Browsing by Subject "Physics, Electricity and Magnetism"

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.

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.