Soliton explosion control by higher-order effects

Abstract

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.

Stability of traveling pulses of cubic–quintic complex Ginzburg–Landau equation including intrapulse Raman scattering

“…The erupting solitons have been found numerically [12] on a relatively large region of the CGLE parameter space, and were experimentally observed in passively mode-locked lasers [14]. Recently, the eruptions were shown to change or even cancel by the introduction of one or more additional terms in the CGLE [15][16][17][18]. In fact, in [18] we have shown that the intrapulse Raman scattering (IRS), if sufficiently strong, may stabilize the propagation of the single pulse on the eruption parameter region, thus eliminating the eruptions.…”

Control of complex Ginzburg–Landau equation eruptions using intrapulse Raman scattering and corresponding traveling solutions

“…In fact, terms similar to intrapulse Raman scattering (IRS) and selfsteepening (SS) were used by Tian et al [18] to control the eruptions, thus obtaining fixed shape soliton propagation with nonzero velocity. Also, more recently, Latas et al [19] obtained asymmetric eruptions or complete elimination of eruptions by adding IRS, SS and third order dispersion to the CGLE.…”

Plain and oscillatory solitons of the cubic complex Ginzburg-Landau equation with nonlinear gradient terms

“…Nevertheless, from all of these, the only stable pulse is the high amplitude solution allowed when R r ̸ = 0 in region 1, but for ϵ that obeys condition (6). In some cases, as is the case S i = 0, the condition (6) reduces to ϵ < ϵ max = β and the existence of a finite region with stable solitons implies that ϵ min < ϵ max , which imposes an additional restriction on the coefficients of (1), they will exist as long as |R r | < 5 12 β…”

“…However, it has been recently shown that the inclusion in the CGLE of a term that, in optics, models the delayed Raman scattering, allows the existence of stable solutions in a parameter region where the background is also stable [4]. Note that this higher order term has also been associated with the stabilization of erupting solitons of the quintic CGLE [5][6][7].…”