  Acoustic flat lensing is achieved here by tuning a phononic array to have
indefinite medium behaviour in a narrow frequency spectral region along the
acoustic branch. This is confirmed by the occurrence of a flat band along an
unusual path in the Brillouin zone and by interpreting the intersection point
of isofrequency contours on the corresponding isofrequency surface; coherent
directive beams are formed whose reflection from the array surfaces create
lensing. Theoretical predictions are corroborated by time-domain experiments,
airborne acoustic waves generated by a source with a frequency centered about
$10.6$ kHz, placed at three different distances from one side of a finite
phononic crystal slab, constructed from polymeric spheres, yield distinctive
focal spots on the other side. These experiments evaluate the pressure field
using optical feedback interferometry and demonstrate precise control of the
three-dimensional wave trajectory through a sonic crystal.

Classical Physics