Superpositions of light fields carrying orbital angular momentum.
The work presented in this thesis is centred on the generation of superimposed optical fields which each carry orbital angular momentum (OAM) and the development of OAM measurement techniques. Optical fields which carry OAM have found applications ranging from optical tweezing to quantum cryptography. Due to the fact that they offer a potentially infinite-dimensional state space, much interest has been generated in the measurement of OAM in optical fields, in order for higher-dimensional quantum information processing to be realised. In this study we generate superpositions of higher-order Bessel beams and show that even though we can create a field which carries no overall OAM, we can still witness an angular rotation in the intensity profile of the beam. We also develop two new OAM measurement techniques: (1) a robust odd-even-OAM interferometer and (2) a method to measure the OAM density of an optical field by means of a single spatial light modulator (SLM). In the first chapter we give an overview of the literature regarding optical OAM, followed by the derivation of the Helmholtz wave equation from Maxwell’s equations. We illustrate that helically-phased beams, having a phase factor of exp(ilθ), possess a well-defined OAM. Definitions for the fundamental Gaussian mode, as well as two OAM-carrying modes: Laguerre-Gaussian (LG) and Bessel-Gaussian (BG) modes are also given. Since a majority of this thesis involves generating superimposed OAM fields as well as the measurement of OAM, chapter 2 contains detailed discussions on the optical components used to generate and measure OAM. In section 2.9 we present one of our contributions to the field of OAM-measurement, which involves a stable Dove-prism embedded Mach-Zehnder interferometer, capable of sorting 41 OAM states into odd and even ports with a contrast ranging from 92% to 61%. We implement the Dove prism embedded Mach-Zehnder interferometer to mimic an amplitude damping channel for OAM states in chapter 3. Our device is useful in modelling a ‘lossy’ environment for OAM states. In chapter 4 we develop a new technique for the generation of superimposed Bessel beams through the use of a single digital hologram and theoretically and experimentally show that even though the superimposed Bessel beams can be constructed to produce no overall OAM, a rotation in the beam’s intensity profile is still present, as the field propagates. This rotation is due to the differing longitudinal wave-vectors present in the field and we make quantitative, experimental measurements of the angular rotation rates, which are in very good agreement with our theoretical predictions. We also show that the far-field of these superimposed Bessel beams, exhibit no rotation in their intensity profile and we offer a theoretical explanation for this occurrence. In chapter 5, we adapt our technique for generating superimposed Bessel beams to create non-diffracting speckle fields, which are known to possess optical vortices, and show that by controlling the standard deviation of the phase distribution within the digital hologram, we are able to control the evolution of the non-diffracting speckle field into a non-diffracting zero-order Bessel beam. Our final chapter contains a novel technique for the measurement of the OAM density of optical fields, by implementing two optical components: an SLM and a lens.