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

摘要

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 astationary wave with constant intensity. The most familiar example is that of aplane wave propagating in free space. In the presence of any Hermitianpotential, a wave's constant intensity is, however, immediately destroyed dueto scattering. Here we show that this fundamental restriction is convenientlylifted when working with non-Hermitian potentials. In particular, we present awhole new class of waves that have constant intensity in the presence of linearas well as of nonlinear inhomogeneous media with gain and loss. These solutionsallow us to study, for the first time, the fundamental phenomenon of modulationinstability in an inhomogeneous environment. Our results pose a new challengefor the experiments on non-Hermitian scattering that have recently been putforward.