Inherent negative refraction on acoustic branch of two dimensional phononic crystals

Guided by theoretical predictions, we have demonstrated experimentally the existence of negative refraction on the two lowest acoustic-branch 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. We experimentally distinguished the shear and longitudinal modes to ensure that there are no couplings between the two modes and that the shear-mode negative refraction is an inherent property of periodic composites with stiff matrix and compliant inclusions. We have also discovered that a composite with compliant (PMMA) matrix and stiff (aluminum) inclusions does not display negative shear-mode refraction on its first branch. At frequencies and wave vectors where the refraction on the acoustic-branch passbands is negative, the effective mass-density and the effective stiffness tensors of the crystal are positive-definite, and this is an inherent property of such phononic crystals.The equi-frequency contours and energy flux vectors as functions 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 minimum. 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.