Three-dimensional ultrathin planar lenses by acoustic metamaterials.

Acoustic lenses find applications in various areas ranging from ultrasound imaging to nondestructive testing. A compact-size and high-efficient planar acoustic lens is crucial to achieving miniaturization and integration, and should have deep implication for the acoustic field. However its realization remains challenging due to the trade-off between high refractive-index and impedance-mismatch. Here we have designed and experimentally realized the first ultrathin planar acoustic lens capable of steering the convergence of acoustic waves in three-dimensional space. A theoretical approach is developed to analytically describe the proposed metamaterial with hybrid labyrinthine units, which reveals the mechanism of coexistence of high refractive index and well-matched impedance. A hyperbolic gradient-index lens design is fabricated and characterized, which can enhance the acoustic energy by 15 dB at the focal point with very high transmission efficiency. Remarkably, the thickness of the lens is only approximately 1/6 of the operating wavelength. The lens can work within a certain frequency band for which the ratio between the bandwidth and the center frequency reaches 0.74. By tailoring the structure of the metamaterials, one can further reduce the thickness of the lens or even realize other acoustic functionalities, opening new opportunity for manipulation of low-frequency sounds with versatile potential.