Spatial rogue waves in photorefractive ferroelectrics

We report the observation of anomalous waves as light propagates in the highly nonlinear regime that occurs when a photorefractive crystal is undergoing the ferroelectric phase transition. The transmitted spatial light distribution contains bright-localized spots of extreme intensity that follow a signature long-tail statistics that disappears as the nonlinearity is weakened. The rogue events form as out-of-equilibrium response and disorder affect the Kerr-saturated nonlinearity at the critical point. Self-similarity of the individual filaments and numerical simulations suggest that cascading dynamics of soliton mergers and scale-invariance can microscopically play a key role in the observed rogue intensities and statistics.