Analytic-domain lens design with proximate ray tracing.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

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.