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On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime

1
Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa, Chiba 277-8563, Japan
2
Corporate Planning Department, MS&AD InterRisk Research & Consulting, Inc., Tokyo 101-0063, Japan
3
School of Civil Engineering, The University of Sydney, Sydney NSW 2006, Australia
*
Author to whom correspondence should be addressed.
Fluids 2019, 4(2), 84; https://doi.org/10.3390/fluids4020084
Received: 8 February 2019 / Revised: 1 April 2019 / Accepted: 16 April 2019 / Published: 2 May 2019
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Abstract

Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497–21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin–Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA. View Full-Text
Keywords: hydrodynamic rogue waves; optical rogue waves; scale separation; high-order spectral method; nonlinear Schrödinger equation hydrodynamic rogue waves; optical rogue waves; scale separation; high-order spectral method; nonlinear Schrödinger equation
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Waseda, T.; Fujimoto, W.; Chabchoub, A. On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime. Fluids 2019, 4, 84.

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