Phase transitions in coherent and incoherent light walks with imaginary AAH potentials

Abstract

The scattering of waves is ubiquitous throughout nature. Depending on the type of crystals and level of disorders, such scattering behaviours can be categorised into three primary behaviours: diffusion, ballistic transport, and localization. Among these, localisation, and more specifically Anderson localisation [1], has drawn considerable attention. Anderson localisation involves a phase transition from delocalisation to localisation, typically observed in systems with spatial or temporal disorder. One model frequently used to explore this phenomenon is the Aubry-Andr´e-Harper (AAH) model [2, 4]. While much research has focused on Anderson localization in Hermitian systems, introducing non-Hermiticity into the system brings additional complexity. This can shift the transition points and alter the overall dynamics of the system. This research aims to delve into Anderson localisation within non-Hermitian photonic crystal lattices, particularly in the presence of temporal disorder, to better understand the effects of non-Hermiticity in such systems.