A fiber mode-lock laser allows generation of the optical rogue wave (ORW) at different time scales. The criteria for distinguishing between them is a comparison of the event lifetime with the main characteristic time of the system. The characteristic time can be estimated from the decay of an autocorrelation function (AF).Thus, in comparison with AF characteristic time, fast optical rogue wave (FORW) events have duration less than the AF decay time and it appeared due to pulse-pulse interaction and nonlinear pulses dynamics. While slow optical rogue wave (SORW) have a duration much more longer than the decay time of the AF which it papered due to hopping between different attractors. Switching between regimes can be managed by change the artificial birefringence that induced in a laser cavity. For understanding the role playing by the periodical amplification and the resonator, we have performed an unidirectional fiber laser experiments without a saturable absorber. This laser experiment allowed to generate of most of the RW patterns which were either observed experimentally or predicted theoretically. In this way, we have observed the generation of an FORW along with SORW under similar conditions. Most of the patterns were found to be mutually exclusive which means that only one RW mechanism was realized in each regime of generation. Keywords: rogue wave, fiber laser, slow rogue wave, fast rogue wave, rogue wave's interaction, rogue waves collision.
INTRODUCTIONA rogue wave as a concept has been initially introduced in oceanography to describe rare events, colloquially called "freak" waves. These waves have amplitudes that were much larger than average ones that resulted in destructive impact in nature and society [1]. Investigation of mechanisms which cause appearing of rogue wave (RW) has practical importance due to the damage which they cause in real-world scenarios. Meanwhile, an intrinsic scarcity of events, as well as evident technical difficulties to perform full-scale experiments, are the main obstacles for understand and predict RWs. Mode-locked lasers are perfect candidates to be test-bed systems for investigating conditions for RWs' emergence and mitigation [2]. Lasers with a high repetition rate of pulses provide an opportunity to obtain a huge amount of data under laboratory-controlled conditions in relatively short time. Previously, in the context of mode-locked fiber lasers, the ORW mostly have been observed at regimes of chaotic bunches of noise-like pulses or soliton rain [3]. Also, it has been found that ORW can be generated in mode-locked lasers as a result of the interaction of dissipative solitons interacting through overlapping of their tails or by dispersive pulses [4]. An extensive study of the mechanisms of formation of ORWs have been done either experimentally or theoretically in fiber lasers with nonlinearly driven cavities [5], Raman fiber amplifiers and lasers [6] and fiber lasers via modulation of pump [7]. In the other hand, the hopping has also been investigated as a sour...