Optical Solitons and Frequency Comb Generation - Abstract
For Erbium-doped fibre laser, we review our recent theoretical results on emergence of different spatiotemporal structures including rogue waves driven by polarisation instabilities [1-4]. The recent theoretical analysis demonstrated that the vector model of mode-locked fibre laser presents a heteroclinic system where the laser?s eigenstates ? orthogonal states of polarisation (SOPs) - are quasi-equilibrium points [1-4]. The heteroclinic orbit is a trajectory periodically evolving nearby the neighbourhood of one of the orthogonal SOPs with further switching to and evolving nearby the other SOP [1-4]. The dwelling time for the trajectory near each orthogonal SOP is determined by the cavity anisotropy controlled by the pump power distribution between the eigenstates adjustable with the help of the polarisation controller for the pump wave [1-4]. The escape from the neighbourhood of each SOPs is driven by the in-cavity birefringence tunable with the help of the in-cavity polarisation controller. It has been shown theoretically that adjustment of the in-cavity polarisation controller can result in matching conditions of the Shilnikov chaos [5, 6] and so dynamics quite similar to the experimental was observed [1-4]. References 1. S. V. Sergeyev, Optics Lett. 41, 4700-4703 (2016) 2. S V Sergeyev, et al. In book ?Nonlinear Guided Wave Optics: A testbed for extreme waves?, Chapter 9 ?Vector rogue waves driven by polarisation instabilities?, ed. by Stefan Wabnitz ( IOP Publishing, 2018) p. 9-01 - 9-24. 3. H. Kbashi, S. V. Sergeyev, et al. Annalen der Physik, 530, 1700362 (2018). 4. S.V. Sergeyev et al. Phys. Rev. Lett. 118(3), 033904 (2017). 5. G. Tigan, and D. Opriş, D., Solitons & Fractals, 36, 1315 (2008) 6. C. P. Silva, Shil'nikov's theorem-a tutorial. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 40, 675-682 (1993).