OPTICAL VORTEX RINGS IN ELLIPTIC GAUSSIAN BEAMS: TOPOLOGICAL REACTIONS AND CATASTROPHES

Abstract

Vortex rings are a fascinating subject in physics with a long history, offering insights into the intricate topology of the system. In this thesis, I investigate vortex rings generated by the destructive interference of an elliptic Gaussian beam and a plane wave. The system can be replicated in optics laboratories using readily available equipment, but most importantly, it provides an assessable framework for studying complex topologies of vortex lines and even catastrophes. The main results are split into two sections. In the first, I derive the governing equations of elliptic Gaussian beams. I explore various topological transformations of rings and examine how the underlying beam symmetries affect the dynamics of topological events. In the second, I analyze the effects of heightened ellipticity on the events and beam shapes, and investigate catastrophes occurring in the system. The findings may provide deeper insights into the fine structure of light and potentially lay the foundation for understanding the mechanisms of spontaneous knotting of vortex lines.