Sofia C. V. Latas

Soliton explosion control by higher-order effects

We numerically study the impact of self-frequency shift, self-steepening, and third-order dispersion on the erupting soliton solutions of the quintic complex Ginzburg-Landau equation. We find that the pulse explosions can be completely eliminated if these higher-order effects are properly conjugated two by two. In particular, we observe that positive third-order dispersion can compensate the self-frequency shift effect, whereas negative third-order dispersion can compensate the self-steepening effect. A stable propagation of a fixed-shape pulse is found under the simultaneous presence of the three higher-order effects.

Stable soliton propagation in a system with spectral filtering and nonlinear gain

Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.

Timing jitter in soliton transmission with up- and down-sliding-frequency guiding filters

We derive an analytical expression for the variance of the timing jitter of a soliton transmission system using sliding-frequency guiding filters, taking into account the third-order filter term. An improved analytical result for the upper limit of the sliding rate for stable soliton propagation is also obtained. We show that the variance of timing jitter is significantly increased by the sliding action. As a consequence of the third-order filter contribution, the timing jitter is lower in a system with down-sliding compared with the up-sliding regime at the same sliding rate.

Why can soliton explosions be controlled by higher-order effects?

We investigate numerically the impact of some higher-order effects, namely, self-frequency shift, self-steepening, and third-order dispersion, on the erupting soliton solutions of the quintic complex Ginzburg-Landau equation. We consider particularly the impact of these higher-order effects in the spectral domain from which we can describe the pulse characteristics in the time domain. These effects can filter in different ways the spectral perturbations that contribute to pulse explosions. We show that a proper combination of the three higher-order effects can provide a filtering of the spectral perturbations in such a way that a stable fixed-shape pulse propagation is achieved.

Soliton stability and compression in a system with nonlinear gain

The stability of soliton propagation in a system with spectral filtering and linear and nonlinear gain is investigated numerically, assuming various input waveforms. Our results show that merely giving a linear frequency chirp to the initial pulse is not effective in suppressing the background instability in bandwidth-limited soliton transmission. However, it should be possible to achieve relatively stable pulse propagation over long distances by the use of a suitable combination of linear and nonlinear gains. Truly stable propagation of arbitrary-amplitude solitons can be achieved only in a system with purely nonlinear gain. A new soliton compression effect is demonstrated both for fixed-amplitude and for arbitrary-amplitude solitons. For fixed-amplitude solitons there is an optimum propagation distance for maximum pulse compression, whereas for arbitrary-amplitude solitons the pulse width remains practically constant after some oscillations in the initial compression stage.

Emerging fixed-shape solutions from a pulsating chaotic soliton

The impact of some higher-order effects (HOEs), namely, intrapulse Raman scattering, self-steepening, and third-order dispersion, on a chaotic pulsating soliton, solution of the quintic complex Ginzburg-Landau equation, is numerically investigated. We show that a proper combination of the three HOEs can control the pulse chaotic behavior and provide a fixed-shape solution. The region of existence of fixed-shape pulses is also presented for some range of the parameter values.

Stable soliton propagation with self-frequency shift

We investigate the propagation of ultrashort solitons in fiber-optic systems in the presence of the soliton self-frequency shift effect. It is demonstrated that both the self-frequency shift and the background instability can be effectively controlled using spectral filters of moderate strength together with nonlinear gain proportional to the second and fourth power of the amplitude. These results are verified both for plain pulses and for composite pulses. In the last case, however, an asymmetry of the pulse induced by the Raman effect is observed.

High-energy plain and composite pulses in a laser modeled by the complex Swift–Hohenberg equation

In this work, new plain and composite high-energy solitons of the cubic–quintic Swift–Hohenberg equation were numerically found. Starting from a composite pulse found by Soto-Crespo and Akhmediev and changing some parameter values allowed us to find these high energy pulses. We also found the region in the parameter space in which these solutions exist. Some pulse characteristics, namely, temporal and spectral profiles and chirp, are presented. The study of the pulse energy shows its independence of the dispersion parameter but its dependence on the nonlinear gain. An extreme amplitude pulse has also been found.

Ultrashort high-amplitude dissipative solitons in the presence of higher-order effects

In this work, the propagation of high-amplitude solitons of the cubic-quintic complex Ginzburg–Landau equation in the presence of higher-order effects, namely, the intra-pulse Raman scattering (IRS) and the third-order dispersion (TOD), has been studied. Starting from a singularity found by Akhmediev and co-workers, high-amplitude pulses are predicted using a perturbation approach and numerically obtained. We have found that this singularity is no longer present if the intra-pulse Raman scattering effect is considered and zero velocity pulses may be achieved in the presence of both IRS and TOD. The predictions from perturbation theory are numerically confirmed to a certain extent.

Propagation of pulsating, erupting, and creeping solitons in the presence of higher order effects

We investigate numerically the temporal and spectral characteristics of fixed-shape pulses, resulting from pulsating, erupting and creeping soliton solutions of a generalized complex Ginzburg-Landau equation (CGLE), which includes the third-order dispersion, intrapulse Raman scattering, and self-steepening effects. In general, the resulting fixed-shape solutions are asymmetric and chirped pulses. The interaction between such fixed-shape pulses is also investigated, and we show that a stable propagation is achieved, except when the pulses have an oscillating tail.