Far-field focusing of acoustic waves by a two-dimensional phononic crystal with surface grating

We show that by adding a surface grating onto a two-dimensional phononic crystal slab, negative refraction of acoustic waves can be observed in the originally forbidden frequency region. Far-field focusing by this mechanism is demonstrated with exact numerical simulations, which is in agreement with the physical analysis based on the wave-beam negative-refraction law. Potential applications of the effect in acoustic devices are expected