Bright-Dark Rogue Wave in Mode-Locked Fibre Laser Hani Kbashi1*, Amos Martinez1, S. A. Kolpakov1, Chengbo Mou, Alex Rozhin1, Sergey V. Sergeyev1 1Aston Institute of Photonic Technologies, School of Engineering and Applied Science Aston University, Birmingham, B4 7ET, UK email@example.com , 0044 755 3534 388 Keywords: Optical rogue wave, Bright-Dark rogue wave, rogue wave, mode-locked fiber laser, polarization instability. Abstract: Rogue waves (RWs) are statistically rare localized waves with high amplitude that suddenly appear and disappear in oceans, water tanks, and optical systems . The investigation of these events in optics, optical rogue waves, is of interest for both fundamental research and applied science. Recently, we have shown that the adjustment of the in-cavity birefringence and pump polarization leads to emerge optical RW events [2-4]. Here, we report the first experimental observation of vector bright-dark RWs in an erbium–doped stretched pulse mode-locked fiber laser. The change of induced in-cavity birefringence provides an opportunity to observe RW events at pump power is a little higher than the lasing threshold. Polarization instabilities in the laser cavity result in the coupling between two orthogonal linearly polarized components leading to the emergence of bright-dark RWs. The observed clusters belongs to the class of slow optical RWs because their lifetime is of order of a thousand of laser cavity roundtrip periods. References: 1. D. R. Solli, C. Ropers, P. Koonath,and B. Jalali, Optical rogue waves," Nature, 450, 1054–1057, 2007. 2. S. V. Sergeyev, S. A. Kolpakov, C. Mou, G. Jacobsen, S. Popov, and V. Kalashnikov, “Slow deterministic vector rogue waves,” Proc. SPIE 9732, 97320K (2016). 3. S. A. Kolpakov, H. Kbashi, and S. V. Sergeyev, “Dynamics of vector rogue waves in a fiber laser with a ring cavity,” Optica, 3, 8, 870, (2016). 5. S. Kolpakov, H. Kbashi, and S. Sergeyev, “Slow optical rogue waves in a unidirectional fiber laser,” in Conference on Lasers and Electro-Optics, OSA Technical Digest (online) (Optical Society of America, 2016), paper JW2A.56.
We present an experimental and theoretical results of a study of a complex nonlinear polarization dynamics in a passively self-mode-locked erbium-doped fiber oscillator implemented in a ring configuration and operating near lasing threshold. The theoretical model consists of seven coupled non-linear equations and takes into account both orthogonal states of polarizations in the fiber. The experiment confirmed the existence of seven eigenfrequencies, predicted by the model due to polarization instability near lasing threshold. By adjusting the state of polarization of the pump and in-cavity birefringence we changed some eigenfrequencies from being different (non-degenerate state) to matching (degenerate state). The non-degenerate states of oscillator lead to the L-shaped probability distribution function and true rogue wave regime with a positive dominant Lyapunov exponent value between 1.4 and 2.6. Small detuning from partially degenerate case also leads to L-shaped probability distribution function with the tail trespassing eight standard deviations threshold, giving periodic patterns of pulses along with positive dominant Lyapunov exponent of a filtered signal between 0.6 and 3.2. The partial degeneration, in turn, guides to quasi-symmetric distribution and the value of dominant Lyapunov exponent of 42 which is a typical value for systems with a source of the strongly nonhomogeneous external noise.
For an erbium-doped fiber laser mode-locked by carbon nanotubes, we demonstrate experimentally and theoretically a new type of the vector rogue waves emerging as a result of the chaotic evolution of the trajectories between two orthogonal states of polarization on the Poincare sphere. In terms of fluctuation induced phenomena, by tuning polarization controller for the pump wave and in-cavity polarization controller, we are able to control the Kramers time, i.e. the residence time of the trajectory in vicinity of each orthogonal state of polarization, and so can cause the rare events satisfying rogue wave criteria and having the form of transitions from the state with the long residence time to the state with a short residence time.