Enhancing imaging systems using transformation optics.

We apply the transformation optical technique to modify or improve conventional refractive and gradient index optical imaging devices. In particular, when it is known that a detector will terminate the paths of rays over some surface, more freedom is available in the transformation approach, since the wave behavior over a large portion of the domain becomes unimportant. For the analyzed configurations, quasi-conformal and conformal coordinate transformations can be used, leading to simplified constitutive parameter distributions that, in some cases, can be realized with isotropic index; index-only media can be low-loss and have broad bandwidth. We apply a coordinate transformation to flatten a Maxwell fish-eye lens, forming a near-perfect relay lens; and also flatten the focal surface associated with a conventional refractive lens, such that the system exhibits an ultra-wide field-of-view with reduced aberration.

Designing three-dimensional transformation optical media using quasiconformal coordinate transformations.

We introduce an approach to the design of three-dimensional transformation optical (TO) media based on a generalized quasiconformal mapping approach. The generalized quasiconformal TO (QCTO) approach enables the design of media that can, in principle, be broadband and low loss, while controlling the propagation of waves with arbitrary angles of incidence and polarization. We illustrate the method in the design of a three-dimensional carpet ground plane cloak and of a flattened Luneburg lens. Ray-trace studies provide a confirmation of the performance of the QCTO media, while also revealing the limited performance of index-only versions of these devices.

Adapting Arthur: The transformations and adaptations of Wirnt von Graffenberg's Wigalois

The stories of King Arthur and his noble knights have fascinated audiences for many centuries and continue to being retold and fashioned to attract modern audiences. Amongst these stories is the tale of Wigalois, the son of the reputable Gawain. This dissertation traces the story of Wigalois across different languages, cultures, and media in order to show how this is a shared German-Yiddish narrative. Furthermore, this dissertations challenges traditional understanding of adaptation within a diachronic and teleological framework by uncovering dialogical and dynamic processes inherent in this narrative tradition. Using the theoretical framework of a combined Adaptation Studies and Medieval Literature Studies’ notions of unstable texts my argumentation focuses on eight specific examples: Wirnt von Grafenberg’s Wigalois (1st half 13th ct.), Italian murals from the fourteenth century, Wigoleis von dem Rade (1483/93), Viduvilt (Yiddish, 16th ct.), Johann Christoph Wagenseil’s Belehrung der Jüdisch-Teutschen Red- und Schreibart (Yiddish and German, 1715), Gabein (Yiddish, 1789), the illustrations by Ludwig Richter (before 1851), and Die phantastischen Abenteuer der Glücksritters Wigalois (Comic, German, 2011).

Moduli Space of (0,2) Conformal Field Theories

In this thesis we study aspects of (0,2) superconformal field theories (SCFTs), which are suitable for compactification of the heterotic string. In the first part, we study a class of (2,2) SCFTs obtained by fibering a Landau-Ginzburg (LG) orbifold CFT over a compact K\"ahler base manifold. While such models are naturally obtained as phases in a gauged linear sigma model (GLSM), our construction is independent of such an embedding. We discuss the general properties of such theories and present a technique to study the massless spectrum of the associated heterotic compactification. We test the validity of our method by applying it to hybrid phases of GLSMs and comparing spectra among the phases. In the second part, we turn to the study of the role of accidental symmetries in two-dimensional (0,2) SCFTs obtained by RG flow from (0,2) LG theories. These accidental symmetries are ubiquitous, and, unlike in the case of (2,2) theories, their identification is key to correctly identifying the IR fixed point and its properties. We develop a number of tools that help to identify such accidental symmetries in the context of (0,2) LG models and provide a conjecture for a toric structure of the SCFT moduli space in a large class of models. In the final part, we study the stability of heterotic compactifications described by (0,2) GLSMs with respect to worldsheet instanton corrections to the space-time superpotential following the work of Beasley and Witten. We show that generic models elude the vanishing theorem proved there, and may not determine supersymmetric heterotic vacua. We then construct a subclass of GLSMs for which a vanishing theorem holds.