Date of Award
Master of Science (MS)
Mario C. Diaz
A hallmark of topological physics has been its ability to facilitate wave propagation control and confinement. This thesis will be focused on wave localization and the existence of robust modes for one of the earliest and most important models of topological insulators, known as the Su-Schrieffer-Heeger (SSH) model. The first chapter covers some of the fundamental topics including the general SSH Hamiltonian, as well as the concept of bulk-boundary correspondence, winding number and distinction between the topologically trivial and non-trivial phases. We investigate the existence of two almost-zero energy states for a finite-sized topologically non-trivial SSH array which are exponentially localized on the left and right edge and how the robustness of these hybridized modes is compromised in the presence of disorder. We then introduce two approaches, using Hermitian and non-Hermitian defects to transform at least one of these almost zero modes into an absolute-zero mode localized on one edge. Furthermore, a general approach is introduced for obtaining these modes in non-Hermitian systems. In the second part of this thesis, we discuss unique topological effects in non-Hermitian systems, including topological lasing which can be realized through arrays of coupled optical resonators. We propose a design in which by utilizing non-Hermitian degeneracies known as the exceptional points (EP) and a locally embedded defect in a trivial array of microring resonators, a robust lasing mode will be obtained. Consequently, we form a single-mode robust defect-based laser emission which circumvents previous requirements for generation of topological laser modes and allows to go beyond edge mode lasing.
Seifollahi, Fargol, "Defect-Based Approaches to Achieving Robust Modes in Hermitian and Non-Hermitian Systems" (2023). Theses and Dissertations. 1404.
Available for download on Sunday, August 31, 2025