Lattice solitons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric mixed linear-nonlinear optical lattices

He, Yan; Zhu, Xing; Mihalache, Dumitru; Liu, Jinglin; Chen, Zhanxu

doi:10.1103/physreva.85.013831

Cited by 172 publications

(95 citation statements)

References 37 publications

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“…In particular, the properties of solitons and discrete nonlinear modes have been studied in free-standing PT -symmetric waveguides [5], couplers [6][7][8][9], oligomers [10,11], and periodic lattices with [12] and without [13][14][15][16][17] transverse refractive-index gradients, and in truncated lattices [18], among other settings. An especially interesting situation occurs when the underlying evolution equations contain only nonlinear PT -symmetric terms [19,20], or mixed linear-nonlinear lattices [21][22][23].…”

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confidence: 99%

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

2014

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We consider bright solitons supported by a symmetric inhomogeneous defocusing nonlinearity growing rapidly enough toward the periphery of the medium, combined with an antisymmetric gain-loss profile. Despite the absence of any symmetric modulation of the linear refractive index, which is usually required to establish a parity-time (PT ) symmetry in the form of a purely real spectrum of modes, we show that the PT symmetry is never broken in the present system, and that the system always supports stable bright solitons, i.e., fundamental and multipole ones. This fact is connected to the nonlinearizability of the underlying evolution equation. The high current interest in parity-time (PT )-symmetric systems with complex potentials is partially motivated by the remarkable behavior of the corresponding linear spectrum, which remains purely real until the strength of the imaginary part of the potential attains a certain PTsymmetry breaking threshold, above which it becomes complex [1]. The effect has been experimentally observed in optics, where the similarity of the paraxial evolution equation, governing the propagation of light beams in media with an even spatial profile of the refractive-index modulation and an odd gain-loss profile, with the Schrö-dinger equation governing the evolution of the quantummechanical wave function in a complex potential, enables visualization of the PT symmetry and its breakup at a critical point [2]. While eigenmodes of linear PT -symmetric potentials are well-understood [1,3,4], the evolution of nonlinear excitations in them remains a subject of active research. In particular, the properties of solitons and discrete nonlinear modes have been studied in free-standing As mentioned previously, a generic property of PT -symmetric structures is that they support stable excitations only if the spectrum of the associated linear system is real, i.e., the symmetry is not broken. As a result, the stability domain of nonlinear excitations, if defined in terms of the gain-loss strength, often coincides with the domain of the unbroken PT symmetry in the respective linear system. However, systems may be prepared to be nonlinearizable, i.e., the nonlinear terms in the underlying evolution equation cannot be omitted even for the decaying tails of localized nonlinear excitations. Under such conditions, no direct link can be drawn between the spectra of the nonlinear system and its linear counterpart.In this Letter, we address that case in a system with an odd gain-loss profile and defocusing nonlinearity, whose local strength grows toward the periphery. In the absence of gain and loss, such a system supports bright solitons in all three dimensions [24][25][26][27][28]. Existence of bright solitons in spite of the self-defocusing nature of the nonlinearity is at first counterintuitive, but actually it is a consequence of the nonlinearizability of the respective nonlinear Schrödinger equation on the soliton tails. In this Letter, we show that a system of this type, with an even profile of the growing no...

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confidence: 99%

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

2014

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“…However, a recent discovery is that, in dissipative but parity-time (PT ) symmetric systems, solitons can still exist as continuous families, parameterized by their propagation constants [5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. A novelty of PT -symmetric systems is that, despite gain and loss, the linear spectrum of the system can still be all-real [23,24], thus all linear modes still exhibit regular wave behavior, just as in conservative systems.…”

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confidence: 99%

Necessity of PT symmetry for soliton families in one-dimensional complex potentials

Yang

2014

Physics Letters A

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For the one-dimensional nonlinear Schrödinger equation with a complex potential, it is shown that if this potential is not parity-time (PT ) symmetric, then no continuous families of solitons can bifurcate out from linear guided modes, even if the linear spectrum of this potential is all real. Both localized and periodic non-PT -symmetric potentials are considered, and the analytical conclusion is corroborated by explicit examples. Based on this result, it is argued that PT -symmetry of a one-dimensional complex potential is a necessary condition for the existence of soliton families.

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“…Presently the PT -symmetric models become increasingly demanded by the physical scientific community [1,8,19,27] (especially for the application to nonlinear optics [1,19,27]) inasmuch as they permit to obtain physically meaningful results without invoking the more restrictive condition of Dirac Hermiticity [8].…”

Section: Pt -Symmetry and Remarks On Possible Physical Applicationsmentioning

confidence: 99%

Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

Vakhnenko

2021

JNMP

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The new type of third-order spectral operator suitable to generate new multifield semidiscrete nonlinear systems with two coupling parameters in the framework of zero-curvature equation is proposed. The evolution operator corresponding to the first integrable system in an infinite hierarchy is explicitly recovered and the general form of first integrable system is isolated. The generalized procedure for the direct recursive development of infinite hierarchy of local conservation laws is presented and several lowest local conservation laws and local conserved densities are found. The reduction to the real field amplitudes in general system with unfixed sampling functions is made and the symmetric parametrization of field amplitudes allowing to exclude the redundant field function and to resolve the problem of sampling fixation for the particular realization of reduced integrable system is considered. This parametrization gives rise to the four field nonlinear model which in certain intervals of adjustable coupling parameter could serve as a semidiscrete analogy to the beam-plasma interaction system.

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Lattice solitons inPT-symmetric mixed linear-nonlinear optical lattices

Cited by 172 publications

References 37 publications

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity

Necessity of PT symmetry for soliton families in one-dimensional complex potentials

Four-Wave Semidiscrete Nonlinear Integrable System with 𝒫𝒯-Symmetry

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