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

作者：Farhat Mohamed; Guenneau Sebastien^*; Enoch Stefan; Movchan Alexander

来源：Journal of Computational and Applied Mathematics, 2010, 234(6): 2011-2019.

DOI：10.1016/j.cam.2009.08.052

• Linear water waves
• Periodic structures
• Bloch spectrum
• Negative refraction
• Ultra-refraction

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.

• 出版日期2010-7-15