Influence of higher-order effects on pulsating solutions, stationary solutions and moving fronts in the presence of linear and nonlinear gain/loss and spectral filtering

Uzunov, Ivan M.; Arabadzhiev, Todor N.; Georgiev, Zhivko D.

doi:10.1016/j.yofte.2015.04.003

Cited by 23 publications

(5 citation statements)

References 35 publications

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“…Even though numerical simulations have demonstrated the existence of pulsating solutions and their period bifurcations, the search for analytical expressions of pulsating solutions and bifurcation boundaries has been elusive. The moment method [66][67][68], the Lagrange equation [69], or the variational method [67,70,71] can be used to reduce the infinite-dimensional CQGLEs to the five-dimensional model, then the nonlinear part is solved by the RK4IP method and the linear part is solving in Fourier domain [36,66,72,73], which implements the modeling of passively mode-locked fiber lasers. Researchers uncovered that all soliton solutions of CQGLEs had regular evolution patterns of amplitude, frequency, position, width, and chirp [70].…”

Section: Numerical Simulation Based On Cubic-quinticmentioning

confidence: 99%

“…The TOD has been proven to eliminate the periodicity of soliton pulsations and transform them into stationary solitons [75]. The mutual transformation between stationary solitons and soliton pulsations may be realized by changing higher-order effects such as IRS, SS, and TOD [67,69], and the former two effects (IRS, SS) have a stronger influence on soliton pulsations than the third one (TOD) [66]. In the presence of linear gain, nonlinear gain, gain saturation effect, spectral filtering effect, and IRS, the self-frequency shift of stationary solitons and soliton pulsations can be completely suppressed [73].…”

Section: Numerical Simulation Based On Cubic-quinticmentioning

confidence: 99%

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Paths from stationary to chaos in passively mode-locked fiber lasers: research progress of soliton pulsations and soliton explosions

Han¹,

Gao²,

Hao³

et al. 2022

J. Phys. B: At. Mol. Opt. Phys.

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Research has shown that passively mode-locked fiber lasers produce chaotic output, which has caught the attention of physicists, chemists, and bio-scientists owing to their wide bandwidth, good random characteristics, and strong anti-interference. In passively mode-locked fiber lasers, soliton pulsations and soliton explosions with period bifurcation characteristics have been demonstrated to be effective paths to chaos as far as 20 years ago. However, due to the lack of real-time spectrum measurement techniques, the earlier research investigated their theoretical aspect. In recent years, the rise of the dispersive Fourier transform technique has activated an upsurge of their experimental research. The present work first discussed the theoretical model of passively mode-locked fiber lasers, the computational analysis method of soliton dynamics, and the related theory of dispersive Fourier transform technique. In addition, we presented and evaluated the progress of the theoretical and experimental research on soliton pulsations as well as on soliton explosions in passively mode-locked fiber lasers. Finally, we proposed the future research directions of the soliton pulsations and soliton explosions that offer great promise for scientific discoveries.

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Section: Numerical Simulation Based On Cubic-quinticmentioning

confidence: 99%

Section: Numerical Simulation Based On Cubic-quinticmentioning

confidence: 99%

Paths from stationary to chaos in passively mode-locked fiber lasers: research progress of soliton pulsations and soliton explosions

Han¹,

Gao²,

Hao³

et al. 2022

J. Phys. B: At. Mol. Opt. Phys.

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“…The corresponding cubic-quintic (CQ) nonlinearity, which was first phenomenologically proposed by Petviashvili and Sergeev [14], can be derived as an approximate fiber-laser model, which is commonly and successfully used [15][16][17]. The existence of stable dark [24] and bright [18]-[23] dissipative solitons in the CGLE, as well as of their bound states [25], has been firmly established in theory and experimentally.The form and stability of isolated bright dissipative solitons in the CQ-CGLE with the TOD term was investigated too, but to a lesser degree [26][27][28]. A possibility of the existence of the soliton bound states in this model is a natural extension of the analysis, with obvious perspectives for experimental realization and applications.…”

mentioning

confidence: 99%

“…The form and stability of isolated bright dissipative solitons in the CQ-CGLE with the TOD term was investigated too, but to a lesser degree [26][27][28]. A possibility of the existence of the soliton bound states in this model is a natural extension of the analysis, with obvious perspectives for experimental realization and applications.…”

mentioning

confidence: 99%

Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion

2018

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We consider the model of fiber-laser cavities near the zero-dispersion point, based on the complex Ginzburg-Landau equation with the cubic-quintic nonlinearity and third-order dispersion (TOD) term. It is known that this model supports stable dissipative solitons. We demonstrate that the same model gives rise to several specific families of robust bound states of solitons. There are both stationary and dynamical bound states, with constant or oscillating separation between the bound solitons. Stationary states are multistable, corresponding to different values of the separation. Following the increase of the TOD coefficient, the stationary bound state with the smallest separation gives rise to the oscillatory one through the Hopf bifurcation. Further growth of TOD leads to a bifurcation transforming the oscillatory bound state into a chaotically oscillating one. Families of multistable three- and four-soliton complexes are found too, the ones with the smallest separation between the solitons again ending by the transition to oscillatory states through the Hopf bifurcation.

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“…So, the pulsating solution of Uzunov et al (2014) is not a perturbed version of some of the pulsating solutions of CCQGLE found in Tsoy and Akhmediev (2005) and Tsoy et al (2006). The influence of IRS, self-steepening and third-order of dispersion on the pulsating solutions of Tsoy and Akhmediev (2005) and Tsoy et al (2006) has been recently studied in Uzunov et al (2015). Finally, in Fig.…”

Section: Self-frequency Shift Of Equilibrium and Pulsating Solutionsmentioning

confidence: 97%

Self-frequency shift and nonlinear interaction of equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering

2015

Self Cite

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In this work we study numerically the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering (IRS). It has been established that the stationary value of the central frequency of solutions, which appears as a result of the collective action of these physical effects, is a linearly increasing function of the Raman parameter c for the solution of Tsoy and Akhmediev (Phys Lett A 343:17-422, 2005), Tsoy et al. (Phys Rev E 73:036621, 2006), and the quadratic function of c for the parameters used in Uzunov et al. (Phys Rev E 90:042906, 2014). We have found a complete suppression of the self-frequency shift of the equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the Poincare-Andronov-Hopf bifurcation (PAHB) (Uzunov et al. in Phys Rev E 90:042906, 2014). We have numerically observed stable pairs and sequences of equidistant equilibrium solutions and pulsating solutions propagating in the presence of linear and nonlinear gain, spectral filtering, and IRS below and at the point of the PAHB. The pairs and equidistant sequences of pulsating solutions at the point of bifurcation require larger initial separation and exist at smaller distances of propagation than the pairs and equidistant sequences of the equilibrium solutions below the point of bifurcation.

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Influence of higher-order effects on pulsating solutions, stationary solutions and moving fronts in the presence of linear and nonlinear gain/loss and spectral filtering

Cited by 23 publications

References 35 publications

Paths from stationary to chaos in passively mode-locked fiber lasers: research progress of soliton pulsations and soliton explosions

Paths from stationary to chaos in passively mode-locked fiber lasers: research progress of soliton pulsations and soliton explosions

Stationary and oscillatory bound states of dissipative solitons created by third-order dispersion

Self-frequency shift and nonlinear interaction of equilibrium and pulsating solutions in the presence of linear and nonlinear gain, spectral filtering, and intrapulse Raman scattering

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