## 3 Experimental Observation of Various Soliton Molecules in Different Fibre Lasers
### Anomalous Dispersion Regime
#### 3.1.1 1.5-Micron Wavelength Regime  
Figure 4 shows the laser cavity schematically. A segment of 48-cm long erbium-doped fibre (EDF) is forward pumped by a 980-nm laser diode. The pump laser is coupled into the cavity through a wavelength division multiplexer (WDM). A polarization-independent isolator (PI-ISO) ensures  
Figure 3: Autocorrelation traces of (**a**) a single soliton; (**b**) a twin-soliton bound state; and (**c**) a triple-soliton bound state. Chirp-free sech-shaped pulses with pulse width of 0.8 ps and temporal distance of 4 ps are utilized. unidirectional operation of the fibre laser. A polarization controller (PC) is employed to adjust birefringence and optimize operation of the cavity. A polyimide (PI) film incorporating 1 wt. % single-walled carbon nanotubes (SWNT) [35] acts as the saturable absorber (SA), which is inserted between PC and an output coupler. Ninety percent of the laser power is fed back into the cavity to maintain sufficient gain, while 10% output is detected to investigate the generated soliton states. An optical spectrum analyser with 0.06-nm resolution bandwidth, a 2-GHz oscilloscope and a 13.6-GHz radio-frequency (RF) signal analyser with a 2-GHz photo-detector and a second-harmonic-generation autocorrelator are used to characterize the output pulses in detail. The ring cavity is approximately 13 m in length and the net anomalous group-velocity dispersion (GVD) is \(-\)\(-\)0.28 ps\({}^{2}\). 1. Two-soliton bound states Sufficient pump power ensures gain for stable operation of multi-soliton states within the cavity. When polarization state is adjusted by rotating PC orientation carefully, kinds of bound states with different phase differences could be observed. Figure 5a,b shows optical spectrum and autocorrelation trace for an example of soliton molecules with \(\pi\) phase difference. The experimental result (black solid curve of Figure 5a) agrees well with fitting result (red dashed curve of Figure 5a) of bound solitons comprising two sech-profiled pulses with opposite phases. Some imperfection arises from coexistence of continuous-wave (cw) component, generation of sidebands and a little asymmetry of the spectrum. The first two factors are common in a soliton-type fibre laser. The last one is caused mainly by asymmetry of gain spectrum of the erbium fibre and by the third-order dispersion. Modulation period of 2.7 nm and \(\sim\)100% modulation depth in the experimental spectrum imply that two solitons with 2.8 ps pulse separation have an excellent coherence. Autocorrelation trace (Figure 5b) confirms the temporal distance further, as well as exactly the same pulse width and amplitude of the two bound solitons. Figure 4: Schematic figure of the laser cavity. WDM: wavelength division multiplexer; EDF: erbium-doped fibre;PI-ISO: polarization-independent isolator; PC: polarization controller; SWNT: single-walled carbon nanotube; PI: polyimide; SA: saturable absorber. (Reproduced with permission from [28]. © The Optical Society of America (Washington, DC, USA), 2013). Figure 5c,d shows another example for in-phase bound solitons. The black solid curve of Figure 5c is the experimental optical spectrum with modulation period of 0.6 nm. It can be seen that there is a large cw component existing at the centre of the spectrum and Kelly sidebands observable at trailing edges, which result in slightly imperfect agreement between measurement and fitting by assuming Gaussian-shaped pulses (red dashed). We emphasize that it does not influence the conclusion that the two bound solitons are in phase. Modulation depth of the experimental spectrum seems to be lower than 100%, which is just because a relatively coarse resolution bandwidth (0.2 nm) was used (an optical spectrum analyser is sufficient to resolve the spectrum of a bound state only when modulation period is at least 4 to 5 times the resolution bandwidth [31]). Figure 5d plots the autocorrelation of the bound solitons, indicating pulse full-width at half-maximum (FWHM) of 0.9 ps and pulse separation of 13.5 ps.