Gray solitons in parity-time symmetric potentials

Li, Huagang; Shi, Zhiwei; Jiang, Xingshan; Zhu, Xing

doi:10.1364/ol.36.003290

Cited by 56 publications

(40 citation statements)

References 15 publications

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“…It was also stated the analytical solutions to a class of nonlinear Schrödinger equations with PT-like potentials [11], the stable dissipative defect modes in both focusing and defocusing media where periodic optical lattices were imprinted in the cubic nonlinear media with strong twophoton absorption [12], and the defect solitons in paritytime periodic potentials [13,14]. We also reported the gray solitons in PT symmetric potentials [15] and the gap solitons in PT complex periodic optical lattices with the real part of superlattices [16]. However, thus far all studies focus on the local nonlinear media with the PT symmetry potentials, and the solitons supported by the nonlocal nonlinear media with the PT symmetry optical lattices are hardly reported.…”

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confidence: 80%

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Nonlocal solitons in dual-periodicPT-symmetric optical lattices

Jiang²,

Zhu³

et al. 2012

Phys. Rev. A

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confidence: 80%

“…(3) are in the form of u = F k exp(ikx), where k is the Bloch wave number, and F k is a periodic function of x with the same period as the lattices R. Substituting the Bloch solution into Eq. (3), we can get the eigenvalue equation and then obtain the band structure using the plane wave expansion method [7,15]. The PT symmetric optical lattice is shown in Fig.…”

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confidence: 99%

Nonlocal solitons in dual-periodicPT-symmetric optical lattices

Jiang²,

Zhu³

et al. 2012

Phys. Rev. A

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“…[9]. Dark solitons have been predicted too in this context, assuming the self-defocusing Kerr nonlinearity [10]. In addition, bright solitons have been predicted in PT -symmetric systems with the quadratic (second-harmonic-generating) nonlinearity [11].…”

Section: Introduction and The Modelmentioning

confidence: 95%

Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

D'Ambroise

Malomed

Kevrekidis

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We introduce a simple model for implementing the concepts of quasi-energy and parametric resonances (PRs) in systems with the PT symmetry, i.e., a pair of coupled and mutually balanced gain and loss elements. The parametric (ac) forcing is applied through periodic modulation of the coefficient accounting for the coupling of the two degrees of freedom. The system may be realized in optics as a dual-core waveguide with the gain and loss applied to different cores, and the thickness of the gap between them subject to a periodic modulation. The onset and development of the parametric instability for a small forcing amplitude (V1) is studied in an analytical form. The full dynamical chart of the system is generated by systematic simulations. At sufficiently large values of the forcing frequency, ω, tongues of the parametric instability originate, with the increase of V1, as predicted by the analysis. However, the tongues following further increase of V1 feature a pattern drastically different from that in usual (non-PT ) parametrically driven systems: instead of bending down to larger values of the dc coupling constant, V0, they maintain a direction parallel to the V1 axis. The system of the parallel tongues gets dense with the decrease of ω, merging into a complex small-scale structure of alternating regions of stability and instability. The cases of ω → 0 and ω → ∞ are studied analytically by means of the adiabatic and averaging approximation, respectively. The cubic nonlinearity, if added to the system, alters the picture, destabilizing many originally robust dynamical regimes, and stabilizing some which were unstable. Recently, a great deal of interest has been drawn to systems featuring the PT (parity-time) symmetry. Originally, they were introduced as quantum systems with spatially separated and symmetrically placed linear gain and loss. A fundamental property of non-Hermitian PT -symmetric Hamiltonians is the fact that their spectra remain purely real, like in the case of the usual Hermitian Hamiltonians, provided that the strength of the non-Hermitian part of the Hamiltonian, γ, does not exceed a certain critical value, γ cr , at which the PT symmetry breaks down. Such linear systems were recently implemented experimentally in optics, due to the fact that the paraxial propagation equation for electromagnetic waves can emulate the quantum-mechanical Schrödinger equation. In particular, the PT -symmetric quantum system may be emulated by waveguides with spatially separated mutually balanced gain and loss elements. Additional interest to the optical realizations of the PT symmetry has been drawn by the possibility to implement this setting in nonlinear waveguides. Unlike the ordinary models of nonlinear dissipative systems, where stable modes exist as isolated attractors, in PT -symmetric systems they emerge in continuous families, similar to what is commonly known about conservative nonlinear systems. However, the increase of the gain-loss coefficient, γ, leads to the shrinkage of existence and stability region...

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“…This, in turn, led to the exploration of structures such as bright [12] and dark [13,14] solitons, two-dimensional generalizations of solitons [15], as well as vortices [14]. Generalizations of one-dimensional [16,17] and two-dimensional [18] such entities were predicted to exist as stable objects in dual-core couplers (with the gain and loss being present in different cores).…”

Section: Introductionmentioning

confidence: 99%

Generalized dimers and their Stokes-variable dynamics

Xu¹,

Kevrekidis²,

Saxena³

2015

J. Phys. A: Math. Theor.

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In the present work, we generalize the setting of dimers with potential gain and loss which have been extensively considered recently in PT -symmetric contexts. We consider a pair of waveguides which are evanescently coupled but may also be actively coupled and may possess onsite gain and loss, as well as (possibly non-uniform) nonlinearity. We identify (and where appropriate review from earlier work) a plethora of interesting dynamical scenaria ranging from the existence of stable and unstable fixed points and integrable dynamics, to the emergence of pitchfork or Hopf bifurcations and the generation of additional fixed points and limit cycles, respectively, as well as the potential deviation of trajectories to infinity. Thus, a catalogue of a large number of possible cases is given and their respective settings physically justified (where appropriate).

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Gray solitons in parity-time symmetric potentials

Cited by 56 publications

References 15 publications

Nonlocal solitons in dual-periodicPT-symmetric optical lattices

Nonlocal solitons in dual-periodicPT-symmetric optical lattices

Quasi-energies, parametric resonances, and stability limits in ac-driven PT-symmetric systems

Generalized dimers and their Stokes-variable dynamics

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