#### Degree

Doctor of Philosophy (PhD)

#### Department

Physics and Astronomy

#### Document Type

Dissertation

#### Abstract

Optics is arguably the most important branch of physics that has ever been studied. It is not only an essential ingredient of many other branches of physics that we study, it governs how we see, how we measure, and how we communicate in the modern world. And as the world continues to change, so do our tools and resources. In a relatively short amount of time, we have progressed from rudimentary tools that shape the world around us, to tools that harness the fundamental laws of nature. Unsurprisingly, the laws of nature governing optics remain paramount. This is because many of today's most advanced technologies rely on the classical and quantum properties of specially prepared beams of light. For example, there are quantum computing, quantum information, the quantum internet, quantum-enhanced metrology and quantum-enhanced imaging, to name a few. It is time to go a layer deeper in our understanding of these beams of light, particularly ones generated in nonlinear-optical interactions, since these are commonly the source of beams with quantum properties. The critical observation is that in each spatial mode (or spectral mode) of light exiting a nonlinear interaction, there are actually many transverse-spatial modes that have not been fully investigated. We use a Born-like approximation and a Green's function method to predict the classical mode structure of beams created during nonlinear interactions. Then, we extend the single-mode quantum theory by developing a second-quantization procedure of the classical modes. We derive an amplitude matrix, which governs the interaction between the modes and we calculate the evolution of the system. We show that our classical theory agrees nicely with experimental results, better than previous theories. Furthermore, we present simulations that predict ways to tailor the mode structure while adding, subtracting, and canceling orbital angular momentum transfer in nonlinear interactions. We use our quantum theory to predict the variance, covariance, the coupling of the modes, and how the noise suppression is distributed among the modes. In each case, we focus on exposing the underlying transverse spatial mode structure and suggest ways to tailor it depending on the intended use of the quantum resources. The simulations herein illustrate the utility of our theory, which is a convenient and powerful optimization tool. It can be used to show how the interplay of experimental beam parameters can influence the quantum properties of the beam(s) generated during the interaction. For example, the mode structure of the input beam(s), along with beam waist(s) and focal position(s), can all have significant influence on the quantum properties. Coupling to the generated beam(s) can also be a formidable problem. Thus, it allows one to investigate which beam parameters should be targeted to enhance the quantum resources.

#### Date

10-24-2018

#### Recommended Citation

Lanning, Robert Nicholas, "BEAM THEORY FOR CLASSICAL AND QUANTUM NONLINEAR OPTICS---EXPOSING CLASSICAL AND QUANTUM CORRELATIONS OF TRANSVERSE-SPATIAL MODES" (2018). *LSU Doctoral Dissertations*. 4764.

https://digitalcommons.lsu.edu/gradschool_dissertations/4764

#### Committee Chair

DOWLING, JONATHAN P.