Focal shaping with pupil filters.

Abstract

The ability to shape a focus of light would improve many fields of study, including microscopy and optical trapping. In the field of optical data storage, elongating the focus along the optical axis would relax constraints on alignment between the optical head and storage medium, and indirectly improve storage density. Filtering the pupil of a lens can shape the focus in this way. In this dissertation, we describe the theory, design, and implementation of pupil filters. We describe theoretical methods of modeling pupil filters, particularly the Debye approximation for focusing at high numerical aperture. We apply the theory to focusing linear and novel cylindrical polarizations. We also apply the theory to focusing with an aplanatic lens and, to our knowledge for the first time, an aspheric lens. We describe analytical and numerical methods of designing pupil filters, particularly a genetic algorithm. We apply the algorithm to shrinking and elongating the focus. We describe practical methods of implementing pupil filters, including fabrication, illumination, and measurement. Particularly, we describe a method to generate cylindrical polarizations with a single-substrate birefringent hologram, to our knowledge for the first time. Finally, we demonstrate a pupil filter that successfully elongates the focus.