Spontaneous modulation instability in a noninstantaneous self-defocusing medium within a cavity longer than the coherence length

We study, theoretically and experimentally, the spontaneous pattern formation of modulation instability (MI) in a non-instantaneous self-defocusing medium, which is placed in a cavity longer than the coherence length of the circulating light. The delayed response of the nonlinearity can amplify the noise of certain spatial and temporal frequencies. Although it lacks the resonance condition resulted from the interference between different cycles, the cavity can still select one specific frequency. A pattern of this frequency can emerge spontaneously if its gain from the nonlinearity is larger than the total cavity loss.