Non-Hermitian topological states in photonic systems

Abstract

In this thesis I explore non-Hermitian topological photonics with the aim of describing new phenomena which question our understanding of how far the current classification of topological states extends. This work invigorates the search for topological states in photonic systems with the hope of describing new mechanisms for controlling and increasing the number of physical systems in which robust light transport can be achieved. In coupled resonator optical waveguides, I demonstrate the formation of topological defect states in one dimensional systems and topological edge states in two dimensional systems, which only occur for a system with open boundaries. Since a non-Hermitian system displaying topological defect states with a trivial Hermitian limit has not been seen before, these results are both novel and paradigm breaking. Topological mode selection is another mechanism unique to controlling topological states in non-Hermitian photonic system. I consider a non-linear extension to this notion for a complex wave equation describing lasing elements with saturable gain. I show that beyond the categorisation of topological stationary-states, which continue from the underlying linear system, new power-oscillating topological states form. These power-oscillations have not yet been seen in experiments but ongoing collaborations aim to see these solutions in the near future.