Stability of Multihump Optical Solitons

Ostrovskaya, Elena A.; Kivshar, Yuri S.; Skryabin, Dmitry V.; Firth, W. J.

doi:10.1103/physrevlett.83.296

Cited by 130 publications

(123 citation statements)

References 22 publications

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“…Examples are three-wave [14] and four-wave [42,43] systems with quadratic nonlinearity. Similar states were also found in a model with saturable nonlinearity, but without the BG-induced coupling [44].…”

Section: B Bound States Of Solitonssupporting

confidence: 61%

Solitons in Bragg gratings with saturable nonlinearities

et al. 2007

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We introduce two different systems of coupled-mode equations to describe the interaction of two waves coupled by the Bragg reflection in the presence of saturable nonlinearity. The basic model assumes the ordinary linear coupling between the modes. It may be realized as a photorefractive waveguide, with a Bragg lattice permanently written in its cladding. We demonstrate the presence of a cutoff point in the system's bandgap, with gap solitons existing only on one side of it. Close to this point, the soliton's norm diverges with power −3 / 2. The soliton family between the cutoff point and the edge of the bandgap is stable. In this model, stationary bound states of two in-phase solitons are found too, but they are unstable, transforming themselves into breathers. Another model assumes a photoinduced longitudinal bulk grating, with the corresponding intermode coupling subject to saturation along with the nonlinearity. In that model, another cutoff point is found, with the soliton's norm diverging near it with power −2. Solitons are stable in this model too (while it does not give rise to twosoliton bound states). Collisions between moving solitons are always quasi-elastic, in either model.

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Section: B Bound States Of Solitonssupporting

confidence: 61%

Solitons in Bragg gratings with saturable nonlinearities

et al. 2007

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“…Families of two-component composite solitons are found by numerical relaxation technique [13], and some results of these calculations are presented in Fig. 6, for |0, 1 and |0, 2 solitons at s = 0.8.…”

Section: Multi-hump Solitary Wavesmentioning

confidence: 99%

“…In the framework of this theory, the unstable eigenvalue of the associated linear spectral problem is treated as a small parameter of the asymptotic expansions [10], and the resulting equation for the slowly varying soliton propagation constant may also account for weakly nonlinear effects that describe the long-time evolution of linearly unstable solitary waves, and an effective saturation of the soliton instability due to higher-order nonlinear effects. In the case of multi-parameter solitary waves, a simplified version of this asymptotic method applied near a marginal stability point (or, in general, a surface) is reduced to finding certain determinants constructed from the derivatives of the system invariants [11,12,13,14]. However, the validity of this bifurcation theory has no rigorous proof, and it can only be used to estimate the domains of the soliton stability and instability.…”

Section: Introductionmentioning

confidence: 99%

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Stability of Spatial Optical Solitons

Kivshar¹,

Sukhorukov²

2001

Springer Series in Optical Sciences

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“…The new DVS showing a stable ring profile is different from a ring-DVS with high intensity demonstrated in Ref. [25] and can be understood as composite solitons with the DFS [31,37]. The OAM transfer between the two solitons is not observed due to the phase-independence, however, the OAM of DVS arises a transfer from four-lobes into a single port.…”

Section: Incoherent Interactionsmentioning

confidence: 99%

Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton

et al. 2014

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Abstract:We study coherent and incoherent interactions between discrete vortex and fundamental solitons in two-dimensional photonic lattices, presenting a new scheme for all-optical routings and topological transformations of vorticities. Due to the multi-lobe intensity and step-phase structure of the discrete vortex soliton, the coherent soliton-interactions allow both solitons to be steered into multiple different possible destination ports depending on the initial phase of the discrete fundamental soliton. We show that charge-flipping of phase singularities and orbital angular momentum transfer can occur during the coherent interactions between the two solitons. For incoherent interactions, by controlling the relative intensities of the two solitons, we reveal that soliton-steering can be realized by either attracting the discrete fundamental soliton to four ports or localizing the four-lobe discrete vortex soliton into a ring soliton.

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Stability of Multihump Optical Solitons

Cited by 130 publications

References 22 publications

Solitons in Bragg gratings with saturable nonlinearities

Solitons in Bragg gratings with saturable nonlinearities

Stability of Spatial Optical Solitons

Beam steering and topological transformations driven by interactions between a discrete vortex soliton and a discrete fundamental soliton

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