Optical skyrmions and polarizations of highly focused structured light

Abstract

Structured light refers to the controlled tailoring of light fields, encompassing customized attributes such as intensity, phase, and polarization. The study of structured light is motivated by its broad applications, including optical tweezers for trapping and manipulating microscopic particles, multiplexed optical communication, advanced imaging techniques like super resolution microscopy, and quantum information processing. Additionally, structured light offers unique properties such as orbital angular momentum (OAM), which allows information encoding in the twisted phase of light, and spatially varying polarization patterns, which facilitate precise control over light-matter interactions. In this thesis, we investigate various topics related to structured light, including the Faraday effect in strongly focused fields, optical skyrmions, and a two-sphere method for analyzing 3D polarization fields generated by strong focusing. We demonstrate that, for structured light, magneto-optical interactions, specifically the well-known Faraday effect, exhibit a more intricate pattern, which we term the secondary Faraday effect. This effect, arising from the same mechanism as the linear Faraday effect, becomes significant in a strong focusing system, where it reaches a magnitude comparable to the linear effect. We also introduce skyrmionic beams, a class of structured light that has attracted significant research attention. Building on existing methods for calculating skyrmion numbers, we propose a novel approach that explicitly links these numbers to their topological definitions. Furthermore, we identify that skyrmions and bimerons—configurations involving two distinct regions of opposite topological charge—are topologically equivalent by generalizing the definition of their parameters. Emphasis is placed on the geometrical interpretations, which lead to an extended definition of singularities. Throughout the thesis, we are particularly interested in highly focused systems, where additional spatial dimensions play a crucial role compared to paraxial optics. To investigate this, we introduce a two-sphere method to comprehensively describe general 3D polarization fields and apply it to a focused, hence non-paraxial skyrmion beam, as an example