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.

Initial conditions for dissipative solitons in a strict polarization-controlled passively mode-locked Er-Fiber laser.

We report the dynamics of dissipative solitons in a ring cavity passively mode-locked fiber laser with a strict control of the polarization state. We study the relation between the polarization state of the pulses propagating in the cavity and the regimes of generation. We have found that at pulse ellipticities between 5° and 15°, the laser generates one bunch of pulses in the cavity, while at higher ellipticities the laser generates multiple bunches. At constant ellipticity we rotated the polarization azimuth and observed a regime transition from the generation of noise-like pulses (NLP) to that of soliton crystal. The NLP regime was found when the azimuth was rotated towards smaller low-power transmission through the polarizer. The number of solitons in the soliton crystal also depended on the azimuth in a straightforward way: the higher the initial transmission, the bigger the number of solitons.

Polarization evolution of vector wave amplitudes in twisted fibers pumped by single and paired pulses.

Nonlinear polarization dynamics of single and paired pulses in twisted fibers is experimentally and numerically studied. Accompanying a dramatic difference in the output spectrum when a single- or double-amplified soliton pulse is launched in the fiber, the output polarization for the two cases also reveals very different characteristics.

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.