Numerical study of complex dynamics and extreme events within noise-like pulses from an erbium figure-eight laser.

Some complex dissipative dynamics associated with the noise-like pulse (NLP) regime of a passively mode-locked erbium-doped fiber laser are studied numerically. By means of a convenient 3D mapping of the spatio-temporal pulse evolution, for properly chosen dispersion parameters, several puzzling dissipative dynamics of NLPs are identified, including the expelling of sub-packets that move away from the main bunch, the sudden extinction of isolated sub-pulses, the collision between different internal fragments travelling at different speeds, the rising of sub-pulses, the formation of complex trajectories by substructures that first move away and then return to the main bunch, and so on. In addition, the emergence of optical rogue waves (ORWs) within NLPs is also demonstrated numerically; to help understand these behaviors evidenced in the time domain, spectral analyzes were also performed that show, among other things, that the spectrum of a NLP is notoriously distorted when it hosts an ORW phenomenon. These numerical results are consistent with previously published experimental results.

Gain-driven spectral-temporal noise-like pulse dynamics in a passively mode-locked fiber laser.

We study numerically complex noise-like pulse dynamics in a passively mode-locked erbium-doped fiber laser. Wavelength-dependent gain dynamics is modeled as a combination of a three-level and a four-level system, which approximate the gain behavior in the 1530-nm and 1560-nm regions, respectively. The typical deformation of the erbium gain spectrum as it saturates is properly reproduced by this approach. Several puzzling noise-like pulse dynamics that were recently observed experimentally are qualitatively reproduced numerically, in particular slow quasi-periodic energy variations and the emergence and walkoff of wavelength-shifted radiation components. These results clearly reveal that gain dynamics is deeply involved in the onset of such complex temporal and spectral instabilities in these sources.

Simultaneous temporal and spectral analysis of noise-like pulses in a mode-locked figure-eight fiber laser.

We present an experimental study of complex noise-like pulse dynamics in a passively mode-locked figure-eight fiber laser, by performing simultaneous temporal and spectral mapping of the waveform sequences. The simultaneous measurements allow us to relate temporal and spectral events. We found in particular that the evolution of energy and of temporal features such as the number and width of the wave packets is correlated to spectral variations, namely of the central wavelength and bandwidth of the instantaneous spectrum. The simultaneous temporal and spectral measurements also allowed a substantial improvement in the precision of the latter, which was performed using the dispersive Fourier transform method. In particular, this enhanced precision allowed measuring the subtle spectral differences between the two laser outputs and tracking their evolution over the cycles, providing crucial information that allowed to determine the physical phenomena involved in the observed dynamics.

Complex dynamics of a fiber laser in non-stationary pulsed operation.

Conventional mode locking is characterized by the generation of a stable train of optical pulses. Even in the noise-like pulsing regime of fiber lasers, sometimes described as partial mode locking, a periodic train of waveforms is still generated. In this work we study the dynamics of a figure-eight fiber laser away from the stable noise-like pulsing regime. By analyzing sequences of time-domain measurements performed with ns resolution, we reveal a wide range of puzzling dynamics, in which sub-structures emerge and drift away from the main bunch, decay or grow in a step-like manner, before vanishing abruptly. In some cases, sub-packets also concentrate in the central part of the period, forming one or multiple wide clouds that merge or split over time scales of seconds or minutes. Spontaneous transitions between these multiple states occur in a non-periodic manner, so that no quasi-stationary behavior is found over long time scales. These results provide a dramatic illustration of the extremely rich dynamics taking place in fiber lasers at the frontier of mode locking.

High energy noise-like pulsing in a double-clad Er/Yb figure-of-eight fiber laser.

In this work, we study a 215-m-long figure-of-eight fiber laser including a double-clad erbium-ytterbium fiber and a nonlinear optical loop mirror based on nonlinear polarization evolution. For proper adjustments, self-starting passive mode-locking is obtained. Measurements show that the mode-locked pulses actually are noise-like pulses, by analyzing the autocorrelation, scope traces and the very broad and flat spectrum extending over a record bandwidth of more than 200 nm, beyond the 1750 nm upper wavelength limit of the optical spectrum analyzer. Noise-like pulsing was observed for moderate and high pump power preserving the same behavior, reaching pulse energies as high as 300 nJ, with pulse durations of a few tens of ns and a coherence length in the order of 1 ps. Stable fundamental mode locking as well as harmonic mode locking up to the 6th order were observed. The bandwidth was further extended to more than 450 nm when a 100-m piece of highly nonlinear fiber was inserted at the laser output. The enhanced performances obtained compared to other similar schemes could be related to the absence of a polarizer in the present setup, so that the state of polarization along the cavity is no longer restricted.

Dynamics of noise-like pulsing at sub-ns scale in a passively mode-locked fiber laser.

We report an original noise-like pulse dynamics observed in a figure-eight fiber laser, in which fragments are continually released from a main waveform that circulates in the cavity. Particularly, we report two representative cases of the dynamics: in the first case the released fragments drift away from the main bunch and decay over a fraction of the round-trip time, and then vanish suddenly; in the second case, the sub-packets drift without decaying over the complete cavity round-trip time, until they eventually merge again with the main waveform. The most intriguing result is that these fragments, as well as the main waveform, are formed of units with sub-ns duration and roughly the same energy.