Date of Award
Master of Science (MS)
Controlling the localization of light has been studied through many approaches and has become a subject matter of interest due to potential applications in various fields. In this thesis, we will explore discrete systems with conducted symmetries, in both quantum and classical aspects, to establish a deeper understanding of light localization. First, we investigate atom-light interactions through exploring the Jaynes-Cummings model. We then introduce coupled cavity arrays (CCAs) where photons can hop between neighboring cavities and each cavity in the array may interact with one or more atoms. Specifically, we focus on systems in which one two-level atom is connected to a cavity in the CCA. The propagation of the initially excited photon and its localization along the CCA, as well as the effect of the topological properties of the system and the position of the two-level atom in the array, are discussed in this thesis. Additionally, we investigate a classical approach to the localization of light which is the emergence of flat bands. It has been previously established that at the exceptional point of a non-Hermitian Parity-Time (PT) symmetric system, an entirely flat band can emerge as a bound state in the continuum (BIC). However, our research demonstrates that by engineering the lattice couplings, the emergence of flat bands is not solely limited to the exceptional point and under a certain condition, there will be a gradual energy shift away from the dispersive bands. These results allow us to induce a flat band which is a bound state out of the continuum at a critical point before reaching the exceptional point. Also, by expanding our investigations to a tetramer array of waveguides, we show the coexistence of two flat bands, one of which always manifests as a BIC.
Hajikhani, Aria, "Exploring the Localization of Light in Discrete Systems With Conducted Symmetries" (2023). Theses and Dissertations - UTRGV. 1301.
Available for download on Sunday, August 31, 2025