Order and chaos in fiber lasers

We analyse the nonlinear stage of modulation instability in passively mode locked fiber lasers, leading to either stable or chaotic or noise-like emission. We present the diagram of phase transitions among stable temporal patterns and different regimes of chaotic emission in terms of the key cavity parameters such as dispersion and nonlinearity: amplitude or phase turbulence, and spatio-temporal intermittency. Whenever the polarizer is removed from the cavity, stabilization of the chaotic emission may occur via spatio-temporal synchronisation induced by the nonlinear coupling among two the orthogonal polarization modes.