## 3 Pulsed Fibre Lasers Using 2D Materials
### Mode-Locked Fibre Lasers  
Mode-locking can arise when a SA modulates the loss once per cavity round-trip, thus phase-locking the oscillating longitudinal modes, leading to the generation of a train of ultrashort (ps-fs duration) pulses at a defined repetition rate corresponding to the free spectral range of the cavity (typically MHz for few meter-long fibre lasers). Mode-locked pulse sources have a wide range of applications, notably for metrology, frequency comb generation and biophotonic imaging [1]. Typically, fibre lasers incorporating an SA can exhibit both Q-switching and mode-locking. The transition between the two regimes is mediated by a balance between gain and loss and can be controlled by the pump power; for example, the threshold for CW mode-locking is higher than that for Q-switching. However, the duration of the circulating pulse in the mode-locking regime is typically  
Figure 5: Q-switched fibre lasers with MoSe\({}_{2}\)-PVA saturable absorber, after [55]: (**a–c**) cavity schematics; (**d–f**) output pulse trains showing the repetition rate \(f\) and pulse duration \(\tau\); (**g–i**) spectra. The columns (left to right) show Yb, Er and Tm laser results. on the order of a few ps or even hundreds of fs, such that effects arising from cavity nonlinearity and dispersion influence pulse formation. Thus, a Q-switched fibre laser may not be able to access the mode-locking regime, even at higher pump powers, without management of the cavity dispersion map and careful design of the SA device, e.g., modulation depth and reduction of the \(\alpha_{\mathrm{non-sat}}\)[1, 68]. As with Q-switching, mode-locking has been demonstrated using a variety of 2D material SAs [16, 30, 69], with the first report in 2009 employing graphene [14, 15], followed by the TIs Bi\({}_{2}\)Te\({}_{3}\)[70] and Sb\({}_{2}\)Te\({}_{3}\)[71], the TMD MoS\({}_{2}\)[33] and, recently, utilizing BP [65, 72]. The first TMD mode-locked laser was reported by [PERSON] _et al._, where MoS\({}_{2}\) was deposited on a fibre ferrule and integrated into a Yb:fibre ring cavity [33]. The laser produced 800 ps pulses at a 6.6 MHz pulse repetition frequency, with an average output power of 9.3 mW [33]. Further work through cavity dispersion engineering resulted in sub-picosecond pulse generation [39, 45, 66, 73], down to 637 fs [45]. These ultrafast lasers operated in the net anomalous dispersion regime, generating solitons. However, recent work has shown that all-normal and net-normal dispersion maps, producing dissipative solitons, can enable higher pulse energies [1, 74]. Such designs have also been exploited for TMD-based mode-locked fibre lasers [33, 44, 45, 53]. For accessing higher repetition rates, harmonic mode-locking has been demonstrated. The highest result to date has been 2.5 GHz, mode-locking up to the 369 th harmonic of a \(\sim\)30 m cavity [46]. In terms of wavelength coverage, Yb:fibre lasers have been mode-locked using MoS\({}_{2}\)[33, 44] and WS\({}_{2}\)[53], Er:fibre lasers with MoS\({}_{2}\)[34, 39, 45, 46, 75, 76], WS\({}_{2}\)[52, 53, 54, 66], MoSe\({}_{2}\)[56] and Tm:fibre lasers with MoS\({}_{2}\)[49] and WS\({}_{2}\)[51]. Continuously tunable mode-locking in the erbium gain band has also been demonstrated with a single MoS\({}_{2}\)-PVA composite device [37]. The laser and output characteristics shown in Figure 6 confirm the generation of stable trains of ultrashort pulses, tunable from 1535-1565 nm. To date, only modest output powers have been achieved in TMD-based mode-locked lasers. Typical output powers are \(<\)10 mW [30], although notably, the highest output power reported is 150 mW from a few-layer MoS\({}_{2}\) mode-locked Tm:fibre laser operating in the dissipative soliton regime [49]. Amplification and power scaling will enable such laser systems to access higher powers.