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- W2548657314 abstract "The first sections of this thesis explore a construction of electromagnetic fields first proposed by Bateman [2] and recently rediscovered [8] and expanded upon. With this powerful and elegant tool, I show that it is possible to construct families of EM fields that have a common topological structure that is preserved throughout time. This topological structure, known as the Hopf fibration, has been found to manifest itself in many areas of physics. Due to its utility, I have made a detailed study of it. The final section of this thesis develops an algorithm to parameterize a closed, bounded, and oriented surface that has as its boundary a torus knot. These types of surfaces, known as Seifert surfaces [17], contain information about the energy structure of the EM fields developed in the earlier sections of this thesis and may also lead to detection protocols for such fields. Because these surfaces are closed, bounded and oriented then Stokes’ theorem should be valid. A verification of this proposition is included. iii Acknowledgements I would like to thank my advisor, Dr. Bernard Zygelman, for the guidance and direction he provided me throughout the entire process of producing this thesis, and also for supplying me with the ideas in the first place. I would also like to acknowledge the other members of my committee, Drs. Lepp, Pravica, and Phanord, for their patience with me during the weeks leading to my defense. Finally, I would like to thank my wife, Kelly, for the sacrifices she was required to make in my behalf for the past two years. iv Dedication This thesis is dedicated to my dear wife Kelly. Without your support this project would never have started in the first place. v Table of" @default.
- W2548657314 created "2016-11-11" @default.
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- W2548657314 date "2016-01-01" @default.
- W2548657314 modified "2023-09-23" @default.
- W2548657314 title "The Hopf Fibration and Encoding Torus Knots in Light Fields" @default.
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- W2548657314 doi "https://doi.org/10.34917/9112204" @default.
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