Phononic crystal lens with an asymmetric scatterer

A novel 2D gradient index phononic crystal (GRIN PC) lens was designed by rotating scatterers that theoretically differs from the traditional GRIN PC lens by altering fill fraction, lattice constant or material parameters. Three-petal epoxy cylinders were designed as scatterers and embedded into a homogenous steel matrix. Rotation of the three-petal cylinder results in an asymmetry about x axis, and there is a change in the first dispersion band which is related to group velocity and the refractive index. The equivalent refraction index along the y direction was modulated to satisfy the distribution of a hyperbolic secant profile using a specific rotation angle of the scatterer. The focus of the acoustic wave in the PC lens with a rotating three-petal scatterer was investigated using a numerical method, and the results showed that the focus length agreed with the trajectories derived from the analytical solution. Results also showed that the range of the operation reduced frequency is 0.18. The influence of the operation frequency on the focusing efficiency and focal length was also discussed. The work provides a convenient method for fabricating a phononic crystal lens and makes the lens suitable for relevant applications.