Bifurcation structure of dissipative solitons

Gomila, Damià; Scroggie, A.J.; Firth, W. J.

doi:10.1016/j.physd.2006.12.008

Cited by 77 publications

(89 citation statements)

References 24 publications

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“…While our primary motivation is provided by the VCSEL-FSF, similar soliton phenomena have been found in systems such as lasers with saturable gain and absorption [28][29][30][31][32] and with a holding beam [33][34][35][36], as well as in VCSEL experiments employing coupled cavities [37] and a built-in saturable absorber [38], see also Ref. [39] for a review.…”

Section: Introductionmentioning

confidence: 63%

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

et al. 2011

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We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D) self-localized mode. We aim to extend the analysis to 2D stripe-shaped and vortex solitons. The radius of the vortices increases linearly with their topological charge, m, therefore the flat-stripe soliton may be interpreted as the vortex with m = ∞, while vortex solitons can be realized as stripes bent into rings. The results for the vortex solitons are applicable to a broad class of physical systems. There is a qualitative agreement between our results and those recently reported for models with saturable nonlinearity.

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Section: Introductionmentioning

confidence: 63%

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

et al. 2011

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“…Taking into account only second order dispersion (SOD) two regimes can be identified, characterized by either normal or anomalous chromatic dispersion. In the latter case the only type of DSs that exist are bright solitons arising in both the monostable [9] and bistable regimes [10][11][12]. In contrast, in the normal SOD case the main type of DSs that appear are dark solitons [12][13][14][15].…”

Section: Introductionmentioning

confidence: 95%

“…The parameters ρ, θ ∈ R correspond to the normalized injection and detuning, respectively, and serve as the control parameters of this system. The parameter ν represents the SOD coefficient and is also normalized: ν = −1 in the normal dispersion case and ν = 1 in the anomalous dispersion case [9][10][11][12]. The present work is restricted to the case ν = −1.…”

Section: The Lugiato-lefever Equationmentioning

confidence: 99%

Dark solitons in the Lugiato-Lefever equation with normal dispersion

et al. 2016

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The regions of existence and stability of dark solitons in the Lugiato-Lefever model with normal chromatic dispersion are described. These localized states are shown to be organized in a bifurcation structure known as collapsed snaking implying the presence of a region in parameter space with a finite multiplicity of dark solitons. For some parameter values dynamical instabilities are responsible for the appearance of oscillations and temporal chaos. The importance of the results for understanding frequency comb generation in microresonators is emphasized.

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“…This type of bifurcation structure is called collapsed snaking [16,17,41,42], which is significantly different from the homoclinic snaking appearing for dissipative solitons associated with subcritical patterns. Such homoclinic snaking, where many solutions coexist over a fixed parameter range around the Maxwell point, is probably better known and has been widely studied in physics [43,44] and optics [13,[45][46][47]. When TOD is taken into account, S u gradually develops oscillations when increasing d 3 , which allows bright solitons to come into existence.…”

Section: Modification Of the Bifurcation Structure Of The Solitonsmentioning

confidence: 99%

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

2017

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Using the Lugiato-Lefever model, we analyze the effects of third-order chromatic dispersion on the existence and stability of dark-and bright-soliton Kerr frequency combs in the normal dispersion regime. While in the absence of third-order dispersion only dark solitons exist over an extended parameter range, we find that third-order dispersion allows for stable dark and bright solitons to coexist. Reversibility is broken and the shape of the switching waves connecting the top and bottom homogeneous solutions is modified. Bright solitons come into existence thanks to the generation of oscillations in the switching-wave profiles. Temporal oscillatory instabilities of dark solitons are suppressed in the presence of sufficiently strong third-order dispersion, while bright solitons are never found to oscillate in time. As a result of third-order dispersion both bright and dark solitons are found to move with a velocity that depends on their width.

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Bifurcation structure of dissipative solitons

Cited by 77 publications

References 24 publications

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

From one- to two-dimensional solitons in the Ginzburg-Landau model of lasers with frequency-selective feedback

Dark solitons in the Lugiato-Lefever equation with normal dispersion

Coexistence of stable dark- and bright-soliton Kerr combs in normal-dispersion resonators

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