## 3 Experimental Observation of Various Soliton Molecules in Different Fibre Lasers
### Anomalous Dispersion Regime
#### 3.1.1 1.5-Micron Wavelength Regime
The pulse separation is the same as that calculated through modulation period of the optical spectrum. In addition, \(\pm\pi/2\) phase-difference bound states were obtained in this laser cavity, as shown by the spectra in Figure 6. Both Figure 6a,b have a prominent asymmetry, which indicates that their phase differences are neither \(\pi\) nor 0. The excellent fitting with sech-shaped pulses concludes the phase differences in both figures, despite of a large cw component coinciding with the maximum peak in Figure 6b. Figure 5: (**a**) The optical spectrum and (**b**) autocorrelation trace of an out-of-phase two-soliton bound state; (**c**) The optical spectrum and (**d**) autocorrelation trace of an in-phase two-soliton bound state. (Reproduced with permission from [28]. © The Optical Society of America (Washington, DC, USA), 2013). Figure 6: (**a**) Experimental and fitting spectra of a -\(\pi/2\) phase-difference two-soliton bound state; (**b**) Experimental and fitting spectra of a \(\pi/2\) phase-difference two-soliton bound state. Fitting spectra of the envelope (unbound) are also presented. (Reproduced with permission from [28]. © The Optical Society of America (Washington, DC, USA), 2013). 2. Triple-soliton bound states  
According to soliton energy quantization, higher pumping levels can correspond to more numbers of pulses affordable in the cavity. Under appropriate pump power and PC orientation, triple-soliton bound states can be observed experimentally owing to a balance between repulsive and attractive forces. Figure 7 is the optical spectrum of such a state as an example. The spectral shape is very modulated and symmetrical with respect to the centre wavelength and can be nicely fitted by using the analytical expression of a triple-soliton molecule in Equation (4) (fitted parameters are given in the inset). 3. Widely spaced bound states  
The above-mentioned experimental observations prove existence of tightly bound soliton molecules in fibre lasers, in which the constant and fixed phase relationship is clearly evidenced by the fully modulated spectral fringes. They are ones of the most common examples since the ratio of pulse separation to pulse width (RSW) ranges from a few to a few tens, typical for optical Kerr effect and Raman effects that dominate if two pulses are partially overlapped. In comparison to the strong and short-range mutual interaction between neighbouring solitons, weak and long-range interaction mediated by continuous wave could lead to less bound soliton molecules, which is much more widely spaced. Typically, the temporal separations of such distant multiple solitons can be as large as 100 times pulse durations. Figure 8 exhibits the optical spectra and autocorrelation traces of several examples. The laser cavity to generate those widely spaced bound solitons is very similar to that in Figure 4 [31]. Differently, multilayer graphene with modulation depth of 6% and insertion loss of 2.5 dB is utilized as the saturable absorber. Output coupling ratio is also tailored in order to control the nonsoliton intensity and measure the autocorrelation traces. As we can see from the optical spectra in Figure 8, the intensity of the continuous-wave component is usually very gigantic in the situations of widely spaced bound solitons, indicating the important role of nonsoliton component in the generation of loosely bound states. In most cases, loosely bound states were produced from states of two-pulse bunches with small separation assisted by nonsoliton components. In the state of two-pulse bunches, energy of nonsoliton components can range from several to tens of percent soliton energy. The residual continuous wave in the cavity works as efficient medium to balance solitons with temporal separation of two orders of magnitude of pulse width.