# Real-Time Intensity Domain Characterization of Fibre Lasers Using Spatio-Temporal Dynamics
## 1 Introduction  
Fiber lasers are systems capable of exhibiting nonlinear dynamics over a staggering array of operational regimes spanning a multi-dimensional parameter space [1]. The complete characterization of a fibre laser over this whole space is a daunting task, especially when the regime of operation can become highly dynamic or chaotic, and the typical time scales of evolution are of the order of the laser cavity round trip time, or even less. Such dynamics can manifest themselves in the form of soliton rains [2, 3] and molecules [4], soliton explosions [5, 6, 7], optical turbulence [8, 9, 10, 11, 12, 13, 14, 15] and rogue waves [16, 17, 18, 19, 20, 21]. An understanding of such dynamic regimes is of interest from both an academic and experimental perspective, as one would like to ensure stable operation and avoid excursions between operational regimes.  
The inherent complexity of such systems do not always facilitate a direct theoretical or numerical investigation. An experimental characterization of such regimes is thus highly desirable--but herein lies the challenge. While the typical evolutionary time scales can be anywhere between a few hundred nanoseconds for metre long cavities, to microseconds for kilomet long cavities, conventionally used experimental devices like grating based optical spectrum analyzers (OSAs) or radio frequency (RF) analyzers average several times over this time scale as they have very slow acquisition rates (<10\({}^{2}\) Hz). Pulse characterization devices like autocorrelators or Frequency Resolved Optical Gating (FROG) [22]apparatuses operate under the _apriori_ assumption that the laser operates in a stationary state, and thus present an averaged picture of the underlying dynamic. Single shot equivalents of the FROG devices do exist [23], but they again are limited by the data acquisition rates of the CCD sensors to kilohertz orders. The complexity is increased further, depending on the operational regime of the laser (continuous wave, quasi-continuous wave, or pulsed). Thus, recent times have seen in a growing interest in _real-time_ measurement methodologies for the characterization of such dynamical systems [24; 25; 26; 27]. Here, the terminology _real-time_ is used to emphasize that the methods are capable of resolving the evolutionary behaviour of the operational regime.  
In this paper, the experimental methodology of spatio-temporal dynamics is presented as a way for the unambiguous identification of lasing regimes in fibre lasers. In this method, the intensity evolution in the fibre laser is traced as it makes round trip circulations within the laser cavity. Employing state of the art, high bandwidth real-time digital storage oscilloscopes (DSOs), it is shown how long term records of _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. The strength of the technique lies in the fact that it is not limited to mode locked lasers, and can also be used for the characterization of continuous and quasi-continuous wave sources. The organization of the paper is as follows. Section 2 details the principle and experimental aspects of the spatio-temporal methodology. The methodology is then applied in the study of Raman fibre lasers (Section 3.1) and partially mode locked fibre lasers (Section 3.2), highlighting its strengths and salient features in the process.