title: Constant-intensity waves and their modulation instability in non-Hermitian potentials.
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 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 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.
authors.affiliation: 1] Institute for Theoretical Physics, Vienna University of Technology, Vienna A-1040, Austria. [2] Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544 USA.
authors.forename: K G
authors.initials: KG
authors.lastname: Makris
authors.affiliation: Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510, USA.
authors.forename: Z H
authors.initials: ZH
authors.lastname: Musslimani
authors.affiliation: College of Optics-CREOL, University of Central Florida, Orlando, Florida 32816, USA.
authors.forename: D N
authors.initials: DN
authors.lastname: Christodoulides
authors.affiliation: Institute for Theoretical Physics, Vienna University of Technology, Vienna A-1040, Austria.
authors.forename: S
authors.identifier: 0000000241231417
authors.initials: S
authors.lastname: Rotter