Bandgap properties of phononic crystals with L-shape scatters

In this paper, we study the complete and directional bandgap properties of two-dimensional mercury/air phononic crystals (PnCs) with L-shape scatters based on the plane wave expansion method combined with a parallel shift scheme. As the symmetry of the scatters is lower than the symmetry of a square lattice, we scan the whole first Brillouin zone when performing the calculation. The relationships between the parameters (including geometry and filling fraction) of L-shape scatters and bandgaps are simulated in detail. The complete bandgap could be gained at a very low filling fraction (even below 0.076). The bandgap and directional bandgap width could be adjusted widely by changing its geometry and rotating the L-shape scatters, which could be useful for applications such as an acoustic directional filter or acoustic isolator.