Interplay of disorder and $\mathcal{PT}$-symmetry

TL;DR

This paper investigates how disorder and $ ext{PT}$-symmetry influence wave transport in a one-dimensional binary lattice, revealing that gain and loss parameters can enhance localization or inhibit transport depending on the excitation type.

Contribution

It provides an exact expression for light localization evolution in $ ext{PT}$-symmetric systems and explores how disorder affects transport phenomena.

Findings

Localization is enhanced with increased gain and loss in pure $ ext{PT}$-symmetric systems.

Gain and loss inhibit transport for localized excitations in disordered systems.

Gain and loss favor transport for extended excitations in disordered systems.

Abstract

We examine a one-dimensional $\mathcal{PT}$-symmetric binary lattice in the presence of diagonal disorder. We focus on the wave transport phenomena of localized and extended input beams for this disordered system. In the pure $\mathcal{PT}$-symmetric case, we derive an exact expression for the evolution of light localization in terms of the typical parameters of the system. In this case localization is enhanced as the gain and loss parameter in increased. In the presence of disorder, we observe that the presence of gain and loss inhibits (favors) the transport for localized (extended) excitations.