Effect of nonlinear gain and filtering on soliton interaction

Uzunov, Ivan M.; Muschall, R.; Gölles, M.; Lederer, F.; Wabnitz, Stefan

doi:10.1016/0030-4018(95)00283-e

Cited by 26 publications

(8 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…the distance between the solitons in the BS is large, and, accordingly, the corresponding binding energy is exponentially small. Nevertheless, existence and stability of the BS's predicted by the perturbation theory was confirmed by direct numerical simulations [26] of the driven damped NLS equation [8] (see also [9]); recently, this prediction was also confirmed, with a fairly good accuracy, for the cubic GL equation (1) [27]. In the present model, the BS's can be rendered more robust by increasing the dissipative constant Γ 0 in the passive core.…”

supporting

confidence: 73%

Stable solitons in two-component active systems

1996

View full text Add to dashboard Cite

As is known, a solitary pulse in the complex cubic Ginzburg-Landau (GL) equation is unstable. We demonstrate that a system of two linearly coupled GL equations with gain and dissipation in one subsystem and pure dissipation in another produces absolutely stable solitons and their bound states. The problem is solved in a fully analytical form by means of the perturbation theory. The soliton coexists with a stable trivial state; there is also an unstable soliton with a smaller amplitude, which is a separatrix between the two stable states. This model has a direct application in nonlinear fiber optics, describing an Erbium-doped laser based on a dual-core fiber.

show abstract

supporting

confidence: 73%

Stable solitons in two-component active systems

1996

View full text Add to dashboard Cite

show abstract

“…For certain parameter sets this equation was shown to support solitary wave solutions, called dissipative solitons, as well as bound states (BS) of pairs of SPs [13,14,15,16,17,18,19,20,21]. Careful numerical investigations [16] have demonstrated BS formation from a pair of initially resting SPs.…”

Section: Introductionmentioning

confidence: 99%

Discrete family of dissipative soliton pairs in mode-locked fiber lasers

et al. 2009

View full text Add to dashboard Cite

We numerically investigate the formation of soliton pairs (bound states) in mode-locked fiber ring lasers. In the distributed model (complex cubic-quintic Ginzburg-Landau equation) we observe a discrete family of soliton pairs with equidistantly increasing peak separation. This family was identified by two alternative numerical schemes and the bound state instability was disclosed by a linear stability analysis. Moreover, similar families of unstable bound state solutions have been found in a more realistic lumped laser model with an idealized saturable absorber (instantaneous response). We show that a stabilization of these bound states can be achieved when the finite relaxation time of the saturable absorber is taken into account. The domain of stability can be controlled by varying this relaxation time.

show abstract

“…It turned out that the chirp of these solutions influences significantly the process of nonlinear interactions (Malomed 1991). There has been established a significant reduction of nonlinear interactions in both cases: BLA (Kodama and Wabnitz 1993) and BLA with nonlinear gain (Kodama et al 1992;Afanasjev and Akhmediev 1995;Uzunov et al 1995;Afanasjev and Akhmediev 1996;, respectively. Next, there has been shown that in nonlinear dissipative systems governed by the CCQGLE new types of vibrating and shaking soliton pairs exist ).…”

Section: Introductionmentioning

confidence: 98%

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

View full text Add to dashboard Cite

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.

show abstract

Effect of nonlinear gain and filtering on soliton interaction

Cited by 26 publications

References 11 publications

Stable solitons in two-component active systems

Stable solitons in two-component active systems

Discrete family of dissipative soliton pairs in mode-locked fiber lasers

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

Contact Info

Product

Resources

About