Advances in complex electromagnetic media
Abstract
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 dielectriconly implementation. 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 quasiconformal 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 cloaka 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 quasiconformal 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 twodimensional field mapping waveguide to have a field of view of ̃ 140° and a bandwidth exceeding a full decade. In this work I proposed the idea of using the inverse of the quasiconformal 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 lensestwo of which are described in this thesisand 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 cloakits crosssectionhas 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 metamaterialsstrong anisotropy, inhomogeneity and both magnetic and electric response. Thus, a cloaking crosssection 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 twodimensional 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 crosssection of a concealed metal cylinder in a frequency band from 9.91 to 10.14 GHz. The maximum crosssection reduction was determined to be 24%. The total crosssection and the Bessel decomposition of the scattered wave are compared to an analytical model for the cloaking design which assumes a discrete number of lossless, homogenized cylinders. While the qualitative features of the cloaka reduced crosssection at the cloaking frequencyare realized, there is significant deviation from the homogenized calculation. These deviations are associated with loss and inaccuracies of the effectivemediummodel for metamaterials. In this work I proposed of direct integration of the fields to perform crosssection measurements. I worked out the necessary formulas to determine the coefficients in the Bessel expansion and the resulting scattering crosssection. (Abstract shortened by UMI.)
 Publication:

Ph.D. Thesis
 Pub Date:
 2009
 Bibcode:
 2009PhDT.......185K
 Keywords:

 Physics, Electricity and Magnetism