| The central topic of this dissertation is how to make classical light, comprised of many photons, behave in a manner similar to massive quantum particles in potentials. This document describes how one can relate classical wave variables, such as ray paths, frequency scales, and group velocities, to variables associated with classical point particles. A novel Dirac-equation formulation of Maxwell's equations will be presented. We will explain the connection between classical optical and quantum mechanical spin-orbit coupling. We describe a variety of different optical phenomena, including spin-orbit coupling in epsilon-near-zero [ENZ] metamaterials and other optical systems, Darwin terms, and other pseudo-relativistic effects. Resulting mathematical techniques can be used to describe generic optical systems with spatially varying values of mu and epsilon. Further discussed is the importance of mode-mixing in the control of polarization states of cavity fields. Also discussed is how tensor, ENZ, optical metamaterials can be constructed that give an analog of magnetic fields for light. Finally, we will discuss challenges with solving problems with a Kerr nonlinearity in ENZ materials. Additionally described are problems involved in quantizing nonintegrable optical cavities. This study is undertaken with the goal of suggesting future research directions regarding metamaterials. This dissertation includes both previously published/unpublished and co-authored material. |
