"Extraordinary" modulation instability in optics and hydrodynamics

Abstract

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 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.

9 pages, 10 figures

References in corpus (4)

• Rogue waves and analogies in optics and oceanography
• Doubly periodic solutions of the focusing nonlinear Schrödinger equation: recurrence, period doubling and amplification outside the conventional modulation instability band
• Spontaneous emergence of rogue waves in partially coherent waves: a quantitative experimental comparison between hydrodynamics and optics
• Optical amplification and transmission of attenuated multi-soliton based on spectral characteristics of Akhmediev breather

Cited by in corpus (10)

• Experimental evidence of nonlinear focusing in standing water waves
• Modulation instability and non-degenerate Akhmediev breathers of Manakov equations
• Localized Nonlinear Waves on Spatio-Temporally Controllable Backgrounds for a (3+1)-Dimensional Kadomtsev-Petviashvili-Boussinesq Model in Water Waves
• Fundamental and second-order dark soliton solutions of 2- and 3-component Manakov equations in the defocusing regime
• The nonlinear Benjamin-Feir instability -- Hamiltonian dynamics, primitive breathers, and steady solutions
• Gain assisted controllable fast light generation in cavity magnomechanics
• Domain formation of modulation instability in spin-orbit-Rabi coupled Gross-Pitaevskii equation with cubic-quintic interactions
• Modulational instability of nonuniformly damped, broad-banded waves: applications to waves in sea-ice
• Nonlinear compact localized modes in flux-dressed octagonal-diamond photonic lattice
• Modulational instability and quantum droplets in a two-dimensional Bose-Einstein condensate