# Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics
## 3 Results
### Spatio-Temporal Dynamics of Partially Mode Locked Fibre Lasers  
The spatio-temporal methodology is not limited to Raman fibre lasers, and can be extended to other varieties of lasers. Of particular interest is the study of long and ultralong mode locked fibre lasers. There is constant effort to construct mode locked fibre lasers that can produce shorter pulses (\(\sim\)fs) at higher energies (\(>\)_n1_) or more). Considerable progress has been made in this regard, particularly with the development of normal dispersion fibre lasers [69; 70; 71]. The stretched pulse operation, together with increased cavity length [60; 72], helps in realization of pulse energies much higher than conventional soliton based mode locked lasers. However, higher pulse energies bring about additional nonlinear interactions, resulting in dispersive wave generation [73; 74], pulse break up and formation of noisy pulses [75], and even generation of rogue waves [76; 77; 78; 79]. The intrinsic variability of the mode locked regimes gives rise to further diversity of outputs [80]. Such fibre lasers, wherein mode-locked pulses co-exist with highly transient radiation components, embedded in a sea of dispersive waves are said to operate in a _partially mode locked regime_[33]. Here, it is shown how the spatio-temporal methodology can be applied to lasers exhibiting such complex mode locked regimes. The laser used in the experiment is a 1 km long ring fibre laser operating in the normal dispersion regime (\(D=-44\) ps nm\({}^{-1}\) km\({}^{-1}\)) employing Erbium gain [33]. The laser exhibits a staggering diversity of operational regimes, which can be accessed simply by adjusting the polarization controllers along its cavity. While these regimes exhibit stationary behaviour over long time scales, characterized by a well defined periodicity and without any pulse-drop outs, the pulses themselves exhibit seemingly non-stationary behaviour (Figure 5a,b), making it difficult to determine whether there is significant coherence in the pulse characteristics from shot to shot, or if the laser actually hops from one lasing regime to another. The result of the application of the spatio-temporal methodology to the time dynamics is shown in Figure 5c. Firstly, it is confirmed that the laser operates in one lasing regime, which is characterized by a well defined intensity evolution over round trips. Secondly, the spatio-temporal dynamics reveal that the noise like features observed riding the one dimensional intensity dynamics of Figure 5a,b actually correspond to bright and dark features that survive and evolve over time scales ranging from tens to several hundred round trips. Figure 6 shows a small subset of the vastly diverse spatio-temporal regimes of the fibre laser. These were accessed just by controlling the polarization controllers for a fixed pump power. The regimes range from stationary ones, wherein the average pulse characteristics remain fairly constant from pulse to pulse (Figure 6a)--to those exhibiting more complex breathing dynamics, where the pulse characteristics evolve with a well defined periodicity along the evolution co-ordinate (Figure 6b). Regimes where the pulse interacts extensively with the background are also spotted (Figure 6c, and also Figure 5c). Figure 6d shows a highly chaotic spatio-temporal regime, with features much similar to puffs observed in turbulent fluid dynamics [81]. The observed diversity clearly highlights the advantage of identifying lasing regimes based on their _two-dimensional_ spatio-temporal dynamics, rather than the simple one-dimensional intensity dynamics. Figure 5: Spatio-temporal dynamics of a partially mode locked fibre laser regime—(**a**,**b**) Typical intensity dynamics observed at different time instants; and (**c**) the spatio-temporal dynamics of the operational regime. Figure 6: Spatio-temporal diversity of the partially mode locked regimes—Different spatio-temporal regimes with varying characteristics accessed via tuning of the polarization controllers.