"Extraordinary" modulation instability in optics and hydrodynamics

TL;DR

This paper presents experimental evidence in optics and hydrodynamics showing that modulation instability (MI) has a broader unstable frequency band than linear theory predicts, aligning well with nonlinear wave propagation models.

Contribution

It provides experimental validation of the nonlinear theory of MI, revealing a wider unstable frequency range than linear analysis suggests.

Findings

MI has a wider band of unstable frequencies than linear theory predicts.

Experimental results agree with nonlinear wave theory.

The nonlinear theory's applicability extends beyond previous assumptions.

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.