Fibre lasers are light sources that are synonymous with stability. They are known to give rise to highly monochromatic radiation, or a highly stable train of mode locked pulses. However, they can also exhibit an exceedingly diverse range of nonlinear operational regimes spanning a multi-dimensional parameter space (see for example Grelu et al^{1}). The complex nature of the dynamics poses significant challenges in the theoretical and experimental studies of such systems. Specifically, the typical evolutionary time scales can be anywhere between a few hundred nanoseconds to microseconds. Conventionally used methods average several times over this time scale, and all fine information about the evolution is lost.

To obtain a better insight into the underlying dynamics, we propose a real-time intensity measurement called *spatio-temporal dynamics ^{2,3}*. In a laser, light effectively bounces back and forth between the mirrors. So, if we measure the light output from one end of the laser exactly at round trip time intervals, we will actually see the pulse every time as it comes out. This is much like stroboscopic measurements, where a pulsating light source brings a fast rotating object to apparent rest. Thus, each snapshot captures the the pulse shape, and successive snapshots of the pulse shows how it evolves over round trips. By this process, we have essentially taken the depiction of laser dynamics from mundane one dimensional intensity vs. time plots, to two-dimensional evolution maps, which we call

*spatio-temporal dynamics*.

**
Figure 1.** Principle of spatio-temporal dynamics—(

**a**) Intensity dynamics \(I(t)\) (simulated) depicting evolution over multiple round trips; (

**b**) The autocorrelation \(\kappa(\tau)\) of the intensity dynamics \(I(t)\). The periodic interval between the peaks gives the round trip time \(\tau_{RT}\); (

**c**) The spatio-temporal dynamics, describing evolution of the pulse features. Horizontal co-ordinate—temporal, vertical co-ordinate—spatial.

Employing state of the art, high bandwidth real-time digital storage oscilloscopes (DSOs), using the above principle one-dimensional intensity vs. time information can be used to experimentally arrive at a round-trip resolved two-dimensional intensity domain representation for laser dynamics. This methodology has been applied to partially mode-locked fibre lasers, conventional mode-locked fibre lasers, and also Raman fibre lasers to reveal the complex underlying dynamics in these systems.

The visualisations above show spatio-temporal dynamics of some lasing regimes experimentally obtained in a 1-km long NPE-based quasi-mode locked laser^{2,3}. The lower panels show what would one might see on an oscilloscope if the dynamics are played back one million times slower. The top panels then show how the different features evolve, and how the noisy dynamics we observe in the one dimensional time domain actually have well-defined, albeit complex evolution dynamics.

**Some more examples of spatio-temporal dynamics**

**Bibliography**

*Nature Photon*. 2012;6(2):84-92. doi:10.1038/nphoton.2011.345

*Applied Sciences*. 2016;6(3):65. doi:10.3390/app6030065

*Nat Comms*. 2015;6:7004. doi:10.1038/ncomms8004