All-angle-negative-refraction and ultra-refraction for liquid surface waves in 2D phononic crystals |
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Authors: | Mohamed Farhat Stefan Enoch |
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Affiliation: | a Institut Fresnel (UMR CNRS 6133), University of Aix-Marseille, France b Department of Mathematical Sciences, Peach Street, Liverpool L69 3BX, UK |
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Abstract: | We analyse transport properties of linear liquid waves propagating within arrays of immersed rigid circular cylindrical obstacles fixed to a rough bottom. A comparison between Multipole and Finite Element methods is drawn in the case of Robin boundary conditions coupled with Floquet-Bloch boundary conditions. We find that the first band is concave yet nearly flat (associated waves of small negative group velocity) and it displays a cut-off (zero-frequency stop band associated with a singular perturbation). Thanks to this anomalous dispersion in such fluid filled structures, we achieve both ultra-refraction and negative refraction for waves propagating at their surface. Potential applications lie in a omnidirective ‘water antenna’ and a convergent flat ‘water lens’. The latter one is demonstrated experimentally. |
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Keywords: | Linear water waves Periodic structures Bloch spectrum Negative refraction Ultra-refraction |
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