Date of Award

2019

Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy in Physics (PhD)

Administrative Home Department

Department of Physics

Advisor 1

Ramy El-Ganainy

Committee Member 1

Miguel Levy

Committee Member 2

Jae Yong Suh

Committee Member 3

Durdu Guney

Abstract

Exceptional points (EPs) are singularities that arise in non-Hermitian physics. Crossing EPs is believed to be related with phase transitions between parity-time-(PT-)symmetric phase and broken PT phase. Owing to their peculiar topology, EPs can remotely induce observable effects when encircled by closed trajectories in the parameter space. In this dissertation, first of all, we investigate the extreme dynamics of non-Hermitian systems near higher order EPs constructed using the bosonic algebra method. The strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. And in the PT phase near EPs, the logarithm of the maximum optical power amplification scales linearly with the order of EPs. Secondly, we show that the theoretical framework linking EPs to phase transitions in PT-symmetric Hamiltonians is incomplete. Particularly, the application of the squaring operator to a Jx PT lattice can result in a system that can cross an EP without undergoing a symmetry breaking, which is elucidated by invoking the notion of phase diagrams in the parameter space. We also develop a general approach for encircling EPs by utilizing permutation operators and the representation theory, and reveal that loops that enclose the same EPs starting from the same point and traveling in the same direction, do not necessarily share the same end outcome. Instead, this equivalence can be established by invoking the topological notion of homotopy. All these findings are general with far reaching implications in various fields ranging from photonics and atomic physics to microwaves and acoustics.

In the aspect of applications, current research efforts focus only on systems supporting isolated EPs characterized by increased sensitivity to external perturbations, which makes them potential candidates for building next generation optical sensors. On the downside, they are very sensitive to fabrication errors and experimental uncertainties. To overcome this problem, we propose a photonic structure exhibits a hypersurface of EPs embedded in a larger space, in which perturbations due to back reflection/scattering force the operating point out of the exceptional surface, leading to enhanced sensitivity. Also, this proposed structure can relax the finite gain-bandwidth product limitation in optical amplifiers and allows for building a new generation of optical amplifiers that exhibits better gain-bandwidth scaling relations.

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