All-angle-negative-refraction and ultra-refraction for liquid surface waves in 2D phononic crystals

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.