# Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics
## 3 Results
### Spatio-Temporal Dynamics of Raman Fibre Lasers
For example, Figure 3 shows some of the operational regimes exhibited by a 1 km long Raman fibre laser operating in the normal dispersion in a linear cavity configuration similar as above, obtained at different pump powers. Figure 3a depicts a regime obtained for a pump power \(P_{p}\) = 1.5 W. Here, the laser can be thought to be operating in a partially harmonic-mode locked regime, giving rise to a periodic train of nanosecond order pulses, with a repetition period shorter than the average round trip time. These pulses in turn are criss-crossed by dark coherent features that undergo round-trip circulations, and survive over time scales of several tens of round trips. Upon increasing the pump power to \(P_{p}\) = 2.0 W, Figure 3b, the operational regime transfers to a noisy one, resulting in the generation of bright coherent features surviving over time scales of 40-50 round trips, much longer than the typical nonlinear length. Increasing the pump power \(P_{p}\) to 3.0 W (Figure 3c) results in the narrowing of the above coherent features along both the temporal and spatial co-ordinates. A further increase of pump power to \(P_{p}\) = 3.25 W (Figure 3d) results in a drastic transition of the operational regime to one comprising of picosecond order pulses that survive over time scales as large as 200 to 300 times the characteristic round trip time period. It is speculated that at this pump power level, the gain in the cavity becomes high enough to support the formation of parabolic pulses, and is currently being studied. As the spatio-temporal dynamics allows one to track the evolution of particular features of interest, they are particularly well suited in the study of the rogue wave formation in such system. It was shown theoretically [19; 57; 66] and experimentally [31] that Raman fibre lasers including random fibre lasers can exhibit such rare, short lived, high intensity events, facilitated by the underlying turbulent four wave mixing dynamics. The polarized nature of rogue events have been reported in numerical solutions of the Manakov system of Schrodinger equations [67], and in the vector Ginzburg Landau model simulations of the Raman fibre laser [68]. This aspect can be verified by obtaining polarization diverse spatio-temporal dynamics of the Raman laser. Here, the output from the Raman fibre laser is fed to a polarization beam splitter that resolves the incoming radiation along two orthogonal polarizations. The resulting outputs are then measured simultaneously using a multi-channel DSO. The differences in the lengths of the arms of the beam splitter then are compensated off-line to arrive at the time-aligned polarization spatio-temporal dynamics of the Raman fibre laser. Figure 4a shows an instance of such measurements, where the intensity has been normalized to the mean intensity level. Short lived rogue events as high as 12 times the mean level are observed. Also, these events exhibit a high degree of linear polarization, as evidenced by the extinction ratio of the signals arriving from the two arms of the beam splitter. Figure 4b and c are the corresponding polarization resolved spatio-temporal dynamics, which trace the formation and  
Figure 2: Spatio-temporal dynamics of Raman fibre lasers—Typical quasi-continuous wave intensity dynamics of a Raman fibre laser over (**a**) long and (**b**) short time scales; (**c**) The corresponding spatio-temporal dynamics. The color scale indicates normalized intensity. evolution of this rogue event over the time scale of tens of round trips. The striations (which are complementary in orthogonal polarizations) arise from period doubling dynamics--a phenomenon yet to be explored. Figure 4: Polarized rogue waves in the Raman fibre laser—(**a**) Experimentally measured polarization resolved intensity dynamics of the Raman fibre laser, and (**b**,**c**) corresponding polarization resolved spatio-temporal dynamics ((**b**)—blue curve, (**c**)—red curve), revealing the existence of linearly polarized rogue waves.