Universality of the Peregrine Soliton in the Focusing Dynamics of the Cubic Nonlinear Schrödinger Equation

Abstract

We present experimental evidence of the universal emergence of the Peregrine soliton predicted in the semi-classical (zero-dispersion) limit of the focusing nonlinear Schrödinger equation [Comm. Pure Appl. Math. 66, 678 (2012)]. Experiments studying higher-order soliton propagation in optical fiber use an optical sampling oscilloscope and frequency-resolved optical gating to characterise intensity and phase around the first point of soliton compression and the results show that the properties of the compressed pulse and background pedestal can be interpreted in terms of the Peregrine soliton. Experimental and numerical results reveal that the universal mechanism under study is highly robust and can be observed over a broad range of parameters, and experiments are in very good agreement with numerical simulations.

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

“…Contrary to the so-called cutback technique [32,[43][44][45], the technique used here (and similar for example to the one used in [31]) allows to explore various normalized propagation lengths with only one optical fiber having a fixed length. The key point is to adjust the spectral width and the optical power in order to change proportionally the number of linear lengths and of nonlinear lengths experienced by the waves.…”

“…In particular this allowed us to study the statistics as a function of the propagation distance without the use of the so-called "cut-back" technique [32,[43][44][45].…”

Experimental observation of the emergence of Peregrine-like events in focusing dam break flows

“…Taking advantage of the advanced control provided by the components of the telecommunication industry and new ultrafast characterization methods, Peregrine wave [2,3], higher-order or superregular breathers [4,5,6] have been experimentally generated. Recent other works have stressed the crucial importance and universality of such structures, especially the Peregrine wave [7,8,9] which can also be detected in deep water and other nonlinear medium governed by the NLSE [10,11]. Normally dispersive fibers have also stimulated experimental research, mainly driven by the interest in the study of dispersive shock waves (DSW) [12] : optical equivalent of undular bores [13], reproduction of dam-breaking problems [14], or the Riemann simple waves [15], have provided recent examples of the insights that can be obtained in the defocusing regime of propagation.…”

“…Here we also clearly note that each oscillation of the generated modulated wave presents successive growth-decay cycles, which is a key feature of breather solutions to the focusing NLSE. Inspired from the recent confirmation of the universal emergence of the Peregrine soliton (PS) in the focusing dynamics near a gradient catastrophe [7], we checked their temporal profile at the point of each maximum compression by using the Peregrine profile:…”

Nonconservative higher-order hydrodynamic modulation instability

“…Note that when a −→ 0.5, the modulation period becomes infinite, the growth becomes algebraic rather than exponential and the wave dynamics is then described by the universal Peregrine breather solution [30][31][32][33]. The AB-type wave motion has been observed in a wide-range of physical media and provides an ideal framework to control MI in space and time in laboratory environments [16,17,34].…”