## 3 Dispersion-Managed Versatile Ultrafast Fibre Laser
### Setup and Experimental Results  
Figure 6 shows a schematic of our passively-mode-locked EDF ring laser. The mode-locking mechanism was nonlinear polarisation rotation (NPR), facilitated through the inclusion of a combination of two polarisation controllers (PCs) and an in-fibre polarisation-dependent isolator. The EDF was 1.2 m long (\(\beta_{2}=65.05~{}\mathrm{fs^{2}/mm}\) at 1550 nm) and was pumped through a 980/1550 wavelength-division multiplexer by a 976-nm laser diode providing up to 300 mW optical power. Additional anomalous-dispersion fibre associated with the various components of the laser cavity amounted to a length of \(\sim 8\) m. A programmable LCoS phase and amplitude filter was used to realise different regimes of pulse generation in the cavity. Under mode-locking conditions, the laser operated at a repetition period of 89 ns (Figure 6b), which remained constant throughout the experiments described below (since there was no change in the optical length of the cavity). The net dispersion of the cavity was adaptively managed by changing the curvature of the parabolic spectral phase profile of the filter (Section 2). As pulse formation at net anomalous or slightly normal GVD does not depend on  
Figure 5: Misfit parameter to a sinc shape at the output of the laser (red circles) _versus_ filter bandwidth \(B\) for (**a**) a flat-top and (**b**) a Gaussian-top spectral pulse shaper and a laser without in-cavity dispersion control. The evolutions of the peak nonlinear phase shift (blue squares) and the correction factor \(\alpha\) (grey open squares) are also shown. Adapted from [36]. Copyright 2015, IEEE. spectral filtering, for such dispersion regimes, the amplitude filtering ability of the filter was not used: we employed the default flat-top filter's shape with the maximum achievable bandwidth. On the other hand, for the operation of the laser in the strong net-normal dispersion regime, the filter was programmed to have a narrow-bandwidth Gaussian spectral profile, as detailed below. Two 90:10 fibre couplers were employed to tap 10% of laser power out of the cavity, where one was for laser outputs after the NPR components; the other one was located after the programmable filter for investigating the pulse dynamics inside the laser cavity. The output port was connected by a 3-m long segment of standard telecom fibre (\(\beta_{2}=-22.8\;\mathrm{fs^{2}/mm}\)) to an optical spectrum analyser, an auto-correlator and a fast photo-detector to characterise the pulses. When there was no dispersion applied on the programmable filter, the cavity had an anomalous net dispersion. By properly adjusting the two PCs in the system, stable mode-locked pulses could be obtained (Figure 6b). The characterisations of the laser output are given in Figure 7 (blue curves) for an average pulse power of 0.15 mW after the fibre of the output port. The optical spectrum profile, centred at \(\sim 1560\,\mathrm{nm}\) and with a spectral bandwidth at FWHM of 4.7 nm, exhibits Kelly side-bands [48], indicating the fundamental soliton shape of the output pulse. The net dispersion of the cavity, calculated from the side-bands, is \(-0.3967\;\mathrm{ps^{2}}\) (at 1555 nm). The measured autocorrelation trace of the pulse corresponds to an FWHM pulse duration of 0.8 ps when a hyperbolic secant fit is assumed. This gives a time-bandwidth product (TBP) of 0.46 (at 1560 nm), indicating that the pulse is slightly chirped. The soliton-like single-pulse generation regime was observed for a pump power of 20 to 26 mW and bore an average output power of 0.12 to 0.21 mW, corresponding to a pulse energy of 10.7 to 18.7 pJ. Multiple solitons were generated in the system for pump powers above 26 mW. When some normal dispersion was applied on the filter while keeping the net cavity dispersion anomalous, the spectral width of the pulses increased, which is in agreement with soliton-type pulse behaviour [49]. Figure 6: (**a**) Schematic of a filter-based dispersion-managed passively-mode-locked EDF laser.