The Hopf Fibration and Encoding Torus Knots in Light Fields

The first sections of this thesis explore a construction of electromagnetic fields first proposed by Bateman and recently rediscovered 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, 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\u27 theorem should be valid. A verification of this proposition is included