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Effects of nonlinearity on Anderson localization of surface gravity waves

Author

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  • Guillaume Ricard

    (Université Paris Cité, CNRS, MSC, UMR 7057)

  • Filip Novkoski

    (Université Paris Cité, CNRS, MSC, UMR 7057)

  • Eric Falcon

    (Université Paris Cité, CNRS, MSC, UMR 7057)

Abstract

Anderson localization is a multiple-scattering phenomenon of linear waves propagating within a disordered medium. Discovered in the late 50s for electrons, it has since been observed experimentally with cold atoms and with classical waves (optics, microwaves, and acoustics), but whether wave localization is enhanced or weakened for nonlinear waves is a long-standing debate. Here, we show that the nonlinearity strengthens the localization of surface-gravity waves propagating in a canal with a random bottom. We also show experimentally how the localization length depends on the nonlinearity, which has never been reported previously with any type of wave. To do so, we use a full space-and-time-resolved wavefield measurement as well as numerical simulations. The effects of the disorder level and the system’s finite size on localization are also reported. We also highlight the first experimental evidence of the macroscopic analog of Bloch’s dispersion relation of linear hydrodynamic surface waves over periodic bathymetry.

Suggested Citation

  • Guillaume Ricard & Filip Novkoski & Eric Falcon, 2024. "Effects of nonlinearity on Anderson localization of surface gravity waves," Nature Communications, Nature, vol. 15(1), pages 1-8, December.
    • Handle: RePEc:nat:natcom:v:15:y:2024:i:1:d:10.1038_s41467-024-49575-5
    DOI: 10.1038/s41467-024-49575-5
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    References listed on IDEAS

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    2. A. A. Chabanov & M. Stoytchev & A. Z. Genack, 2000. "Statistical signatures of photon localization," Nature, Nature, vol. 404(6780), pages 850-853, April.
    3. M. Torres & J. P. Adrados & F. R. Montero de Espinosa, 1999. "Visualization of Bloch waves and domain walls," Nature, Nature, vol. 398(6723), pages 114-115, March.
    4. Giacomo Roati & Chiara D’Errico & Leonardo Fallani & Marco Fattori & Chiara Fort & Matteo Zaccanti & Giovanni Modugno & Michele Modugno & Massimo Inguscio, 2008. "Anderson localization of a non-interacting Bose–Einstein condensate," Nature, Nature, vol. 453(7197), pages 895-898, June.
    5. Juliette Billy & Vincent Josse & Zhanchun Zuo & Alain Bernard & Ben Hambrecht & Pierre Lugan & David Clément & Laurent Sanchez-Palencia & Philippe Bouyer & Alain Aspect, 2008. "Direct observation of Anderson localization of matter waves in a controlled disorder," Nature, Nature, vol. 453(7197), pages 891-894, June.
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