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Negative refraction of water waves by hyperbolic metamaterials

Published online by Cambridge University Press:  19 April 2023

Leo-Paul Euvé ,
Kim Pham  and
Agnès Maurel Open the ORCID record for Agnès Maurel [Opens in a new window]
Leo-Paul Euvé*
Affiliation:
PMMH, ESPCI, Sorbonne Université, Université PSL, 1 rue Jussieu, 75005 Paris, France
Kim Pham*
Affiliation:
IMSIA, CNRS, EDF, CEA, ENSTA Paris, Institut Polytechnique de Paris, 828 Bd des Maréchaux, 91732 Palaiseau, France
Agnès Maurel*
Affiliation:
ESPCI Paris, Institut Langevin, PSL University, CNRS, 1 rue Jussieu, 75005 Paris, France
*
†Email addresses for correspondence: leo-paul.euve@espci.fr, kim.pham@ensta-paris.fr, agnes.maurel@espci.fr
†Email addresses for correspondence: leo-paul.euve@espci.fr, kim.pham@ensta-paris.fr, agnes.maurel@espci.fr
†Email addresses for correspondence: leo-paul.euve@espci.fr, kim.pham@ensta-paris.fr, agnes.maurel@espci.fr
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Abstract

We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 961 , 25 April 2023 , A16
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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