Singularities and special soliton solutions of the cubic-quintic complex Ginzburg-Landau equation

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

doi:10.1103/physreve.53.1190

Cited by 219 publications

(147 citation statements)

References 25 publications

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“…Haus et al [1,2] have developed a model based on the addition of the different effects assuming that all effects are small over one round-trip of the cavity. 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].…”

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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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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“…Coming from interactive coupling, they can become the dominant terms in the system, exceeding in strength the typical nonmechanical contribution to the Kerr-type nonlinearity. We show that this very unique form of nonlinearity supports bright flattop solitons [51], which may form spontaneously in polariton condensates, representing a translational symmetry breaking.…”

Section: Introductionmentioning

confidence: 99%

Interactive optomechanical coupling with nonlinear polaritonic systems

et al. 2017

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We study a system of interacting matter quasiparticles strongly coupled to photons inside an optomechanical cavity. The resulting normal modes of the system are represented by hybrid polaritonic quasiparticles, which acquire effective nonlinearity. Its strength is influenced by the presence of a mechanical mode and depends on the resonance frequency of the cavity. This leads to an interactive type of optomechanical coupling, which is distinct from previously studied dispersive and dissipative couplings in optomechanical systems. The emergent interactive coupling is shown to generate effective optical nonlinearity terms of high order, which are quartic in the polariton number. We consider particular systems of exciton polaritons and dipolaritons, and show that the induced effective optical nonlinearity due to interactive coupling can exceed in magnitude the strength of Kerr nonlinear terms, such as those arising from polariton-polariton interactions. As applications, we show that the higher-order terms give rise to localized bright flattop solitons, which may form spontaneously in polariton condensates.

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“…The one dimensional (1D) CGLE [23] is a generic equation which describes dissipative systems near a subcritical bifurcation to traveling waves. The 1D CGLE possesses a rich variety of solutions such as pulses (solitary waves), breathing solitons, pulsating, erupting and creeping solitons, multisolitons, fronts (shock waves), sinks (propagating hole with negative asymptotic group velocity), sources (propagating hole with positive asymptotic group velocity), periodic and quasi periodic solutions, periodic unbounded solutions [24]. For some dissipative systems, 1D CGLE needs to be modified to include nonlinear gradient terms resulting in 1D modified CGLE (1DMCGLE) [25].…”

Section: Introductionmentioning

confidence: 99%