Propagation of surface acoustic waves through sharply bent two-dimensional phononic crystal waveguides using a finite-difference time-domain method

In this paper, we adopt the finite-difference time-domain (FDTD) method to analyze surface acoustic waves propagating in two-dimensional phononic waveguides. To implement the FDTD program for dealing with surface acoustic waves, the Bloch theorem and absorbing boundary conditions are employed to deal with the periodic boundary condition and reflection from a numerical boundary. A phononic crystal consisting of circular steel cylinders that form a square lattice in an epoxy matrix is considered as an example to study phononic crystal waveguides. The dispersion relation and displacement fields are calculated to identify the band gaps and eigenmodes. The result shows the existence of a complete band gap of surface waves and thus an acoustic waveguide is created accordingly. Eigenmodes of surface waves inside the waveguide are indicated and pseudo surface acoustic waves propagating inside the straight waveguide are demonstrated. Further, waveguides with a sharp bend are reported and an improved design is suggested to enhance energy transmission.