• Open Access

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

B. Kibler, A. Chabchoub, A. Gelash, N. Akhmediev, and V. E. Zakharov
Phys. Rev. X 5, 041026 – Published 13 November 2015

Abstract

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

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  • Received 25 June 2015

DOI:https://doi.org/10.1103/PhysRevX.5.041026

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Authors & Affiliations

B. Kibler1,*, A. Chabchoub2, A. Gelash3, N. Akhmediev4, and V. E. Zakharov3,5,6

  • 1Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS–Université de Bourgogne Franche-Comté, 21078 Dijon, France
  • 2Department of Ocean Technology Policy and Environment, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan
  • 3Novosibirsk State University, Novosibirsk 630090, Russia
  • 4Optical Sciences Group, Research School of Physics and Engineering, The Australian National University, Canberra, ACT 2600, Australia
  • 5Lebedev Physical Institute, Russian Academy of Sciences, Moscow 119991, Russia
  • 6University of Arizona, Tucson, Arizona 857201, USA

  • *Corresponding author. bertrand.kibler@u-bourgogne.fr

Popular Summary

Instabilities are frequently observed in nature, and they can lead to unexpected catastrophes and disasters in seemingly normal conditions. The simplest form of instability in a distributed system is its response to a harmonic modulation. In water waves, this form of instability is known as the Benjamin-Feir instability, which is the disintegration of periodic wave trains on the surface of deep water. In optics, this instability is known as the Bespalov-Talanov instability, which leads to small-scale filamentation of optical beams. These pioneering discoveries, found independently in the 1960s, resulted in a better understanding of the universal nature of modulation instability and led to observations of a multiplicity of modulation instability examples in physics. However, even now, over 50 years later, more practical but complex forms of this old physical phenomenon have still not been revealed. Here, thanks to our exceptional technical capability to manipulate light and water waves, we make the next crucial step in observing the growth of more sophisticated modulation instability perturbations.

We study the dynamics of modulation instability using an optical fiber and water-wave tank. Each of these systems is subjected to small, localized perturbations, and we study the creation and annihilation dynamics of superregular breather waves, which are the building blocks of modulation instability. Our experiments, which are conducted on time scales of seconds in the water-wave tank and picoseconds in the optical fiber, confirm analytical predictions of nonlinear wave theory developed recently. Demonstrating simultaneous experimental results at drastically different scales, in two different branches of wave physics, is of considerable importance in and of itself and is extremely rare. To the best of our knowledge, our methodology is the first of its kind in wave physics.

We expect that our findings will strongly impact numerous disciplines related to nonlinear wave dynamics.

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Vol. 5, Iss. 4 — October - December 2015

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