Chapter 9: Vector rogue waves driven by polarisation instabilities

Using an Er-doped fibre laser mode-locked with carbon nanotubes, here we review our recent experimental and theoretical results on a new type of bright-dark (anomalous spikes-dips) vector rogue waves. The coherent coupling of the orthogonal states of polarisation causes localisation of the trajectories in the vicinity of these states, whereas polarisation instability drives escape taking the form of chaotic anomalous spikes-dips satisfying rogue waves criteria. For a long fibre laser without a generic mode-locking mechanism, we demonstrate that the emergence of the bright rogue waves is also connected with switching between orthogonal states of polarisation driven by polarisation instability.