Stability of solitons in PT-symmetric couplers

Abstract

Families of analytical solutions are found for symmetric and antisymmetric solitons in the dual-core system with the Kerr nonlinearity and PT-balanced gain and loss. The crucial issue is stability of the solitons. A stability region is obtained in an analytical form, and verified by simulations, for the PT-symmetric solitons. For the antisymmetric ones, the stability border is found in a numerical form. Moving solitons of both types collide elastically. The two soliton species merge into one in the "supersymmetric" case, with equal coefficients of the gain, loss and inter-core coupling. These solitons feature a subexponential instability, which may be suppressed by periodic switching ("management").

Optics Letters 2011 (in press)

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• Physical realization of $\mathcal{P}\mathcal{T}$-symmetric potential scattering in a planar slab waveguide
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Cited by in corpus (116)

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• New topological invariants in non-Hermitian systems
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• Nonlinear modes in finite-dimensional PT-symmetric systems
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• Parity-Time Symmetry in Non-Hermitian Complex Optical Media
• Nonlinear localized modes in PT-symmetric Rosen-Morse potential well
• $\mathcal{P}\mathcal{T}$-symmetry breaking in a necklace of coupled optical waveguides
• Quasi PT-symmetry in passive photonic lattices
• Stability boundaries and collisions of two-dimensional solitons in PT-symmetric couplers with the cubic-quintic nonlinearity
• Integrable nonlocal vector nonlinear Schrödinger equation with self-induced parity-time-symmetric Potential
• Symmetry breaking of solitons in one-dimensional parity-time-symmetric optical potentials
• Optical waveguide arrays: quantum effects and PT symmetry breaking
• Partially-PT-symmetric optical potentials with all-real spectra and soliton families in multi-dimensions
• Instabilities, solitons, and rogue waves in PT-coupled nonlinear waveguides
• All-real spectra in optical systems with arbitrary gain and loss distributions
• Vector solitons in PT-symmetric lattices
• Unbreakable PT-symmetry of solitons supported by inhomogeneous defocusing nonlinearity
• Symmetry breaking of solitons in two-dimensional complex potentials
• Discrete solitons and vortices on two-dimensional lattices of $\mathcal{P}\mathcal{T}$-symmetric couplers
• A solvable model for solitons pinned to a PT-symmetric dipole
• Linear and Nonlinear PT-symmetric Oligomers: A Dynamical Systems Analysis
• Hamiltonian formulation of the standard $\mathcal{P}\mathcal{T}$-symmetric nonlinear Schrödinger dimer
• Nonlinear PT-symmetric plaquettes
• Solitons in $\mathcal{P}\mathcal{T}$-symmetric periodic systems with the quadratic nonlinearity
• Necessity of PT symmetry for soliton families in one-dimensional complex potentials
• Wave scattering on a domain wall in a chain of PT-symmetric couplers
• PT-symmetry in optics beyond the paraxial approximation
• Peregrine Rogue Wave dynamics in the continuous nonlinear Schrödinger system with parity-time symmetric Kerr nonlinearity
• Dynamics of Localized Structures in Systems with Broken Parity Symmetry
• Using PT-symmetry for switching applications
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• Flat band in two-dimensional non-Hermitian optical lattices
• Reversible ultrafast soliton switching in dual-core highly nonlinear optical fibers
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• Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
• Tailoring $\mathcal{P}\mathcal{T}$-symmetric soliton switch
• Stability of soliton families in nonlinear Schroedinger equations with non-parity-time-symmetric complex potentials
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• Parametric instability of non-Hermitian systems near the exceptional point
• Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential
• New classes of solutions in the Coupled PT Symmetric Nonlocal Nonlinear Schrodinger Equations with Four Wave Mixing
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• PT-symmetry in nonlinear twisted multi-core fibers
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• Parity-time symmetric optical coupler with birefringent arms
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• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Mode pairs in $\mathcal{P}\mathcal{T}$-symmetric multimode waveguides
• Resonant mode conversion in the waveguides with an unbroken and broken PT-symmetry
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• PT-symmetric lattices with spatially extended gain/loss are generically unstable
• Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
• Solitons in a $\mathcal{P}\mathcal{T}$- symmetric ${\chi }^{(2)}$ coupler
• Nonlinear parity-time-symmetric transition in finite-size optical couplers
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• Supercritical blowup in coupled parity-time-symmetric nonlinear Schrödinger equations
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• Effects of the third-order dispersion on continuous waves in complex potentials
• Tunable nonlinear spectra of anti-directional couplers
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• Solitons in a Hamiltonian $PT$-symmetric coupler
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• Nonlinear behaviors of parity-time-symmetric lasers
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• Classical Hamiltonian Systems with Balanced loss and gain