## 3 Dispersion-Managed Versatile Ultrafast Fibre Laser
### Setup and Experimental Results
WDM: wavelength-division multiplexer; EDF: erbium-doped fibre; PC: polarisation controller; PDI: polarisation-dependent isolator; SA: saturable absorber. (**b**) Typical output pulse train observed on the oscilloscope. Next, we applied a dispersion of \(0.385\,\mathrm{ps}^{2}\) (at 1555 nm) on the filter to shift the net cavity GVD close to a zero value. In this case, after adjustment of the PCs, the laser generated pulses (Figure 7, black curves) with a Kelly side-band-free, wide spectrum, which is a signature of the DM soliton operation regime. An even wider output pulse spectrum was obtained by establishing the net GVD to be slightly normal [49]. Single-pulse DM soliton mode locking existed under a pump power of 28.5 to 42 mW and bore an average output power of 0.24 to 0.41 mW, yielding a pulse energy of 21 to 36 pJ, which is significantly higher than that of soliton-like mode locking. A further increase in the pump power resulted in multiple pulse generation. The autocorrelation trace of the pulse with 0.20 mW of average power after the fibre of the laser output port indicates an FWHM pulse duration of 2.78 ps when a Gaussian fit is assumed. It is well known that DSs occur in all-normal [12, 13] or strong net-normal dispersion cavities [14, 15, 16]. In our laser design, strong net-normal dispersion can be achieved by configuring the dispersion of the in-cavity filter; meanwhile, the filter bandwidth also needs to be properly controlled, as DSs require additional amplitude modulation besides saturable absorber action [12, 18]. Self-starting mode-locked operation was achieved by adjustment of the PCs with a filter bandwidth of 0.8 THz. No stable mode-locked pulses were found for larger bandwidths, consistent with the discussion above. The characterisations of the laser output are given in Figure 7 (red curves) for a net GVD of \(0.502\,\mathrm{ps}^{2}\) in the cavity and 0.48 mW of average pulse power after the fibre of the output port. The output pulse spectrum is steep at the edges and has a dip in the top, typical characteristics of DS lasing [12, 18]. The spectral width at FWHM is 9.7 nm. Incidentally, we also note that the spectrum is centred at the central wavelength of the filter (1555 nm), which confirms the ability of an in-cavity programmable filter to tune the laser wavelength [31]. The average output power for the DS mode-locking regime was 0.45 to 0.69 mW under a pump power of 56.5 to 72 mW, giving a pulse energy of 39 to 61 pJ. The pulse autocorrelation trace corresponds to an FWHM pulse duration of 3.5 ps when a Gaussian fit is assumed. This gives a TBP of 4.21 (at 1555 nm), indicating that the pulse is highly chirped inside the cavity [12, 18]. Figure 7: Typical (**a**) measured optical spectra and (**b**) autocorrelation traces for the output soliton (blue), dispersion-managed (DM) soliton (black) and dissipative soliton (DS) (red). Adapted from [37]. Laser-generated DSs were found to exist in the net cavity dispersion range of 0.247 to 0.505 \(\mathrm{ps^{2}}\), and their spectral width decreased when the in-cavity GVD was increased, as was expected.