The Peregrine soliton in nonlinear fibre optics

The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system1. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation2 to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions that do not correspond to the mathematical ideal, our results may impact widely on studies of hydrodynamic wave instabilities where the Peregrine soliton is considered a freak-wave prototype3–7. Solitons are localized waves arising from nonlinear and dispersive interactions, and are central objects of nonlinear science. The well-known envelope solitons of the NLSE have been studied in many different systems including plasmas, optical fibres and cold atoms8–10. In addition to envelope solitons, the NLSE admits other classes of localized structure, and there has been significant interest in spatio-temporal breather solutions that undergo periodic energy exchange with a finite background11,12. However, despite extensive mathematical studies4,5, experiments have been limited to only a small number of discrete systems9,13. Indeed, to our knowledge no studies have explicitly characterized nonlinear breather localization in any system described by the continuous NLSE. As a result, predictions such as Peregrine’s that are central to nonlinear wave theory have remained untested. In a sense, this is surprising because the theory of NLSE breather evolution also describes induced modulation instability, a process extensively studied in hydrodynamics and fibre optics14–18. Experiments in optics, however, have been strongly motivated by telecommunications goals to generate high-contrast pedestalfree pulses19–22, and the opportunity to characterize solitons on a finite background seems to have been overlooked. Indeed, even fundamental studies of Fermi–Pasta–Ulam recurrence in modulation instability have been carried out using initial conditions far from those that would excite Peregrine soliton features23. Here, we report experiments in optical fibre specifically designed to study breather evolution in a regime approaching the excitation of the Peregrine soliton. We demonstrate explicitly its spatio-temporal localization and, at the point of maximum temporal compression, use frequency-resolved optical gating (FROG) to explicitly measure the temporal soliton characteristics on a finite background. Our results are in very good agreement with numerical simulations and Peregrine’s analytic prediction.