  Guided by theoretical predictions, we have demonstrated experimentally the
existence of negative refraction on the lowest two (acoustic) passbands (shear
and longitudinal modes) of a simple two dimensional phononic crystal consisting
of an isotropic stiff (aluminum) matrix and square- patterned isotropic
compliant (PMMA) circular inclusions. At frequencies and wave vectors where the
refraction is negative, the effective mass density and the effective stiffness
tensors of the crystal can be positive-defnite, and that, this is an inherent
property of phononic crystals with an isotropic stiff matrix containing
periodically distributed isotropic compliant inclusions. The equi-frequency
contours and energy ux vectors as fuctions of the phase-vector components,
reveal a rich body of refractive properties that can be exploited to realize,
for example, beam splitting, focusing, and frequency filtration on the lowest
passbands of the crystal where the dissipation is the least. By proper
selection of material and geometric parameters these phenomena can be realized
at remarkably low frequencies (large wave lengths) using rather small simple
two-phase unit cells. Keywords: Doubly periodic phononic crystals, acoustic
branch negative refraction, beam splitting, focusing, imaging, frequency
filtration at large wave lengths

Classical Physics;Applied Physics