Optimal Condition for Suppressing Gain Dispersion Effects in Dissipative Soliton Generation
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Gain dispersion impedes the generation of ultrashort dissipative solitons, especially in mode-locked lasers, by limiting the transform-limited pulse width and causing instability near zero dispersion. We have found a hyper-surface in the parameter space of a mode-locked laser for the best suppression of the gain dispersion effects. This is achieved by analyzing the proximity of a dissipative soliton to the stationary solution of the complex cubic-quintic Ginzburg–Landau equation in the absence of gain dispersion with the method of moments. Theoretical and experimental investigations show that the combinations of system parameters in a specific region near the hyper-surface allow for a dissipative soliton width that is very close to the minimum value, as well as a large stable mode-locking region at anomalous group delay dispersion. These findings provide new insights into ultrashort dissipative soliton generation and help to optimize mode-locked lasers with dispersion, nonlinearity, loss, and gain all taken into account simultaneously.Keywords:
Dissipative soliton
We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite dissipative layer as well as a wave passing from a dissipative layer into a non-dissipative one and vice versa. New effects are presented in the case of numerically finite barrier on the soliton path: first, if the form of dissipation distribution has a form of a frozen soliton, the wave that leaves the dissipative barrier becomes a bi-soliton and a reflection wave arises as a comparatively small and quasi-harmonic oscillation. Second, if the dissipation is negative (the wave, instead of loosing energy, is pumped with it) the passed wave is a soliton of a greater amplitude and velocity. Third, when the travelling wave solution of the KdV-Burgers (it is a shock wave in a dissipative region) enters a non-dissipative layer this shock transforms into a quasi-harmonic oscillation known for the KdV.
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We study the behavior of the soliton which, while moving in non-dissipative medium encounters a barrier with dissipation. The modelling included the case of a finite dissipative layer as well as a wave passing from a dissipative layer into a non-dissipative one and vice versa. New effects are presented in the case of numerically finite barrier on the soliton path: first, if the form of dissipation distribution has a form of a frozen soliton, the wave that leaves the dissipative barrier becomes a bi-soliton and a reflection wave arises as a comparatively small and quasi-harmonic oscillation. Second, if the dissipation is negative (the wave, instead of loosing energy, is pumped with it) the passed wave is a soliton of a greater amplitude and velocity. Third, when the travelling wave solution of the KdV-Burgers (it is a shock wave in a dissipative region) enters a non-dissipative layer this shock transforms into a quasi-harmonic oscillation known for the KdV.
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An attractor of dissipative structures in solitons described by the Korteweg-de Vries (K-dV) equation with a viscous dissipation term is investigated, with the use of an eigenfunction spectrum analysis associated with the dissipative dynamical operator [Phys. Rev. E 49 (1994) 5546]. It is shown numerically and quantitatively that the basic procesess for the self-organization of dissipative soliton are spectrum transfer by nonlinear interaction and selective dissipation among the eigenmodes of the dissipative operator. It is quantitatively shown that an interchange between the dominant operators occurs during nonlinear self-organization processes, which leads to a final self-similar coherent structure uniquely determined by the dissipative operator.
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We have experimentally investigated the propagation of a soliton in a nonlinear LC circuit with inhomogeneity and dissipation. In a homogeneous and dissipative circuit, the amplitude of a soliton decreases with the distance. The damping of a soliton is weakened if the inhomogeneity is introduced in a dissipative circuit, and the amplitude begins to increase in the circuit of strong inhomogeneity. The disintegration of soliton is not clearly observed in the present experiment. The experimental result is qualitatively explained by the Korteweg-de Vries equation with inhomogeneity and dissipation.
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In the third and final talk on dissipative structures in fiber applications, we discuss mathematical techniques that can be used to characterize modern laser systems that consist of several discrete elements. In particular, we use a nonlinear mapping technique to evaluate high power laser systems where significant changes in the pulse evolution per cavity round trip is observed. We demonstrate that dissipative soliton solutions might be effectively described using this Poincare mapping approach.
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We report on the evolution of dissipative-soliton laser from single pulse to soliton molecule, lastly to multiple pulses. The experimental observations show that the pulse separation of soliton molecules is oscillating stochastically. It is found that the proposed fiber laser delivers pulses from a soliton to a soliton molecule, two solitons, a soliton molecule together with a soliton, and three solitons, respectively, when, the pump strength is enhanced gradually.
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