Date of Award
Physics and Astronomy, College of Natural Science and Mathematics
Mark E. Siemens
Maria M. Calbi
Mark T. Lusk
Shannon M. Murphy
Compressible hydrodynamics, Digital holography, Optical vortices, Two-dimensional fluids, Vortex dynamics
The ubiquity of vortices nearly rivals that of the innumerable fluids and spaces in which they live. Not only do they exist in systems such as superfluids, superconductors, optical fields, or cold atomic gases, for example, but they also exist in our atmospheres, oceans, and even in our veins. This makes understanding and accurately predicting the dynamics of vortices in various systems a relevant and meaningful endeavor.
From a typical hydrodynamic perspective, vortices move within a given fluid because of the background fluid density and phase gradients at the vortex location. However, we find that these gradients alone are insufficient for describing vortex motion. Vortex ellipticity plays a crucial role in vortex dynamics in two-dimensional fluids, particularly during nucleation and annihilation events of oppositely charged vortex pairs. This dissertation presents a novel hydrodynamic theory that accounts for vortex ellipticity that applies to both quantum and classical hydrodynamic settings. This is achieved by viewing the two-dimensional vortex as a virtual three-dimensional circular vortex projected into the two-dimensional plane whose orientation (otherwise referred to as vortex tilt) quantifies the degree of ellipticity. The vortex ellipticity is coupled to the density gradient of the fluid, and accurate predictions of vortex motion can be made, even during nucleation and annihilation events.
A linear optical experiment used to test the new hydrodynamic theory is also discussed in detail. The experiment consists of free-space laser propagation and a spatial light modulator that projects computer generated holograms for producing vortex beams. Procedures for generating effective holograms and efficiently measuring vortex beams include a novel colinear phase-shifting digital holography technique using composite holograms that enables both amplitude and phase measurement of optical beams. Modal decompositions of experimentally generated fields show that our methods can yield vortex purities > 99.9% in the intended mode. Additional experimental details and alignment requirements are also introduced.
This experimental setup is used for two test cases that are compared with the new hydrodynamic theory: (i) a single, tilted vortex in a Gaussian beam and (ii) the annihilation of an oppositely charged vortex pair in a Gaussian beam. In both cases we find agreement between the experimental results and the hydrodynamic theory, confirming not only that the theory accurately predicts vortex motion, but also that optical systems can be described hydrodynamically. Lastly, because of the compressible fluid nature of optical systems, we show that annihilation dynamics can be altered by simply changing the initial core overlap between an oppositely charged vortex pair. Both numerical simulations and experiments confirm that annihilation dynamics are highly impacted by the initial condition, and one can even prevent the annihilation between oppositely charged vortex pairs by simply modifying this initial core overlap.
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Jasmine M. Andersen
Received from ProQuest
Andersen, Jasmine M., "Compressible Hydrodynamics of Few Body Optical Vortices" (2021). Electronic Theses and Dissertations. 1923.
Condensed matter physics