Dark lattice solitons in one-dimensional waveguide arrays with defocusing saturable nonlinearity and alternating couplings

Kanshu, A.; Rüter, Christian E.; Kip, Detlef; Cuevas, J.

doi:10.1140/epjd/e2012-30204-4

Cited by 11 publications

(8 citation statements)

References 30 publications

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“…Dark breathers (DBs), i.e., breather states on a nonvanishing background, have been far less widely studied. Their recent realization in contexts such as surface water waves [9], Bose-Einstein condensates [10] (see also [11] for a recent review), ferromagnetic film strips [12], or optical waveguide arrays (for a recent example see, e.g., [13], and references therein) has received considerable attention. Note, however, that the DBs reported on in these works are based on the observation of dark (envelope) solitary waves.…”

Section: Introductionmentioning

confidence: 99%

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Damped-driven granular chains: An ideal playground for dark breathers and multibreathers

Chong

Yang

et al. 2014

Phys. Rev. E

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By applying an out-of-phase actuation at the boundaries of a uniform chain of granular particles, we demonstrate experimentally that time-periodic and spatially localized structures with a nonzero background (so-called dark breathers) emerge for a wide range of parameter values and initial conditions. We demonstrate a remarkable control over the number of breathers within the multibreather pattern that can be "dialed in" by varying the frequency or amplitude of the actuation. The values of the frequency (or amplitude) where the transition between different multibreather states occurs are predicted accurately by the proposed theoretical model, which is numerically shown to support exact dark breather and multibreather solutions. Moreover, we visualize detailed temporal and spatial profiles of breathers and, especially, of multibreathers using a full-field probing technology and enable a systematic favorable comparison among theory, computation, and experiments. A detailed bifurcation analysis reveals that the dark and multibreather families are connected in a "snaking" pattern, providing a roadmap for the identification of such fundamental states and their bistability in the laboratory.

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Section: Introductionmentioning

confidence: 99%

“…Their recent robust realization in contexts such as surface water waves [9], or Bose-Einstein condensates [10] (see also [11] for a recent review), ferromagnetic film strips [12] or optical waveguide arrays (see e.g. for a recent example [13] and references therein) has received considerable attention [34].…”

mentioning

confidence: 99%

Damped-driven granular chains: An ideal playground for dark breathers and multibreathers

Chong

Yang

et al. 2014

Phys. Rev. E

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“…For instance, defocusing lithium niobate waveguide arrays exhibit a different type of nonlinearity, namely a saturable, defocusing one due to the photovoltaic effect [21]. In the latter context, dark solitons have been identified not only in regular homogeneous lattices, but also in higher gaps [22], as parts of multi-component soliton complexes (such as dark-bright solitary waves) [23], and even in heterogeneous chains with alternating couplings [24].…”

Section: Introductionmentioning

confidence: 99%

Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

et al. 2014

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In the present paper we consider nonlinear dimers and trimers (more generally, oligomers) embedded within a linear Schr{\"o}dinger lattice where the nonlinear sites are of saturable type. We examine the stationary states of such chains in the form of plane waves, and analytically compute their reflection and transmission coefficients through the nonlinear oligomer, as well as the corresponding rectification factors which clearly illustrate the asymmetry between left and right propagation in such systems. We examine not only the existence but also the dynamical stability of the plane wave states. Lastly, we generalize our numerical considerations to the more physically relevant case of Gaussian initial wavepackets and confirm that the asymmetry in the transmission properties also persists in the case of such wavepackets

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“…Recently, there has been a lot of interest in binary PLs-a special type of nonuniform PL whose additional periodicity gives rise to an extra mini-gap [19] in the corresponding spectra. One-dimensional binary PLs were examined both theoretically and experimentally in structures composed of optical waveguides with alternating widths [20][21][22] or periodically modified spacing between them [23][24][25]. In both configurations mini-gaps occur and an additional narrow frequency region for formation of (mini-) gap solitons opens.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of gap solitons in one-dimensional binary lattices with saturable self-defocusing nonlinearity and alternating spacing

et al. 2012

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The existence and stability of spatial solitons in one-dimensional binary photonic lattices with alternating spacing and a saturable defocusing type of nonlinearity are investigated. Five types of nonlinear localized structures are found to exist: two in the mini-gap in the energy spectrum and others in the regular gap. It is proved that some of them are stable in certain ranges of the system parameters. Interactions between two identical localized structures propagating parallel to each other are investigated, too. It is shown that this interaction leads to formation of different localized patterns, such as solitons, breather-like modes, and breather complexes. The interaction output depends on the power and type of interacting identical solitons, the separation between them, the width of the mini-gap, and the phase relation between the tails of interacting solitons.

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Dark lattice solitons in one-dimensional waveguide arrays with defocusing saturable nonlinearity and alternating couplings

Cited by 11 publications

References 30 publications

Damped-driven granular chains: An ideal playground for dark breathers and multibreathers

Damped-driven granular chains: An ideal playground for dark breathers and multibreathers

Asymmetric Wave Propagation Through Saturable Nonlinear Oligomers

Dynamics of gap solitons in one-dimensional binary lattices with saturable self-defocusing nonlinearity and alternating spacing

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