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Rogue wave formation by accelerated solitons at an optical event horizon

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Abstract

Rogue waves, by definition, are rare events of extreme amplitude. At the same time, they are surprisingly ubiquitous, in the sense that they can exist in a wide range of physical contexts and possess probability distributions that exhibit heavier tails than the normal Gaussian distribution. While many mechanisms have been demonstrated to explain the appearance of rogue waves in various specific systems, there is no known generic mechanism or general set of criteria shown to rule their appearance. Presupposing only the existence of a nonlinear Schrödinger-type equation together with a concave dispersion profile around a zero-dispersion wavelength, we demonstrate that solitons may experience acceleration and strong reshaping due to the interaction with continuum radiation, giving rise to extreme-value phenomena. The mechanism appears to be widely independent from interactions specific to the optical context, e.g., the Raman effect or other scattering processes that have no equivalent in other wave-supporting physical systems. In our system, a strong increase in the peak power may appear via reshaping while the pulse energy is nearly conserved. The conservative nature of the proposed reshaping-induced appearance of rogue waves makes this mechanism particularly robust.

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Acknowledgments

The following support is gratefully acknowledged: A. D. partially by DFG, Sh. A. by the DFG Research Center MATHEON (project D 14), F. M. by DFG, G. S. by the Academy of Finland (project Grant 128844), and C.M. partially by DFG.

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Authors and Affiliations

  1. Institute for Quantum Optics, Leibniz Universität Hannover, Welfengarten 1, 30167, Hannover, Germany

    A. Demircan

  2. Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117, Berlin, Germany

    Sh. Amiranashvili & C. Brée

  3. Institute for Physics, University of Rostock, Universitätsplatz 3, 18055, Rostock, Germany

    C. Mahnke & F. Mitschke

  4. Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy, Max-Born-Straße 2A, 12489, Berlin, Germany

    G. Steinmeyer

  5. Optoelectronics Research Centre, Tampere University of Technology, 33101, Tampere, Finland

    G. Steinmeyer

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  1. A. Demircan
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  2. Sh. Amiranashvili
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  3. C. Brée
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  4. C. Mahnke
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Correspondence to A. Demircan.

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Demircan, A., Amiranashvili, S., Brée, C. et al. Rogue wave formation by accelerated solitons at an optical event horizon. Appl. Phys. B 115, 343–354 (2014). https://doi.org/10.1007/s00340-013-5609-9

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  • DOI: https://doi.org/10.1007/s00340-013-5609-9

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