# Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics
## 3 Results
### Spatio-Temporal Dynamics of Raman Fibre Lasers  
Raman fibre lasers are wavelength versatile, high efficiency fibre lasers capable of generating watt order output powers. They find applications in the distributed amplification of optical signals for telecommunications [56; 61], secure key communications [62], and even as astronomical guide stars [63]. They operate via the gain obtained via the Stimulated Raman scattering mechanism in optical fibres, doing away the need of doped fibres and simplifying device construction. However, the relatively low value of the gain in comparison to that obtained with rare earth doped gain media require the use of higher pump powers and longer lengths for achieving the lasing threshold. The length of such fibre lasers can hence be anywhere from a few hundred meters, to hundreds of kilometres [58]. The long lengths lead to extremely high mode densities, which together with the higher intracavity powers, lead to nonlinear interactions between them. These interactions can be described in the framework of weak wave turbulence [9; 10], and hence Raman fibre lasers are considered to give rise to turbulent generation. The turbulent nature of interaction gives rise to a plethora of lasing regimes, which are further diversified by the available variation in dispersion, nonlinearity, and grating parameters (see for example, [64]). While such turbulent lasing regimes have been been discerned on the basis of their experimentally measured intensity probability distribution functions [15; 19; 31], these are ensemble-averaged representations of the underlying dynamics. The identification and classification of such lasing regimes in a Raman fibre laser is thus a challenging task, given the multi-parameter nature of the operational space. The intensity output of Raman fibre lasers can be characterized by a mean intensity level, arising from the average contribution of all the longitudinal modes. Yet, owing to the turbulent nature of the interaction between the modes, the intensity fluctuates seemingly stochastically about this mean level. This quasi-continuous wave nature of Raman fibre lasers makes it particularly hard to discern the operational regimes from the temporal domain alone. Figure 2a shows the time domain variations in intensity from a linear cavity configuration based Raman fibre laser operating in the normal dispersion regime D = \(-\)44 ps/nm/km). The laser comprises of a 770 m long fibre span, encapsulated at both ends by highly reflecting fibre Bragg gratings (FBG), with 1 nm spectral width centred at 1550 nm. The laser is pumped with a watt-order pump source centred at 1450 nm, and lasing near 1550 nm is obtained via SRS gain. The observed time dynamics appear to be highly stochastic, characterized by a mean level over long time scales (\(\sim\)\(\mu\)s), while exhibiting very fast fluctuations with seemingly no correlation over short time scales (\(\sim\)ns), Figure 2b. An application of the spatio-temporal methodology as described in the previous section then clearly reveals the underlying turbulent dynamics, Figure 2c. The spatio-temporal dynamics are composed of intensity undulations, striated by several dark features that frequently intersect with each other. These correspond to the dips in the intensity dynamics of Figure 2a,b, and are dark solitons [32], which survive over time scales of tens of round trips. The differing inclinations of these features are indicative of the differences in their velocities. It must be mentioned that in most of the above cases, the intensity dips are just resolved by the measuring apparatus (_i.e._, sampled by just one data point), and it is in fact the spatio-temporal methodology that reveals the true nature of these features, which would have otherwise been misinterpreted as noise. The spatio-temporal methodology offers a unique tool to identify and distinguish between the staggering diversity of operational regimes exhibited by Raman lasers [65].