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 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.

25 pages (including methods section), 4 figures; to appear in Nature Communications

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Coherent Perfect Absorbers: Time-reversed Lasers
• Loss-induced suppression and revival of lasing
• PT-symmetry breaking and laser-absorber modes in optical scattering systems
• Reversing the Pump-Dependence of a Laser at an Exceptional Point

Cited by in corpus (45)

• Non-Hermitian Physics
• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Light fields in complex media: mesoscopic scattering meets wave control
• Nonlinear switching and solitons in PT-symmetric photonic systems
• $\mathcal{P}\mathcal{T}$ symmetry in a fractional Schrödinger equation
• Roadmap on structured waves
• Non-Hermitian disorder in two-dimensional optical lattices
• Constant-pressure sound waves in non-Hermitian disordered media
• Observation of anti-parity-time-symmetry, phase transitions and exceptional points in an optical fibre
• Parametric amplification and bidirectional invisibility in PT-symmetric time-Floquet systems
• Wave propagation through disordered media without backscattering and intensity variations
• Stability Through Asymmetry: Modulationally Stable Nonlinear Supermodes of Asymmetric non-Hermitian Optical Couplers
• Exceptional points in lossy media enable decay-free wave propagation
• Symmetry in optics and photonics: a group theory approach
• Improving sound absorption through nonlinear active electroacoustic resonators
• Gaussian-like and flat-top solitons of atoms with spatially modulated repulsive interactions
• Shape-preserving beam transmission through non-Hermitian disordered lattices
• Unidirectional zero reflection as gauged parity-time symmetry
• Scattering-free pulse propagation through invisible non-Hermitian disorder
• Stationary through-flows in a Bose-Einstein condensate with a PT-symmetric impurity
• Exactly solvable Wadati potentials in the PT-symmetric Gross-Pitaevskii equation
• Realization of complex conjugate media using non-PT-symmetric photonic crystals
• Transforming space with non-Hermitian dielectrics
• A universal form of complex potentials with spectral singularities
• Effects of non-uniform distributions of gain and loss in photonic crystals
• Exploring Branched Hamiltonians for a Class of Nonlinear Systems
• Anomalous Hall effect from a non-Hermitian viewpoint
• Visualizing Topology of Real-Energy Gapless Phase Arising from Exceptional Point
• Effects of the third-order dispersion on continuous waves in complex potentials
• Time-dependent spectral renormalization method
• Self-acceleration in non-Hermitian Systems
• An Algebraic PT-Symmetric Quantum Theory with a Maximal Mass
• Graph theory approach to exceptional points in wave scattering
• Balanced gain and loss in spatially extended non-$\mathcal{P}\mathcal{T}$-symmetric multi-well potentials
• Controlling wave-front shape and propagation time with tunable disordered non-Hermitian multilayers
• Hybrid patterns and solitonic frequency combs in non-Hermitian Kerr Cavities
• Response of exact solutions of the nonlinear Schrodinger equation to small perturbations in a class of complex external potentials having supersymmetry and parity-time symmetry
• Demonstration of imaginary-mass particles by optical simulation in non-Hermitian systems
• Nonlinear Schrödinger equations with amplitude-dependent Wadati potentials
• Constant intensity acoustic propagation in the presence of non-uniform properties and impedance discontinuities: Hermitian and non-Hermitian solutions
• Robustness of perfect transmission resonances to asymmetric perturbation
• Balancing gain and loss in symmetrised multi-well potentials
• Observing complementary Lucas sequences using non-Hermitian zero modes
• Solitonic dynamics and excitations of the nonlinear Schrodinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
• Stability band structure for periodic states in periodic potentials