## 3 Experimental Observation of Various Soliton Molecules in Different Fibre Lasers
### Nearly Zero Net-Cavity Dispersion Regime  
A dispersion-managed fibre laser is characterized by segments with dispersion of opposite signs and a very small anomalous or normal net-cavity dispersion is caused. The dispersion management effect ensures large breathing of the pulse width along the cavity. Such nearly zero net-cavity dispersion regime allows existence of Gaussian pulses which are more tolerant with nonlinear phase shift compared to traditional sech-profiled solitons in anomalous dispersion fibre lasers. As some of the pioneers who study soliton molecules, [PERSON], [PERSON] et al. have performed remarkable experiments and simulations in both anomalous and normal path-averaged cavity dispersion fibre lasers where kinds of bound solitons were observed [18; 22; 44]. As an example, Figure 13a,b illustrates the temporal and spectral details of a bound state in a laser cavity with normal dispersion-managed configuration. The autocorrelation function in Figure 13a shows a rather triangular shape and the  
Figure 11: **(a)** Optical spectrum of the soliton molecules. The spectrum is fit with parabolic (open circles), Gaussian (closed squares) and sech\({}^{2}\) (closed triangles) pulse shapes. The inset shows a zoomed-in portion of the optical spectrum on a linear scale illustrating the modulation period; **(b)** Second-order intensity autocorrelation trace of the two bound parabolic pulses observed directly at the laser output. Theoretical fits with parabolic (open circles), Gaussian (closed squares) and sech\({}^{2}\) (closed triangles) profiles are also shown. Inset shows detail of the autocorrelation trace on a logarithmic scale. (Reproduced with permission from [20]. © The Optical Society of America (Washington, DC, USA), 2006). Figure 12: **(a)** Optical spectrum and **(b)** autocorrelation trace of a bound state of gain-guided solitons. (Reproduced with permission from [19]. © The Optical Society of America (Washington, DC, USA), 2007). optical spectrum in Figure 13b presents fully modulated fringe pattern. These two records imply a precise phase locking of closely bound chirped pulses. Numerical efforts verify the conclusion that bound states can be supported regardless of dispersion signs of the cavity. For a complete overview, Table 1 lists the most relevant experimental observation of two-soliton molecules exhibiting abundant discrete values of phase difference and interpulse separation in diverse configurations of fibre lasers (different wavelengths, difference dispersion conditions, different mode-locking techniques, etc.). At higher pumping power level, soliton molecules consisting of three and more than three solitons as well as bound states of bound solitons have been reported in sorts of fibre lasers [21; 27; 45; 46; 47; 48]. Figure 14 shows two typical examples of such multisoliton complexes observed by [PERSON] et al. [47]. Indeed, the different peaks of the autocorrelation trace in Figure 14a are equally spaced and exhibit nearly the same width with intensity ratio of 1:2:3:4:5:4:3:2:1, implying that five identical solitons with the same amplitude and width constitute the bound state. In Figure 14b, a two-soliton molecule with pulse separation of about 3 ps behaves as a unit (it is termed twin-pulse in some literatures) and the complete bound state forms by doubling such a unit. The twin-pulses are roughly 8 ps apart from each other in this situation.