Non-Hermitian disorder in two-dimensional optical lattices

TL;DR

This paper investigates how non-Hermitian disorder affects the spectral and localization properties of two-dimensional optical lattices, revealing complex eigenvalue behavior and localization phenomena through systematic analysis.

Contribution

It provides a systematic study of the interplay between disorder and non-Hermiticity in 2D optical lattices, focusing on eigenspectrum and localization properties.

Findings

Complex eigenvalue distribution depends on disorder strength

Localization properties are characterized by participation ratio and level spacing

Modified level distribution function fits computational data

Abstract

In this paper, we study the properties of two-dimensional lattices in the presence of non-Hermitian disorder. In the context of coupled mode theory, we consider random gain-loss distributions on every waveguide channel (on site disorder). Our work provides a systematic study of the interplay between disorder and non-Hermiticity. In particular, we study the eigenspectrum in the complex frequency plane and we examine the localization properties of the eigenstates, either by the participation ratio or the level spacing, defined in the complex plane. A modified level distribution function vs disorder seems to fit our computational results.