“Extraordinary” modulation instability in optics and hydrodynamics

Guillaume Vanderhaegen (1) , Corentin Naveau (1) , Pascal Szriftgiser (1) , Alexandre Kudlinski (1) , Matteo Conforti (1) , Arnaud Mussot (1) , Miguel Onorato (2) , Stefano Trillo (3) , Amin Chabchoub (4) , Nail Akhmediev (5)

1 PhLAM - Laboratoire de Physique des Lasers, Atomes et Molécules - UMR 8523
2 UNITO - Università degli studi di Torino = University of Turin
3 UniFE - Università degli Studi di Ferrara = University of Ferrara
4 The University of Sidney
5 ANU - Australian National University

The classical theory of modulation instability (MI) attributed to Bespalov–Talanov in optics and Benjamin–Feir for water waves is just a linear approximation of nonlinear effects and has limitations that have been corrected using the exact weakly nonlinear theory of wave propagation. We report results of experiments in both optics and hydrodynamics, which are in excellent agreement with nonlinear theory. These observations clearly demonstrate that MI has a wider band of unstable frequencies than predicted by the linear stability analysis. The range of areas where the nonlinear theory of MI can be applied is actually much larger than considered here.

Domaines: Formation de Structures et Solitons [nlin.PS]; Physique [physics]

Guillaume Vanderhaegen, Corentin Naveau, Pascal Szriftgiser, Alexandre Kudlinski, Matteo Conforti, et al.. “Extraordinary” modulation instability in optics and hydrodynamics. Proceedings of the National Academy of Sciences of the United States of America, 2021, 118 (14), pp.e2019348118. ⟨10.1073/pnas.2019348118⟩. ⟨hal-03215313⟩