Modulation instability (MI) is one of the most fundamental processes in nonlinear fiber optics, underlying energy exchange dynamics in parametric amplification and dominating the initial stages of noise-seeded long pulse supercontinuum generation [1]. MI is also linked with the emergence of large amplitude optical rogue wave structures with long-tailed statistics [2]. In particular, numerical simulations of noise-seeded MI show a chaotic pattern of localized peaks that are potential candidates for rogue wave events, but the exact nature of these peaks remains a subject of active study. Although previous studies have shown that the highest-intensity events can be fitted with particular spatio-temporally localized solutions of the nonlinear Schrödinger equation (NLSE) [3], the characteristics over the full intensity range remain unclear. Here we report extensive numerical simulations of the NLSE, ξ + 1/2ψττ + |ψ|2 ψ = 0, showing that the spontaneously emergent peaks due to MI can in fact be globally described by analytic soliton on finite background (SFB) or “breather” solutions and their superpositions. We also report on a detailed statistical analysis, revealing how the Peregrine soliton is not – as widely believed – statistically rare enough to be considered as a rogue wave prototype.

© 2015 IEEE

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