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Dissipative solitons in optical microcavities have attracted significantattention in recent years due to their direct association with the generationof optical frequency combs. Here, we address the problem of dissipative solitonbreathers in a microresonator with second-order nonlinearity, operating at theexact phase-matching for efficient second-harmonic generation. We elucidate thevital role played by the group velocity difference between the first and secondharmonic pulses for the breather existence. We report the dissipative breathergas phenomenon, when multiple breathers propagate randomly in the resonator andcollide nearly elastically. Finally, when the breather gas reaches anout-of-equilibrium statistical stationarity, we show how the velocity lockingbetween first and second harmonic is still preserved, naming such phenomenaturbulence locking.

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