Walk-off-induced dissipative breathers and dissipative breather gas in microresonators

Dissipative solitons in optical microcavities have attracted significant attention in recent years due to their direct association with the generation of optical frequency combs. Here, we address the problem of dissipative soliton breathers in a microresonator with second-order nonlinearity, operating at the exact phase matching for efficient second-harmonic generation. We elucidate the vital role played by the group-velocity difference between the first- and second-harmonic pulses for the breather existence. We report the dissipative-breather-gas phenomenon, in which multiple breathers propagate randomly in the resonator and collide nearly elastically. Finally, when the breather gas reaches an out-of-equilibrium statistical stationarity, we show how the velocity locking between first and second harmonics is still preserved, naming such phenomena turbulence locking.