Positive GDD

A very interesting property of the system is the stable multipulse generation in the region of the positive GDD. This regime excludes the Schrödinger soliton formation mechanism. The pulse width is shown in Fig. in the dependence on GDD. The transition to the multiple pulse generation, as a result of $D\rightarrow$ 0, has the hysteresis character and allows to reduce the ultrashort pulse durations essentially. In the Figure only double and triple pulse regimes are presented, but in the vicinity of zero GDD there may exist even larger number of pulses (up to 28 in our model), which have durations reduced down to 300 fs. There exist certain parameter sets when the pulses fill the whole simulation window. In the vicinity of zero GDD the accuracy of the pulse characteristics is rather low, because our model doesn't take into account the higher-order dispersion, which strongly contributes to the pulse dynamics in this case.

Figure: The dependence of the pulse width on the GDD coefficient (only single, double and triple pulses regimes are shown). P= $1.6\times 10^{-4}$, $\sigma$=20. The insets show the pulse spectrum profiles (a.u. at vertical axes).

As it was in the case of the negative net-GDD, the round-trip phase retardation is not sufficient for the pulse spectrum fragmentation, although it has a more strong dependance on $D$ (see Fig. ). Our analysis demonstrates that the signatures of the transition to the multipulse generation are similar to those for the case of the negative GDD: 1) the approach to zero GDD increases the pulse intensity due to the dispersion spreading decrease; 2) as a result, the fast absorber saturates (although less than in the negative GDD domain); 3) the gain saturation decreases; 4) the multipulse generation appears due to the background amplification (the net-gain becomes positive, see Fig. ). The decrease of the gain saturation results from the pulse energy decrease. The source of the energy decrease for the positive GDD is the spectrum broadening (see inserts in Fig. ) due to the self-phase modulation increase for small $D$, which is caused by the pulse intensity growth in the vicinity of zero GDD. We have thus identified the actual pulse break-up condition which is the same for positive and negative GDD regimes: crossing of the net-gain $\alpha-\rho-\gamma$ of the zero line, caused by the spectral widening of the pulse at decreasing the GDD.

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