|dc.description.abstract||In this thesis, we discuss internal conical refraction. First, we review the theory based on Hamilton’s principle for analyzing the image of rays due to conical refraction, and explain the mechanisms of Poggendorff’s dark ring and Raman spot. Next, we calculate the image intensity using Belsky and Khapalyuk’s exact paraxial theory for internal conical refraction of a Gaussian beam passing through a biaxial crystal along an optical axis. In this theory, the image intensity is obtained from absolute-squaring the electric-displacement field (D-field), which is a superposition of many plane waves of D-field, each carries a phase of the optical path length of the corresponding ray, modified by the Gaussian phase function of the incident beam of a given beam width.
For non-magnetic and non-chiral biaxial crystal, if the input beam is linearly polarized, the output beam is a crescent-shaped ring on the focal image plane, and the polarization direction rotates in a fascinating way as the azimuth angle changes. When chirality is included, the imaging beam will focus at some specific location, and for linearly polarized incident beam the image pattern resembles a coffee swirl. The behavior of the polarization rotation found in this study might be an interesting phenomenon to be verified experimentally in the future.||en_US|