Hypersonic band gaps in two-dimensional piezoelectric phononic crystal slabs

We analyze the propagation of acoustic waves in a phononic crystal slab consisting of metal inclusions placed periodically in a host piezoelectric material. Our system is composed of a square lattice of tungsten (W) cylinders embedded in an Aluminium nitride (AlN) matrix. It is found that several complete band gaps with a variable bandwidth exist for acoustic waves of any polarization and incidence. In addition to the filling fraction, a key parameter for the existence and the width of these complete band gaps is the ratio of the slab thickness (d) to the lattice period (a). We have explored how these absolute band gaps close up as the parameter (d/a) increases. Significantly, it is found that the band gaps of a phononic crystal slab are distinct from those of bulk acoustic waves propagating in the plane of the plate and that they are strongly affected by the presence of cut-off frequency modes. The numerical calculations are performed using the finite element method with periodic boundary conditions derived from the Bloch-Floquet theorem.