Effect of symmetry on sonic band-gap in two-dimensional phononic crystals

Using the plane-wave expansion method, we calculated the sonic band structures of two-dimensional water-mercury phononic crystals of regular triangle, quadrilateral, hexagon, octagon prisms and cylinders arrayed in square lattice respectively. Our study concerns the dependence of band gaps on rotation angle of the noncircular rods. And we found that, for each rod and (relatively small) filling fraction, both the maximum and minimum of band gap present in the case of the crystals' highest symmetry. By adjusting the rods' orientation, the maximum of band gap for each filling fraction can be obtained and, results show that for water/mercury system the width of band-gap increases with the heightening of rods' symmetry, while for mercury/water system the exact opposite is true except for the case of square rods, which produces the largest band-gaps.