Diffraction and pseudospectra in non-Hermitian quasiperiodic lattices

TL;DR

This paper investigates the spectral properties and wave dynamics of non-Hermitian quasiperiodic lattices, revealing how gain, loss, and nonlinearity influence localization, pseudospectra, and quantized jumps in photonic systems.

Contribution

It provides a systematic analysis of the non-Hermitian Aubry-André-Harper model, highlighting the effects of gain, loss, and nonlinearity on spectral sensitivity and wave behavior.

Findings

Quantized jumps occur in strong disorder regimes.

Pseudospectra analysis reveals spectral sensitivity.

Nonlinearity significantly affects diffraction dynamics.

Abstract

Wave dynamics in disordered open media is an intriguing topic, and has lately attracted a lot of attention in non-Hermitian physics, especially in photonics. In fact, spatial distributions of gain and loss elements are physically possible in the context of integrated photonic waveguide arrays. In particular, in these type of lattices, counter-intuitive quantized jumps along the propagation direction appear in the strong disorder limit (where all eigenstates are localized) and they have also been recently experimentally observed. We systematically study the non-Hermitian quasiperiodic Aubry-Andr\'e-Harper model with on-site gain and loss distribution (NHAAH), with an emphasis on the spectral sensitivity based on pseudospectra analysis. Moreover, diffraction dynamics and the quantized jumps, as well as, the effect of saturable nonlinearity, are investigated in detail. Our study reveals the intricate relation between the nonlinearity and non-Hermiticity.