Understanding the fission of higher-order solitons under the action of the higher-order dispersion

Summary form only given. The fission of N-solitons fission is a key mechanism leading to supercontinuum generation and creation of ultra-compressed pulses and solitons featuring strong frequency tuning [1-3]. Surprisingly, the mechanism per se was not studied in detail, beyond the approach treating higher-order dispersive and nonlinear terms as small perturbations to the nonlinear Schrödinger equation (NLS) [4]. This approach has little validity when these terms, in particular, the higher-order dispersion (HOD), dominate the dynamics of femtosecond pulses. We demonstrate that a universal scenario of the HOD-induced fission of higher-order solitons into chains of the fundamental ones proceeds via formation of the soliton Newton's cradle (NC) [5]. After the compression of the initial N-soliton into a chain of fundamental quasi-solitons and dispersion waves, the tallest soliton runs along the chain through consecutive collisions with other solitons, and then escapes, while the remaining pulse peaks stay in a bound state (Fig. 1(a)). This dynamical regime strongly resembles the Newton's cradle in mechanics, with the difference that the solitons building the chain can pass through each other, and some of them can escape. Detailed analysis of the NC mechanism was performed also in the spectral domain, aiming to identify spectral bands containing the ejected solitons, pulse chains, and dispersive waves (which together preserve the total field momentum). Interestingly, at high values of the dominant third-order dispersion (TOD), the pulse chain mostly resides in the normal-dispersion domain, while, with the decrease of the TOD, the chain shifts towards the anomalous dispersion. The peak powers of the ejected solitons and their frequency shifts were measured as a function of the order of the initial N-soliton, with fixed values of input widths. Under strong TOD, a large share of the initial energy is accumulated by the solitons running through the chain, as a result of collisions with the quiescent solitons, which also change the frequency of the traveling tall solitons. Thus, the ejected solitons carry away larger energy, and feature conspicuous down- or upshifts of the frequency, depending on the TOD sign. At higher values of N, the soliton-NC scenario recurs several times. After the release of the first soliton, the cradle retains enough power and momentum to push additional solitons all the way through the chain and eject them (Fig. 1(b)), which is accompanied by strong emission of radiation, which results in a broadband supercontinuum. The robustness of the effects reported above was tested in simulations of the generalized NLS equation, including the Raman and shock terms. The result is that they do not conspicuously affect the formation of the multi-soliton NC and subsequent ejection of the escaping solitons, see Fig. 1 (b). Lending more momentum to the tallest solitons, the Raman term slightly facilitates their ejection without effecting the NC mechanism in a qualitative way. Inclusion of HOD dispersive terms up to the eight's order also did not affect the NC mechanism qualitatively, proving its universality.