Band structure of three-dimensional phononic crystals

By using the plane-wave-expansion method, the band structure of three-dimension phononic crystals was calculated. in which the cuboid scatterers were arranged in a host with a face-centered-cubic (FCC) structure. The influences of a few factors such as the component materials, the filling fraction of scatterers and the ratio (R-HL) of the scatterer s height to its length on the band-gaps of phononic crystals were investigated. It is found that in the three-dimension solid phononic crystals with FCC structure, the optimum case to obtain band-gaps is to embed high-velocity and high-density scatterers in a low-velocity and low-density host. The maximum value of band-gap can be obtained when the filling fraction is in the middle value. It is also found that the symmetry of the scatterers strongly influences the band-gaps. For R-HL >= 1, the width of the band-gap decreases as R-HL increases. On the contrary. the width of the band-gap increases with the increase of R-HL when R-HL is smaller than 1.