Merging of exceptional points in classical waves

Abstract

Non-Hermitian systems, such as open systems and systems with asymmetric losses, are ubiquitous in nature and have drawn a lot of attentions for a long time. The exceptional points (EPs) that can exist in such systems when two eigenstates coalesce are the origin of a wide range of novel phenomena in different branches of physics. Most of these phenomena can be understood by considering a 2 × 2 non-Hermitian matrix. At a higher dimension, more complex EP physics not found in two-state systems arises. Here, we investigate the multi-state non-Hermitian system in both acoustics and photonic crystals. For acoustics systems, we consider the emergence and interaction of multiple EPs in a four-state system theoretically and the system is realized experimentally using four coupled acoustic cavities with asymmetric losses. We found that multiple EPs can emerge and as the system parameters vary, these EPs can collide and merge, leading to higher order singularities and topological characteristics much richer in physics than those seen in two-state systems [1]. For photonic crystals, we study the complex band structures of one-dimensional PT symmetric photonic crystals by setting up a model Hamiltonian, and two types of PT phase diagram are found. Furthermore, by calculating non-Abelian Zak phases, we showed that the standard concept of band inversion in a Hermitian photonic crystal can be extended to non-Hermitian case before the PT-exact phase is broken [2].