title: Hidden structures within structured light. Observing geometric phases and topologies for vector beams and their tomography
Creators: name: McWilliam, Amy
Publisher: name: University of Glasgow
Year: 2024

description: Structured light, recognised for its intricate spatial patterns in amplitude, phase and polarisation, has captivated researchers not only within the field of optics, but across various other disciplines. In this thesis, I cover topics centred around vector beams, known for their spatially varying polarisation distributions, highlighting some of the not so obvious (hidden) properties and structures within shaped light.
Many key aspects of structured light will be explored, ranging from technical considerations, more fundamental concepts (for example, geometric phases and optical skyrmions), and applications. The technical aspects of this thesis surround the generation of arbitrary vector beams using digital devices and their tomography. Applications that will be presented include single-shot Mueller matrix determination and a quantum key distribution protocol.
In optics, additional phase shifts arise due to the geometry of the system in which a beam propagates. Here, we present an experimental investigation into the non-planar propagation of scalar and vector light fields, demonstrating the rotation of both polarisation and intensity profiles and linking the rotations seen to geometric phases. The geometric phase acquired upon non-planar propagation is proportional to the total angular momentum number of the beam, allowing the concept of the angular momentum redirection phase to be introduced.
Optical skyrmions are topological structures embedded within the polarisation structures of vector light beams. We will present a new topological method for identifying and characterising skyrmion beams, using polarisation singularities and associated winding numbers. This approach provides an intuitive geometric insight and can be more robust when analysing noisy experimental data. Additionally, we present the propagation of optical skyrmions and a new method of generating tunable optical multi-skyrmions
The tomography of vector beams is normally carried out using multiple sequential measurements in order to determine spatially varying polarisation profiles as well as spatial mode decomposition. Here, we present a system for the single-shot characterisation of vector beams by performing positive operator valued measurements, building on previous work. The measurements are performed using a Sagnac interferometric setup with proven stability over hours. The single-shot nature allows for superior acquisition speeds in comparison to other techniques, allowing for time-resolved measurements. This will be demonstrated through dynamic Muller matrix polarimetry to measure changing optical activity, with a temporal resolution limited only by the camera frame rate.
Towards the end of this thesis, I also explore how vector beams can be used to implement a rotational reference frame invariant quantum key distribution protocol, their invariance to unitary perturbations, and also introduce and characterise a new family of orthonormal beams, the complex Zernike modes.
This thesis covers a diverse range of concepts, united by the theme of structured light, specifically, the topological structures within vector beams, their fundamental properties and applications. Here, we aim to show that by fully understanding and engaging with the additional degrees of freedom offered by vector light beams, we can unlock new possibilities, applications and theoretical insights that will further the field of optics.