Soliton dynamics in periodically modulated directional couplers

Chu, P.L.; Malomed, Boris A.; Peng, Gang-Ding; Skinner, Iain

doi:10.1103/physreve.49.5763

Cited by 18 publications

(16 citation statements)

References 8 publications

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“…This simple result captures basic features of the SSB in DWP potentials, except for a special feature of the symmetry-breaking bifurcation in solitons, which is, respectively, sub-or supercritical for the attractive and repulsive nonlinearities [5,15,16]. The strong dependence of the stability of the SSB states on the relative phase φ suggests that the periodic sequence of π slips of the phase may indeed be an efficient tool for controlling the stability of these modes.…”

Section: The Two-mode Mean-field Modelmentioning

confidence: 61%

“…This effective dynamical symmetrization of the solitons, observed in Figs. 1(a) and 1(b), is explained by the fact that the noise creates variations in the critical population-difference criterion (see later discussion), causing the actual difference to fall below the threshold necessary for the existence of asymmetric solitons [5,15]. Nevertheless, the simulations clearly demonstrate the stabilization of the asymmetric solitons by π -flip management.…”

Section: Solitonsmentioning

confidence: 84%

“…The model based on Eqs. (1) applies as well to dual-core optical waveguides, with t replaced by the propagation coordinate z [4,5,15]. In that case, the fluctuations in E j represent random variations in the thickness of the barrier separating the cores, while E accounts for a randomly varying difference in the effective cross-sectional areas of the cores.…”

Section: Solitonsmentioning

confidence: 99%

“…A model of this type was considered for solitons in dual-core optical fibers with a periodically modulated coupling strength [15].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical control of nonlinear symmetry breaking under decoherence

et al. 2010

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We propose a control mechanism for the stabilization of symmetry-broken modes in Bose-Einstein condensates and optical beams trapped in double-well potentials in the presence of symmetric or asymmetric noise. The control, based on periodic π shifts of the phase in one well, is demonstrated for solitons and in the two-mode approximation. The latter setting is considered in both the mean-field and quantum (Bose-Hubbard) regimes.

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Section: The Two-mode Mean-field Modelmentioning

confidence: 61%

Section: Solitonsmentioning

confidence: 84%

Section: Solitonsmentioning

confidence: 99%

“…A model of this type was considered for solitons in dual-core optical fibers with a periodically modulated coupling strength [15].…”

Section: Introductionmentioning

confidence: 99%

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Dynamical control of nonlinear symmetry breaking under decoherence

et al. 2010

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“…(1) do not include terms accounting for the transverse diffraction or group-velocity dispersion, in the spatial-domain and temporal-domain realizations, respectively. Variable t is actually the propagation distance, and the ac modulation represents periodic variation of the thickness of the gap separating the cores [30]. As suggested in Refs.…”

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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Why variational approximation reduces solition switching in nonlinear couplers to the CW case

Skinner

1995

Opt Quant Electron

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Soliton dynamics in periodically modulated directional couplers

Cited by 18 publications

References 8 publications

Dynamical control of nonlinear symmetry breaking under decoherence

Dynamical control of nonlinear symmetry breaking under decoherence

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

Why variational approximation reduces solition switching in nonlinear couplers to the CW case

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