## 1 Introduction  
Passively-mode-locked fibre lasers have been the subject of considerable research interest for several decades owing to their potential for realising reliable and cost-effective compact ultrafast light sources [1; 2; 3]. While being very practical devices, mode-locked lasers are still very interesting objects for fundamental research in nonlinear science. From a fundamental standpoint, mode-locked fibre lasers provide convenient and reproducible experimental settings for the study of a variety of nonlinear dynamical processes thanks to the relative simplicity and precision of fibre-optic experiments. Nonlinear effects are usually quite large in mode-locked fibre lasers, but the interplay among the effects of gain/loss, dispersion and nonlinearity can also be used to shape the pulses, manipulate and control the light dynamics and, hence, lead to different regimes of mode locking. Five distinct nonlinear regimes of pulse generation have been demonstrated in passively-mode-locked fibre lasers, including soliton [4] and stretched-pulse [5; 6] regimes, self-similar pulse (similariton) propagation in passive [7] and active [8; 9; 10; 11] fibres and all-normal or strong net-normal dispersion regimes [12; 13; 14; 15; 16]. These mode-locking dynamics have been observed at the emission wavelengths of both ytterbium and erbium, as well as in Raman fibre oscillators and, more recently, also in thulium-doped fibre lasers [17], so they are not specific to the particular gain medium. A conventional soliton formed by the balance of self-phase modulation (SPM) and negative group-velocity dispersion (GVD) is chirp free and propagates unchanged, but its pulse energy is limited to a low level by the soliton area theorem. In a laser with segments of large and nearly equal magnitudes of GVD, but with opposite signs (referred to as a dispersion map), a pulse will stretch and compress, and the nonlinear phase is exactly balanced by the net effect of dispersion. This stretched-pulse or dispersion-managed (DM) soliton operation exists for net anomalous or small normal GVD and allows ultrashort pulses with up to nanojoule energies. Recent work [18] has shown that much higher pulse energies can be achieved in fibre lasers that operate at large normal dispersion. In the normal-dispersion regime, to compensate the nonlinear phase and avoid wave-breaking phenomena, dissipation is required and plays a key role in the pulse shaping. The similariton regime existing in DM cavities with large normal GVD features parabolic pulses that evolve self-similarly in a long segment of passive fibre [7]. These pulses linearise the nonlinear phase in the normal-dispersion fibre, which is compensated by an anomalous GVD segment. Oscillators supporting amplifier similaritons [8; 9; 10; 11] rely on a local nonlinear attraction to stabilise the pulse in the cavity, while spectral filtering plays an important supporting role by undoing the large spectral broadening after the gain segment. It is worth mentioning that the soliton-similariton laser reported in [8; 9] is the only example of a mode-locked laser so far that has two types of nonlinear waves propagating within the cavity. In cavities with only normal-dispersion components or strong net-normal dispersion, the resulting dissipative solitons (DSs) balance nonlinear phase accumulations by spectral or gain filtering of a highly-chirped pulse in the laser cavity. To date, the best energy performance from standard single-mode fibre (SMF) lasers has been achieved with this mode-locking mechanism. Techniques for generating, controlling and manipulating ultrashort optical pulses and specialised waveforms [19] have become increasingly important in many scientific areas, including, amongst others, ultra-high-speed optical communications, optical signal processing and biophotonics. Versatile ultrafast laser sources, which can selectively emit different types of nonlinear waves, are highly desirable in thiscontext.