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.

Optical Control of Magnetic Feshbach Resonances by Closed-Channel Electromagnetically Induced Transparency

Optical control of interactions in ultracold gases opens new fields of research by creating ``designer" interactions with high spatial and temporal resolution. However, previous optical methods using single optical fields generally suffer from atom loss due to spontaneous scattering. This thesis reports new optical methods, employing two optical fields to control interactions in ultracold gases, while suppressing spontaneous scattering by quantum interference. In this dissertation, I will discuss the experimental demonstration of two optical field methods to control narrow and broad magnetic Feshbach resonances in an ultracold gas of $^6$Li atoms. The narrow Feshbach resonance is shifted by $30$ times its width and atom loss suppressed by destructive quantum interference. Near the broad Feshbach resonance, the spontaneous lifetime of the atoms is increased from $0.5$ ms for single field methods to $400$ ms using our two optical field method. Furthermore, I report on a new theoretical model, the continuum-dressed state model, that calculates the optically induced scattering phase shift for both the broad and narrow Feshbach resonances by treating them in a unified manner. The continuum-dressed state model fits the experimental data both in shape and magnitude using only one free parameter. Using the continuum-dressed state model, I illustrate the advantages of our two optical field method over single-field optical methods.