of transformatios which were being explored.

For a particular functionality the choice of transformation is, in general, not unique. It is natural, then, to seek optimized transformations which reduce the complexity of the final structure. It was recently demonstrated that for some transformations a numerical scheme could be employed to find quasi-conformal transformations for which the requisite complex material distribution could be well approximated by an isotropic, inhomogeneous media. This process was previously used to demonstrate a carpet cloak-a device which masks a bump in a mirror surface. Unlike the more common transformation optical media, which exhibit strong losses at high frequencies, isotropic designs can be readily made to function at infrared or even optical frequencies.

The prospect of leveraging transformation optics in devices which operate at high frequencies, into the infrared and visible, motivates the use of quasi-conformal transformations in lens design. I demonstrate how transformation optics can be used to take a classical lens design based on spherical symmetry, such as a Luneburg lens, and warp it to suit the requirements of a planar imaging array. I report on the experimental demonstration of this lens at microwave frequencies. In the final design a lens is demonstrated in a two-dimensional field mapping waveguide to have a field of view of ~140 degrees and a bandwidth exceeding a full decade. In this work I proposed the idea of using the inverse of the quasi-conformal transform to arrive at the lens index profile. I performed all necessary simulations and wrote ray tracing code to confirm the properties of the lens. I proposed the metamaterial realization of the lens and performed the necessary retrievals for material design. I wrote code which would create the layout for an arbitrary gradient index structure in a standard computer aided drafting format. I fabricated three lenses-two of which are described in this thesis-and took all of the data shown in the thesis.

The most well known example of a transformation optical device is the invisibility cloak. Despite the great deal of attention paid to the cloak in the literature, the most natural way in which to quantify the efficacy of the cloak-its cross-section-has never been experimentally determined. This measurement is of practical interest because the cloak provides a useful canonical example of a medium which relies on the unique properties of metamaterials-strong anisotropy, inhomogeneity and both magnetic and electric response. Thus, a cloaking cross-section measurement provides a useful way to quantify advancements in the effective medium theories which form the basis for metamaterials. I report on the first such measurements, performed on the original microwave cloaking design. The experiments were carried out in a two-dimensional TE waveguide. Explicit field maps are used to determine the Bessel decomposition of the scattered wave. It is found that the cloak indeed reduces the scattering cross-section of a concealed metal cylinder in a frequency band from 9.91 to 10.14 GHz. The maximum cross-section reduction was determined to be 24%. The total cross-section and the Bessel decomposition of the scattered wave are compared to an analytical model for the cloaking design which assumes a discrete number of loss-less, homogenized cylinders. While the qualitative features of the cloak-a reduced cross-section at the cloaking frequency-are realized, there is significant deviation from the homogenized calculation. These deviations are associated with loss and inaccuracies of the effective-medium-model for metamaterials. In this work I proposed of direct integration of the fields to perform cross-section measurements. I worked out the necessary formulas to determine the coefficients in the Bessel expansion and the resulting scattering cross-section. I mentored an undergraduate student, Dan Gaultney, who scripted the application of the cross-section analysis and took the necessary data. All of the data in this thesis, however, is based on my own implementation of the data analysis.

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.

Microwave imaging systems often utilize electrically large arrays for remote characterization of spatial and spectral content. Image reconstruction involves computational processing, the success of which depends on adequate spatial and temporal sampling at the array as dictated by the nature of the radiation and sensing strategy. Effective design of an imaging system, consisting of its hardware and algorithmic components, thus requires detailed understanding of the nature of the involved fields and their impact on the processing capabilities. One can sufficiently characterize many of the properties of such fields and systems via coherence, which quantifies their interferometric capacity in terms of statistical correlations and point spread functions. Recent work on dynamic metasurface apertures (DMAs) for microwave imaging has demonstrated the utility of these structures in active, coherent systems, supplanting traditional array architectures with lower-cost designs capable of powerful wavefront shaping. In contrast to arrays of distinct antennas, DMAs are composed of electrically large arrays of dynamically-tunable, radiating metamaterial elements to realize diverse gain patterns that can function as an encoding mechanism for coded aperture image reconstruction. With the appropriate formulation, well-established concepts from the realm of Fourier optics can be transposed from conventional array systems to DMA architectures. This dissertation furthers that task by modeling DMA imaging systems involving partial coherence and incoherence, and demonstrating new reconstruction algorithms in these contexts. Such an undertaking provides convenient opportunities for examining the origins of coherence in computational and holographic imaging systems. This insight is necessary for the development of modern approaches that seek to smoothly integrate hardware and computational elements for powerful, efficient, and innovative imaging tasks.

Accommodating different degrees of coherence in a microwave imaging system can substantially relax demands on hardware components including phase stability and synchronization, or on algorithmic procedures such as calibration. In addition, incoherent operation can yield improved images free of coherent diffraction artifacts and speckle. Finally, an understanding of coherence can unlock fundamentally distinct applications, such as passive imaging and imaging with ambient illumination, that can benefit from the flexibility of a DMA system but have yet to be demonstrated under such an architecture. To this end, I formulate a unified framework for analyzing and processing array imaging systems in the Fourier domain, and demonstrate a method for transforming a DMA-based system to an equivalent array representation under active, coherent operation. I then investigate the role of spatial coherence in a two-dimensional holographic imaging system, and experimentally demonstrate some results using a collection of DMAs. I conduct a similar investigation in the context of single-pixel ghost imaging, which allows coherent and incoherent imaging directly from intensity measurements, thereby relaxing hardware phase requirements. I then formulate a model for partially coherent fields in a DMA imaging system, and provide several reconstruction strategies and example simulations. I finally restrict this general case to passive, spectral imaging of spatially and temporally incoherent sources, and experimentally demonstrate a compressive imaging strategy in this context.

The field of metamaterials has gained much attention within the scientific community over the past decade. With continuing advances and discoveries leading the way to practical applications, metamaterials have earned the attention of technology based corporations and defense agencies interested in their use for next generation devices. With the fundamental physics developed and well understood, current research efforts are driven by the demand for practical applications, with a famous example being the well-known microwave "invisibility cloak." Gaining exotic electromagnetic properties from their structure as opposed to their

intrinsic material composition, metamaterials can be engineered to

achieve tailored responses not available using natural materials. With typical designs incorporating resonant and dispersive elements much smaller than the operating wavelength, a homogenization scheme is possible, which leads to the meaningful interpretation of effective refractive index, and hence electric permittivity and magnetic permeability. The typical metamaterial is composed of arrays of scattering elements embedded in a host matrix. The scattering elements are typically identical, and the electromagnetic properties of the medium can be inferred from the properties of the unit cell. This convenience allows the designer to engineer the effective electromagnetic parameters of the medium by modifying the size, shape, and composition of the unit cell.

This dissertation summarizes several key projects related to my research efforts in metamaterials. The main focus of this dissertation is to develop practical approaches to frequency tunable and reconfigurable metamaterials. Chapter one serves as a background and introduction to the field of metamaterials. The purpose of chapters two, three and four is to develop different methods to realize tunable metamaterials - a broad class of controllable artificially engineered metamaterials. The second chapter develops an approach to characterizing metamaterials loaded with RF MEMS switches. The third chapter examines the effects of loading

metamaterial elements with varactor diodes and tunable ferroelectric

thin film capacitors (BST) for external tuning of the effective medium parameters, and chapter four develops a more advanced method to control the response of metamaterials using a digitally addressable control network. The content of these chapters leads up to an interesting application featured in chapter five - a reconfigurable frequency selective surface utilizing tunable and digitally addressable tunable metamaterials. The sixth and final chapter summarizes the dissertation and offers suggestions for future work in tunable and reconfigurable metamaterials. It is my hope that this dissertation will provide the foundation and motivation for new researchers in the field of metamaterials. I am confident that the reader will gain encouragement from this work with the understanding that very interesting and novel practical devices can be created using metamaterials. May this work be of aid and motivation to their research pursuits.

Acoustic metamaterials are engineered materials that were extensively investigated over the last years mainly because they promise properties otherwise hard or impossible to find in nature. Consequently, they open the door for improved or completely new applications (e.g. acoustic superlens that can exceed the diffraction limit in imaging or acoustic absorbing panels with higher transmission loss and smaller thickness than regular absorbers). Our objective is to surpass the limited frequency

operating range imposed by the resonant mechanism that s1ome of these materials have. In addition, we want acoustic metamaterials that could be experimentally demonstrated and used to build devices with overall performances better than the previous ones reported in the literature.

Here, we start by focusing on the need of engineered metamaterials in general and acoustic metamaterials in particular. Also, the similarities between electromagnetic metamaterials and acoustic metamaterials and possible ways to realize broadband acoustic metamaterials are briefly discussed. Then, we present the experimental realization

and characterization of a two-dimensional (2D) broadband acoustic metamaterial with strongly anisotropic effective mass density. We use this metamaterial to realize a 2D broadband gradient index acoustic lens in air. Furthermore, we optimize the lens design by improving each unit cell's performance and we also realize a 2D acoustic ground cloak in air. In addition, we explore the performance of some novel applications (a 2D acoustic black hole and a three-dimensional acoustic cloak) using the currently available acoustic metamaterials. In order to overcome the limitations of our designs, we approach the active acoustic metamaterials path, which offers a broader range for the material parameters values and a better control over them. We propose two structures which contain a sensing element (microphone) and an acoustic driver (piezoelectric membrane or speaker). The material properties are controlled by tuning the response of the unit cell to the incident wave. Several samples with interesting effective mass density and bulk modulus are presented. We conclude by suggesting few natural directions that could be followed for the future research based on the theoretical and experimental results presented in this work.

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 early as 1949, it was predicted that a technological gap would form in the far infrared. This so-called ``terahertz gap" is the result of two limitations. On one side, the atomic phenomena giving rise to laser technologies are difficult to extend below $10$ terahertz (THz), and on the other, microwave technologies are difficult to extend above $0.1$ THz. Even today, while this gap has closed to some extent, the generation and detection of electromagnetic radiation in this bandwidth remains inefficient and impractical, especially when compared to more mature technologies based in optical and microwave frequencies. The terahertz gap thus provides an exciting opportunity for innovation and the development of novel imaging techniques.

Metamaterials are a natural fit for the above problem because their electromagnetic properties are determined by their geometry, so they are fundamentally less limited by the physical properties of the materials of which they are composed. This means that a designed electromagnetic response can be scaled to many different bands--including the terahertz--simply by scaling the geometry accordingly. However, the process of designing and optimizing metamaterials is nontrivial and still very much an area of active research. Chapter 6 in particular will describe some new approaches for metamaterial design based on machine learning methods.

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.

To date metamaterials and metasurfaces have been studied for over 20 years. Throughout this time sophisticated understanding of their properties and capabilities has been developed, with many significant and exotic properties such as flat lenses, negative refraction, and perfect absorption. In this work significant advances are made in two main areas. First we explore the subject of the all dielectric metasurface, implemented as arrays of dielectric cylinders. Here, we improve upon the current understanding of absorption in all-dielectric metasurfaces; we demonstrate the significance of periodicity, outlining special properties of the dielectric metasurface, and finally we apply developed knowledge about mode confinement in the dielectric metasurface to a novel system utilizing phase change materials. Second, traditional metal-insulator-metal metasurfaces with advanced capabilities are developed. We utilize the electronic compatibility of the MIM system to incorporate spatio-temporal modulation, enabling a new class of nonreciprocal reflectarrays. Finally we present a general, algorithmic optimization that brings our nonreciprocal metasurface to application-relevant efficiencies.

This dissertation examines the use of artificial structured materials -- known as metamaterials -- in two antenna applications in which conventional dielectric materials are otherwise used. In the first application, the use of metamaterials to improve the impedance matching of planar phased array antennas over a broad range of scan angles is explored. A phased array antenna is composed of an array of antenna elements and enables long-distance signal propagation by directional radiation. The direction of signal propagation is defined as the scan angle. The power transmission ratio of a phased array is the ratio of the radiated power to the input power, and depends on the scan angle. The variation in the power transmission ratio is due to the different mutual coupling contributions between antenna elements at different scan angles. An optimized stack of dielectric layers, known as a wide-angle impedance matching layer (WAIM), is used to optimize the power transmission ratio profile over a broad range of scan angles. In this work, the use of metamaterials to design anisotropic WAIMs with access to a larger range of constitutive parameters -- including magnetic permeability -- to offer an improved power transmission ratio at a broad range of scan angles is investigated.

In the second antenna application, a strategy to create maximally transmissive and minimally reflective electromagnetic radome materials using embedded metamaterial inclusions is introduced. A radome is a covering used to protect an antenna from weather elements or provide structural function such as the prevention of aerodynamic drag. A radome should be made from a fully transparent and non-refractive material so that radiated fields from and to the enclosed antenna are not disrupted. The aim of this research was to demonstrate that embedded metamaterial inclusions can be used to isotropically adjust the dielectric properties of a composite material to a desired value. This strategy may lead to the creation of a structural material with electromagnetic properties close to air, thus reducing the detrimental scattering effects often associated with conventional radome materials.

Chapter 1 introduces the concept of metamaterials and discusses the use of subwavelength metallic structures to artificially engineer constitutive parameters such as permeability of permittivity. In Chapter 2, the analytical formulations that enable the characterization of the transmission performance of a planar phased array covered with anisotropic impedance matching layers are developed. Chapter 3 discusses the design rules that must govern the design parameters of anisotropic WAIMs realizable using metamaterials, and also presents examples of anisotropic impedance matching layers that provide a maximum power transmission ratio for most scan angles. In addition, numerical and experimental results on a metamaterial placed over a phased array are presented. In Chapter 4, the feasibility of using metamaterials to realize a minimally transparent and fully transmissive radome material is numerically investigated. In Chapter 5, experimental results that corroborate earlier numerical simulation results are analyzed.

The overarching problem addressed in this dissertation is the restricted number of devices that operate in the millimeter wave, terahertz, and infrared regimes using conventional materials. Devices designed for operation at these wavelengths are incredibly valuable across various applications such as material characterization, imaging technologies, and communication systems. However, the scarcity of devices is attributed, in part, to the limited availability of naturally occurring materials that can operate in these ranges. Therefore, there is an exciting opportunity to tailor electromagnetic metamaterials for millimeter wave, terahertz, and infrared manipulation.

Electromagnetic metamaterials have been shown to enable unique scattering effects leading to advancements in next-generation devices. One important feature of metamaterials is the ability to tune the geometry and engineer the scattered response for nearly any range of the electromagnetic spectrum. Therefore, the exploration and development of advanced electromagnetic metamaterials for use in millimeter wave, terahertz, and infrared regimes is of great importance.

Chapter 1 provides a discussion on the importance of millimeter wave, terahertz, and infrared radiation. In addition, this chapter provides an introduction to electromagnetic metamaterials. Chapters 2 and 3 discuss two metamaterials designed for operation at millimeter wavelengths. In Chapter 2, a metamaterial coherent detector is presented and in Chapter 3, a metamaterial gradient index lens is introduced.

Several metamaterials for operation in the terahertz range are studied and discussed in Chapter 4, 5, and 6. In Chapter 4, exotic physics is studied and results in the excitation of high-quality factor modes. Chapter 5 introduces an electromagnetic absorber for radiometric calibration applications. Lastly, Chapter 6 presents a metamaterial strain sensor. A reflective and transmissive metamaterial diffuser is studied in Chapter 7 for use in the infrared regime. An in-depth discussion on the fabrication of all presented metamaterials is included in Chapter 8. Finally, a summary of all presented works and concluding thoughts is included in Chapter 9.

Metamaterials have gained extensive attention in recent years due to their ability to exhibit material properties otherwise difficult or impossible to obtain using natural materials. Nonlinear and active metamaterials in particular exhibit great promise for exploring new effects and applications, from tunability to mixing. However, nonlinear and active metamaterials have been explored significantly less than linear metamaterials to this point and much work has focused on the fundamental physics of nonlinear metamaterials. Our aim is to further extend the knowledge of practical nonlinear metamaterials and to demonstrate how they can be transformed to real-world applications through the use of embedded devices. In this dissertation, we demonstrate a variety of ways that devices can be embedded within metamaterial unit cells to provide nonlinear and active effects.

Chapter 1 introduces the basic theory of metamaterials, background of existing work, and the current limitations of nonlinear and active metamaterial design. In Chapter 2, we present the design, simulation, fabrication, and verification of an RF limiter metamaterial. We show how a metamaterial can be designed using RF engineering principles to act as an effective limiter in a new topology, relying on nonlinear devices embedded within a metamaterial. Chapter 3 shows our design and demonstration of a power harvesting metamaterial. We design a nonlinear metamaterial towards a potential application, discussing how the selection of an appropriate embedded device provides our desired functionality. In Chapter 4 we show how nonlinear and active metamaterials can be used to realize phase conjugation, including demonstration of negative refraction and imaging through the use of these metamaterials. We also discuss design approaches to moving these metamaterials towards real-world applications. Chapter 5 discusses our work concerning metamaterials based on transistors. First we show that appropriate design of a transistor circuit allows us to tune the quality factor and resonant frequency of a metamaterial. We use this metamaterial for time-varying mixing, as well, demonstrating a mixing metamaterial that remains linear. We then illustrate how using transistors as nonlinear devices provides much greater design freedom for use with metamaterials. We show that the nonlinearity of a metamaterial can be dramatically enhanced through the use of transistors and even dynamically tuned, applying these nonlinear metamaterials to applications including phase conjugation and acoustoelectromagnetic modulation. In Chapter 6 we summarize the achievements of the presented research and directions for future work that build on the work described in this thesis.

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.

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 fÉ = 10.6 fÊm. 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 fÊm. 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.

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 fÊm ~ 750 fÊm. Each pixel is comprised of metamaterial elements. This simple demonstration shows the potential for practical applications of metamaterial based diffractive optics.

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 fÉ = 1.55 fÊm. 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.

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.

The observation and use of thermal radiation has a long history. Significant advance was made in 1879 when Josef Stefan found that “the total radiated power per unit surface area of a black body across all wavelengths is directly proportional to the fourth power of its temperature”, which was later named the Stefan–Boltzmann law. The Stefan–Boltzmann law sets a limit for the thermal radiation from most of natural materials, since their total radiated energy is proportional to the fourth power of their temperature. Thus, use of natural materials for the control and manipulation of thermal emission is hindered from further development. Metamaterials are artificial materials consisting of sub-wavelength unit cells, and good candidates to break these limitations, since the optical properties of metamaterials originates from their geometrical designs, as opposed to their chemical composition. Here we propose and demonstrate the idea of metamaterial based on microelectromechanical system capable of dynamically tailoring the energy emitted from a surface, with its emission performance going beyond the Stefan–Boltzmann law. Our dynamic metamaterial emitters have great application prospects in energy harvesting, space exploration, sensing and detecting, and many other areas. In addition, our results are not limited to the thermal infrared band, demonstrate here, but may be scaled to nearly any sub-optical range of the electromagnetic spectrum, and verify the potential of MEMS metamaterials to operate as reconfigurable multifunctional devices with unprecedented energy control capabilities.

Although metamaterial may yield advanced thermal emission control, they are difficult to apply to some applications, such as in thermal imaging and energy harvesting with thermophotovoltaics. This is because they are typically fashioned with metallic materials and thus possess low melting points, high Ohmic loss, and high thermal conductivity. Here we present an all dielectric metamaterial absorber/emitter. By overlapping the electric and magnetic dipole resonances, a high absorptive / emissive state can be achieved. Due to its great thermal properties, such as heat localization and thermal stability, an all dielectric metamaterial absorber/ emitter can replace metal-based metamaterial in some application areas, and offers a new route for applications in thermophotovoltaics, imaging, and sensing.

This dissertation consists of seven chapters. The first chapter gives a brief introduction to thermal radiation, metamaterials, metamaterial absorbers, and all dielectric metamaterials. The second chapter discusses in detail thermochromic infrared metamaterials. The third chapter demonstrates a reconfigurable room temperature metamaterial infrared emitter. The fourth chapter shows a THz all dielectric metamaterial absorber. The fifth chapter gives another example of all dielectric metamaterial emitters that can be used in thermophotovoltaic systems. The sixth chapter is a summary. The seventh chapter is an executive summary of original contributions.

The advent of resonant metamaterials with strongly dispersive behavior allowed scientists to design new electromagnetic devices -- including (but not limited to) absorbers, antennas, lenses, holograms, and arguably the most well-known of them all, invisibility cloaks -- exhibiting properties that would otherwise be difficult to obtain. At the heart of these breakthrough designs is our ability to model the behavior of individual metamaterial elements as Lorentzian dipoles, and -- in applications that call for it -- collectively model an entire array of such elements as a homogenous medium with effective electromagnetic properties retrieved from measurements or simulations.

Of particular interest in the context of this dissertation is a certain type of metamaterials elements which -- while composed entirely of essentially non-magnetic materials -- respond to a magnetic field, can be modeled as magnetic dipoles, and are able to form a material with effective magnetic response. This thesis describes how such ``magnetic metamaterials'' have been utilized by the author when designing devices for applications in wireless power transfer (WPT) and computational imaging. For the former, I discuss in the thesis a metamaterial implementation of a magnetic `superlens' for wireless power transfer enhancements, and a magnetic reflector for near field shielding. For the latter I detail how we model the imaging capabilities of a recently-introduced class of dispersive metamaterial-based leaky apertures that produce pseudo-random measurement modes, and demonstration of novel Lorentzian-constrained holograms able to tailor their radiation patterns.

To design a magnetic superlens for WPT enhancements, we first demonstrate how an array comprising resonant metamaterial elements can act as an effective medium with negative permeability ($\mu$) and enhance near-field transmission of quasi-static non-resonant coil antennas. We implement a new technique to retrieve all diagonal components of our superlens' permeability, including its normal component, which standard techniques cannot retrieve. We study the effect of different components of the $\mu$ tensor on field enhancements using analytical solutions as well as 2D rotationally-symmetric full-wave simulations which approximate the lens as a disc of equal diameter, enabling highly efficient axisymmetric description of the problem. Our studies indicate enhancements are strongest when all three diagonal components of Re$(\mu)$ are negative, which we attribute to the excitation of surface waves.

The ability to retrieve permeability's normal component, awarded to us with the implementation of the aforementioned retrieval technique, directly enabled the design of a near field magnetic shield, which -- in contrast to the tripple-negative superlens -- relies on the normal component of $\mu$ assuming values near zero. The thesis discusses the theory behind this phenomenon and explains why such an anisotropic slab is capable of reflecting magnetic fields with component of their wave vector parallel to the slab's surface (fields which contain significant portions of the energy transferred in WPT systems with dipole-like coils). Furthermore, the dispersive nature of the resonant metamaterials used to realize the shield grants us the ability to block certain frequencies while allowing the transmission of other, which can be particularly useful in certain applications; conventional materials used for shielding or electromagnetic interference (EMI) suppression, on the other hand, block frequencies indiscriminately.

The thesis also discusses a single-pixel, metamaterial-based aperture we designed for computational imaging purposes. This aperture, termed \textit{metaimager}, forms pseudo-random radiation patterns that vary with frequency by leaking energy from a guided mode via a collection of randomly distributed resonant metamaterial elements. The metaimager, then, is able to interrogate a scene without any moving parts or expensive auxiliary hardware (both are common problems which plague synthetic aperture and phased array systems, respectively). While such a structure cannot be homogenized, when modeling its imaging capabilities we still rely on the fact each of its irises can be modeled analytically as a magnetic dipole using a relatively simple Lorentzian expression. Accurate qualitative modeling of such apertures is of paramount importance in the design and optimization stages, since it allows us to save time and money by avoiding prohibitively slow full-wave simulations of such complex structures and unnecessary fabrication processes.

Lastly, the thesis discusses how such an aperture can be viewed as a hologram in which pixels are realized by the metamaterial elements and the reference wave is realized by the fields that excite them. While the current metaimager implementation produces pseudo-random modes, the last section of the thesis discusses how, by accounting for the Lorentzian constraints of each pixel, a novel metamaterial hologram can be designed to yield tailored radiation patterns. An experiment utilizing a Fraunhofer hologram excited in a free-space illumination configuration indicates tailored modes can indeed be formed by carefully choosing the resonance frequency and location of each metamaterial. While this proof-of-concept example is relatively simple, more sophisticated realizations of such holograms can be explored in future works.

Metamaterials extend the design space, flexibility, and control of optical material systems and so yield fundamentally new computational imaging systems. A computational imaging system relies heavily on the design of measurement modes. Metamaterials provide a great deal of control over the generation of the measurement modes of an aperture. On the other side of the coin, computational imaging uses the data that that can be measured by an imaging system, which may limited, in an optimal way thereby producing the best possible image within the physical constraints of a system. The synergy of these two technologies - metamaterials and computational imaging - allows for entirely novel imaging systems. These contributions are realized in the concept of a frequency-diverse metamaterial imaging system that will be presented in this thesis. This 'metaimager' uses the same electromagnetic flexibility that metamaterials have shown in many other contexts to construct an imaging aperture suitable for single-pixel operation that can measure arbitrary measurement modes, constrained only by the size of the aperture and resonant elements. It has no lenses, no moving parts, a small form-factor, and is low-cost.

In this thesis we present an overview of work done by the author in the area of metamaterial imaging systems. We first discuss novel transformation-optical lenses enabled by metamaterials which demonstrate the electromagnetic flexibility of metamaterials. We then introduce the theory of computational and compressed imaging using the language of Fourier optics, and derive the forward model needed to apply computational imaging to the metaimager system. We describe the details of the metamaterials used to construct the metaimager and their application to metamaterial antennas. The experimental tools needed to characterize the metaimager, including far-field and near-field antenna characterization, are described. We then describe the design, operation, and characterization of a one-dimensional metaimager capable of collecting two-dimensional images, and then a two-dimensional metaimager capable of collecting two-dimensional images. The imaging results for the one-dimensional metaimager are presented including two-dimensional (azimuth and range) images of point scatters, and video-rate imaging. The imaging results for the two-dimensional metaimager are presented including analysis of the system's resolution, signal-to-noise sensitivity, acquisition rate, human targets, and integration of optical and structured-light sensors. Finally, we discuss explorations into methods of tuning metamaterial radiators which could be employed to significantly increase the capabilities of such a metaimaging system, and describe several systems that have been designed for the integration of tuning into metamaterial imaging systems.

Synthetic aperture radar offers unparalleled satellite imaging capabilities for planetary observation. Future systems will realize high resolution with near-real-time revisit rates by using coordinated satellites, but their development has been slowed by the high cost, high power draw, and substantial weight associated with existing antenna technology. Metasurface antennas - a lightweight, low cost, and planar alternative - can address these challenges to make large scale, multi-satellite systems practical. In this work, an electronically steered metasurface antenna prototype is developed for synthetic aperture imaging. A cohesive approach to modeling and design led to a Nyquist sampled layout which minimizes inter-element coupling and suppresses grating lobes. Experimental measurements validate its ability to steer a beam in 2D across a wide bandwidth. Robust performance and favorable hardware characteristics have poised metasurface antennas to affect many microwave industries and to facilitate multi-satellite constellations for spaceborne synthetic aperture radar.

A patterned metasurface can strongly scatter incident light, functioning as an extremely low-profile lens, filter, reflector or other optical devices. Nonlinear metasurfaces‒combine the properties of natural nonlinear medium with novel features such as negative refractive index, magneto-electric coupling‒provide novel nonlinear features not available in nature. Compared to conventional optical components that often extend many wavelengths in size, nonlinear metasurfaces are flexible and extremely compact.

Characterization of a nonlinear metasurface is challenging, not only due to its inherent anisotropy, but also because of the rich wave interactions available. This thesis presents an overview of the work by the author in modeling and application of nonlinear metasurfaces. Analytical methods - transfer matrix method and surface homogenization method - for characterizing nonlinear metasurfaces are presented. A generalized transfer matrix method formalism for four wave mixing is derived, and applied to analyze nonlinear interface, film, and metallo-dielectric stack. Various channels of plasmonic and Fabry-perot enhancement are investigated. A homogenized description of nonlinear metasurfaces is presented. The homogenization procedure is based on the nonlinear generalized sheet transition conditions (GSTCs), where an optically thin nonlinear metasurface is modeled as a layer of dipoles radiating at fundamental and nonlinear frequencies. By inverting the nonlinear GSTCs, a retrieval procedure is developed to retrieve the nonlinear parameters of the nonlinear metasurface. As an example, we investigate a nonlinear metasurface which presents nonlinear magnetoelectric coupling in near infrared regime. The method is expected to apply to any patterned metasurface whose thickness is much smaller than the wavelengths of operation, with inclusions of arbitrary geometry and material composition, across the electromagnetic spectrum.

The second part presents the applications of nonlinear metasurfaces. First, we show that the third-harmonic generation (THG) can be drastically enhanced by the nonlinear metasurfaces – film-coupled nanostripes. The large THG enhancement is experimentally and theoretically demonstrated. With numerical simulations, we present methods to clarify the origin of the THG from the metasurface. Second, the enhanced two-photon photochormism is investigated by integrating spiropyrans with film-coupled nanocubes. This metasurface platform couples almost 100% energy at resonance, and induces isomerization of spiropyrans to merocyanines. Due to the large Purcell enhancement introduced by the film-coupled nanocubes, fluorescence lifetime measurements on the merocyanine form reveal large enhancements on spontaneous emission rate, as well as high quantum efficiency. We show that this metasurface platform is capable of storing information, supports reading and writing with ultra-low power, offering new possibilities in optical data storage.

The design of optical and electromagnetic devices has been an active topic of research for centuries. Despite this, designing devices that perform many functions concurrently and with high efficiency is still a major challenge to this day. The ability to construct optics encoding a large number of functionalities at near-perfect efficiency would have profound repercussions in many fields of basic science, physics, and engineering, from optical and quantum computing to memory storage, scientific instrument design, computer vision, and sensing.

In recent years, the advent of metamaterials and the progress of fabrication techniques has made it possible to construct artificial media with exquisite, subwavelength control over their scattering properties. This vast design space has yet to be exploited fully, because the development of specialized design techniques has lagged behind the availability of new materials and properties.

I contribute to the field of electromagnetic design by exploring what limitations there are on the functionalities that may be achieved with electromagnetic devices, and how the characteristics of metamaterials can be used to formulate a new design method to encode a large number of functions within the same object. This design technique, called the symphotic method, combines the principles of metamaterial, variational, and adjoint-state design to yield multifunctional devices that encode tens of operations at efficiencies exceeding 90\%. In this dissertation, after proving a fundamental information-theoretical limit on the capabilities of electromagnetic scattering devices, I derive the symphotic method, demonstrate its use, corroborate analytical results with experimental evidence, and present examples of application-oriented devices, such as detectors for autonomous vehicles, multifunctional superresolving microscopes, and portable compressive spectrophotometers.