Origin of spectral rogue waves in incoherent optical wave packets

The rogue wave (RW) is a persistent topic in diverse fields of science including optics, hydromechanics, and electromagnetics. Despite the extensive experimental confirmations, the optical RW in the spectral domain is still elusive in aspects of its origination and evolutionary dynamics. Operating the fiber laser in a noiselike pulse (NLP) state, we observe the spectral RW according to the statistics of the shot-to-shot spectral evolution. Simulations consistent with experiments reveal that the spectrograms of NLPs are constituted by multiple localized speckles in the temporal-spectral domain, which originate from the interferences in the temporal and spectral domains. The collective motion of speckles is dominated by the Kerr effect and group-velocity dispersion. Several speckles can be in alignment at the same frequency, promoting the generation of the spectral RW. This paper sparks interest in the physics of incoherent wave packets widely existing in nonlinear optical systems.