Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides

Abstract

We considered the modulational instability of continuous-wave backgrounds, and the related generation and evolution of deterministic rogue waves in the recently introduced parity-time (PT)-symmetric system of linearly-coupled nonlinear Schrödinger equations, which describes a Kerr-nonlinear optical coupler with mutually balanced gain and loss in its cores. Besides the linear coupling, the overlapping cores are coupled through cross-phase-modulation term too. While the rogue waves, built according to the pattern of the Peregrine soliton, are (quite naturally) unstable, we demonstrate that the focusing cross-phase-modulation interaction results in their partial stabilization. For PT-symmetric and antisymmetric bright solitons, the stability region is found too, in an exact analytical form, and verified by means of direct simulations.

accepted for Journal of Optics

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• Harnessing and control of optical rogue waves in supercontinuum generation
• Breathers in PT-symmetric optical couplers
• Stable dark solitons in PT-symmetric dual-core waveguides
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides

Cited by in corpus (21)

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• PT-symmetric coupler with a coupling defect: soliton interaction with exceptional point
• Analytical stable Gaussian soliton supported by a parity-time-symmetric potential with power-law nonlinearity
• Parity-time-symmetric vector rational rogue wave solutions in any n-component nonlinear Schrödinger models
• $\mathcal{P}\mathcal{T}$-symmetric coupler with ${\chi }^{(2)}$ nonlinearity
• Staggered $\mathcal{P}\mathcal{T}$-symmetric ladders with cubic nonlinearity
• Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
• Global existence of solutions to coupled $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger equations
• Supercritical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations
• Dispersion Managed Generation of Peregrine Solitons and Kuznetsov-Ma Breather in an Optical Fiber
• Bistable soliton switching dynamics in a $\mathcal{P}\mathcal{T}$-symmetric coupler with saturable nonlinearity
• $\mathcal{P}\mathcal{T}-$Symmetric Dimers with Time-Periodic Gain/Loss Function
• Nonlinear Parity-Time (PT) symmetric closed-form optical quadrimer waveguides: Attractor perspective
• Effects of the third-order dispersion on continuous waves in complex potentials
• Solvable Limits of a class of generalized Vector Nonlocal Nonlinear Schrödinger equation with balanced loss-gain
• Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing
• Exotic light transition between superluminal and subliminal group velocity in a $\mathcal{P}\mathcal{T}$ coupled slab waveguide
• Stability band structure for periodic states in periodic potentials