Solvable model for solitons pinned to a parity-time-symmetric dipole

Mayteevarunyoo, Thawatchai; Malomed, Boris A.; Reoksabutr, Athikom

doi:10.1103/physreve.88.022919

Cited by 47 publications

(37 citation statements)

References 68 publications

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“…However, continuous models can be used to predict a range of important effects beyond two-mode approximation, such as the appearance of radiation losses in curved PT waveguides [50]. On the other hand, it was predicted that a PT structure placed in a nonlinear medium can trap soliton [53]. Furthermore, soliton scattering by a localized mode of PT coupler can exhibit nonreciprocal and non-conservative scattering, which is strongly dependent on the relative phase between the mode and the soliton [54].…”

Section: Nonlinear Modesmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

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One of the challenges of the modern photonics is to develop all-optical devices enabling increased speed and energy efficiency for transmitting and processing information on an optical chip. It is believed that the recently suggested ParityTime (PT) symmetric photonic systems with alternating regions of gain and loss can bring novel functionalities. In such systems, losses are as important as gain and, depending on the structural parameters, gain compensates losses. Generally, PT systems demonstrate nontrivial non-conservative wave interactions and phase transitions, which can be employed for signal filtering and switching, opening new prospects for active control of light. In this review, we discuss a broad range of problems involving nonlinear PT-symmetric photonic systems with an intensitydependent refractive index. Nonlinearity in such PT symmetric systems provides a basis for many effects such as the formation of localized modes, nonlinearly-induced PT-symmetry breaking, and all-optical switching. Nonlinear PT-symmetric systems can serve as powerful building blocks for the development of novel photonic devices targeting an active light control.

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Section: Nonlinear Modesmentioning

confidence: 99%

Nonlinear switching and solitons in PT‐symmetric photonic systems

Suchkov

Sukhorukov

Huang

et al. 2016

Laser & Photonics Reviews

352

263

View full text Add to dashboard Cite

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“…Exact analytical solutions for localized modes with a point-like (δ-functional) gain-loss dipole were reported [27]. Abrupt phase transitions for solitons in PT -symmetric media were studied [28].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional $${{\varvec{\mathcal {PT}}}}$$ PT -symmetric inhomogeneous nonlinear couplers with gain and loss

Chen

Jiang

et al. 2015

Nonlinear Dyn

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A (3+1)-dimensional variable-coefficient coupled nonlinear Schrödinger equation in parity-time symmetric inhomogeneous nonlinear couplers with gain and loss is studied, and the PT -symmetric and PT -antisymmetric combined Kuznetsov-Ma soliton solutions are obtained via the Darboux transformation method. Nonlinear tunnelling effect of controllable combined Kuznetsov-Ma solitons such as their restraint, maintenance and postpone are discussed when they pass through the dispersion/diffraction barrier and well.

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“…In direct simulations performed at ω = 0, the actually observed stability boundary rises to values exceeding the one (21). For example, if V 1 = 1/2 and E = √ 15, the lower existence bound for solution (17) in Eq.…”

Section: The Cases Of Slow and Fast Modulations (Adiabatic And Amentioning

confidence: 99%

“…[19]. Related to these models are systems featuring discrete PT -balanced elements embedded into continuous nonlinear conservative media [20,21], which, in particular, allow one to find exact solutions for solitons pinned to the PT -symmetric dipole [21].…”

Section: Introduction and The Modelmentioning

confidence: 99%

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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Solvable model for solitons pinned to a parity-time-symmetric dipole

Cited by 47 publications

References 68 publications

Nonlinear switching and solitons in PT‐symmetric photonic systems

Nonlinear switching and solitons in PT‐symmetric photonic systems

Nonlinear tunnelling effect of combined Kuznetsov–Ma soliton in (3+1)-dimensional $${{\varvec{\mathcal {PT}}}}$$ PT -symmetric inhomogeneous nonlinear couplers with gain and loss

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

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