Constant-intensity waves and their modulation instability in non-Hermitian potentials

TL;DR

This paper introduces a new class of constant-intensity waves in non-Hermitian potentials, enabling the study of modulation instability in inhomogeneous media with gain and loss, which was not possible with Hermitian systems.

Contribution

It demonstrates that non-Hermitian potentials support constant-intensity waves, allowing exploration of modulation instability in complex media, a novel finding in wave physics.

Findings

Constant-intensity waves exist in non-Hermitian potentials.

Modulation instability can be studied in inhomogeneous media.

New experimental challenges are identified for non-Hermitian scattering.

Abstract

In all of the diverse areas of science where waves play an important role, one of the most fundamental solutions of the corresponding wave equation is a stationary wave with constant intensity. The most familiar example is that of a plane wave propagating in free space. In the presence of any Hermitian potential, a wave's constant intensity is, however, immediately destroyed due to scattering. Here we show that this fundamental restriction is conveniently lifted when working with non-Hermitian potentials. In particular, we present a whole new class of waves that have constant intensity in the presence of linear as well as of nonlinear inhomogeneous media with gain and loss. These solutions allow us to study, for the first time, the fundamental phenomenon of modulation instability in an inhomogeneous environment. Our results pose a new challenge for the experiments on non-Hermitian scattering that have recently been put forward.