Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion

Soto-Crespo, J. M.; Akhmediev, Nail; Afanasjev, V. V.; Wabnitz, Stefan

doi:10.1103/physreve.55.4783

Cited by 178 publications

(141 citation statements)

References 55 publications

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“…If on the contrary g 1 is negative and D i > 0 (figure 7b), energy appears at the top of the pulse and disappears at its bottom, yielding some pulse narrowing, which could be expected to balance the broadening caused by the nonlinear index variations. In fact the analytical localized solution (45) is never stable when β 2 D r < 0, but can be stabilized when higher order nonlinear terms are taken into account, as shows the study of the so-called quintic CGL equation [18]. The stabilizing term should be a quintic nonlinear absorption.…”

Section: Localized Solutionsmentioning

confidence: 99%

“…Thus they are in fact not equivalent, and the periodicity of the theoretical result is 90 degrees, as that of the experimental one. Further it has been shown [18] that an excessive value of the nonlinear gain might prevent pulse stabilization. A more accurate analysis would thus very likely show that the regions where D i takes its highest values are out of the domain of stability of the localized pulse.…”

Section: The Different Regimesmentioning

confidence: 99%

“…A localized analytical solution of the CGL equation (34) can also be written [18]. It has the following expression:…”

Section: Localized Solutionsmentioning

confidence: 99%

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Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser

et al. 2002

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We consider an Yb-doped double-clad fiber laser in a unidirectional ring cavity containing a polarizer placed between two half-wave plates. Depending on the orientation of the phase plates, the laser operates in continuous, Qswitch, mode-lock or unstable self-pulsing regime. An experimental study of the stability of the mode locking regime is realized versus the orientation of the half-wave plates. A model for the stability of self-mode-locking and cw operation is developed starting from two coupled nonlinear Schrödinger equations in a gain medium. The model is reduced to a master equation in which the coefficients are explicitly dependent on the orientation angles of the phase plates. Analytical solutions are given together with their stability versus the angles.

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Section: Localized Solutionsmentioning

confidence: 99%

Section: The Different Regimesmentioning

confidence: 99%

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Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser

et al. 2002

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“…29 Exact analytical soliton solutions were found, although all of them proved to be unstable. Numerical simulations allowed one to find regions in the parameter space, where stable temporal solitons exist.…”

Section: Stable Stationary "Optical Bullets" In All Dispersion Rmentioning

confidence: 99%

Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes

Akhmediev

Soto-Crespo

Grelu

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Nonlinear dissipative systems display the full ͑3+1͒D spatiotemporal dynamics of stable optical solitons. We review recent results that were obtained within the complex cubic-quintic GinzburgLandau equation model. Numerical simulations reveal the existence of stationary bell-shaped ͑3+1͒D solitons for both anomalous and normal chromatic dispersion regimes, as well as the formation of double soliton complexes. We provide additional insight concerning the possible dynamics of these soliton complexes, consider collision cases between two solitons, and discuss the ways nonstationary evolution can lead to optical pattern formation. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2746830͔The subject of dissipative solitons has emerged recently, driving an impressive number of studies in many areas of nonlinear science. Previous studies of purely temporal dissipative solitons have been highly useful, for both fundamental science and the development of high bit-rate optical telecommunications and passively mode-locked lasers. Now, it is the time for generalizations to "3+1…-D domain. An appropriate term to describe the new structures is "dissipative optical bullets." Spatiotemporal optical dissipative solitons are localized formations in systems with gain, loss, spectral filtering, dispersion, diffraction, and nonlinearity. The combined interplay between these physical effects creates an optical field confined in both temporal and transverse coordinates. The confinement occurs mainly due to the nonlinear gain balanced with a nonlinear loss in the system. The balance between nonlinearity and dispersion/diffraction, which was the main reason for the existence of conservative solitons, can be weakened or even lifted. Consequently, dissipative optical bullets can exist in media with either anomalous or normal dispersion. Optical bullets have extended regions of stability, which allow experimental observation and potential use of these objects. We present here a review of the latest numerical results concerning dissipative spatiotemporal optical solitons and their complexes. The interaction between stable dissipative light bullets reveals the importance of the phase difference between them. Controlling this parameter can lead to fusion, erasure of one of the solitons or to the formation of soliton complexes, or bound states. Collisions of solitons with nonzero velocities can also create these bound states. The bound states in turn can exhibit a wide range of dynamics, such as rotation and vibration, making them akin to atomic molecules. Among other interesting dynamical aspects of dissipative optical bullets presented in this work is a transverse pattern formation out of the light bullets that lack stability.

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“…Analytical studies of Akhmediev et al [16,17] are based on a normalized complex cubic Ginzburg-Landau (CGL) equation and give the stability conditions of the mode-locked solutions. On the other hand, many numerical simulations have been done to complete analytic approaches [18]- [20]. We have recently investigated experimentally and theoretically the mode-locking properties of an Yb-doped double clad fiber laser passively mode-locked through nonlinear polarization rotation [12,21].…”

Section: Introductionmentioning

confidence: 99%

Stability calculations for the ytterbium-doped fibre laser passively mode-locked through nonlinear polarization rotation

Leblond¹,

Sanchez²,

Brunel³

et al. 2004

J. Opt. A: Pure Appl. Opt.

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We investigate theoretically a fiber laser passively mode-locked with nonlinear polarization rotation. A unidirectional ring cavity is considered with a polarizer placed between two sets of a halfwave plate and a quarterwave plate. A master equation is derived and the stability of the continuous and mode-locked solutions is studied. In particular, the effect of the orientation of the four phase plates and of the polarizer on the mode-locking regime is investigated.

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Pulse solutions of the cubic-quintic complex Ginzburg-Landau equation in the case of normal dispersion

Cited by 178 publications

References 55 publications

Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser

Experimental and theoretical study of the passively mode-locked ytterbium-doped double-clad fiber laser

Spatiotemporal optical solitons in nonlinear dissipative media: From stationary light bullets to pulsating complexes

Stability calculations for the ytterbium-doped fibre laser passively mode-locked through nonlinear polarization rotation

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