Breather laser dynamics and their intelligent control

Breathers are localized structures showing periodic variations in parameters. They are found in various fields of science and are currently attracting significant research interest in virtue of their relationship with a rich set of important nonlinear phenomena. They have recently emerged as a universal ultrashort pulse regime in passively mode-locked fibre lasers. Here, we reviewed our recent works in this fast-growing field, including the first observation of breathing dissipative solitons and their complexes in mode-locked fibre lasers, breather explosions, and intelligent control of breathers over breathing periods, breathing ratios, and the number of breathers. Finally, fractal dynamics of breathers are also reported. The winding numbers (the ratio between the breathing frequency and the laser repetition rate) exhibit the hierarchy of the Farey tree and the structure of a devil’s staircase. Numerical simulations of a discrete laser model confirm the experimental findings.