Unravelling the dark focus of light

: a study of knotted optical singularities

Abstract

The discovery of nontrivial topological objects is a challenging task for physicists and mathematicians. This thesis investigates and extends the theory of knotted and linked optical vortex lines to additional singular topological conformations. The study demonstrates that singular optics is deeply connected with the polarisation texture of focused fields characterised by a dark focus. Optical vortices are defined as nodal lines of the intensity in monochromatic scalar fields, e.g. laser light, and correspond to lines of darkness that are usually embedded in a low-intensity volume. Theoretical and numerical topological methods are applied to paraxial and nonparaxial optical fields to analyse their phase and polarisation singularities. New types of knots and links are constructed explicitly in the focal volume of optical wavefunctions propagating in free space. For knot structures approaching the scale of wavelength, a bundle of intertwined knotted nodal structures in the transverse and longitudinal polarisation components of the electric and magnetic fields is described. Additionally, a whole family of Hopfions, which are mathematically described by Hopf fibrations, is shown to emerge in the 3D polarisation texture of focused light. Experiments to measure these phenomena are proposed, some of which have been confirmed in the laboratory. Singular knot bundles and optical Hopfions reveal potential applications of light-matter interaction in nanophotonic systems. Their practical implementation could be used to store topological states into soft-materials or quantum physical systems.

Date of Award	7 May 2019
Original language	English
Awarding Institution	University of Bristol
Supervisor	Mark Dennis (Supervisor)