Gradient negative refraction index phononic crystal lens with a rotating scatterer

In this paper, a novel 2D gradient negative refraction index (GNRI) phononic crystal (PC) lens with a constant filling fraction was proposed through the rotation of the scatterer, which is different from the traditional GNRI PC lens with a varying filling fraction or lattice constant. The present GNRI PC lens is composed of the three-petal steel scatterers arranged in the air periodically, and the rotation of the three-petal scatterer results in a variation in the second dispersion band, which is related to the negative refraction index. Various negative refraction indices were calculated for different rotation angles of the scatterer. Then, a specific gradient distribution of the negative refraction index was designed to focus the acoustic wave. The results showed that the present PC lens exhibits an obvious focus effect at different reduced frequencies. The range of the operation reduced frequency is 0.19, which is from Ω = 0.65 to 0.84 and about 2 times than that of the traditional GNRI PC lens. The effects of the reduced frequency and the dimension of the lens on the focal length were also analyzed. The results in this paper provide a new approach to design and fabricate the flat lens with a broad work frequency range.