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.

Acoustic superlens provides a way to overcome the diffraction limit with respect to the wavelength of the bulk wave in air. However, the operating frequency range of subwavelength imaging is quite narrow. Here, an acoustic superlens is designed using Helmholtz-resonator-based metamaterials to broaden the bandwidth of super-resolution. An experiment is carried out to verify subwavelength imaging of double slits, the imaging of which can be well resolved in the frequency range from 570 to 650 Hz. Different from previous works based on the Fabry-Pérot resonance, the corresponding mechanism of subwavelength imaging is the Fano resonance, and the strong coupling between the neighbouring Helmholtz resonators separated at the subwavelength interval leads to the enhanced sound transmission over a relatively wide frequency range.

We show that sound waves can resonantly transmit through Bragg bandgaps in an acoustical duct periodically attached with an array of Helmholtz resonators, forming within the normally forbidden band a transparency window with group velocity smaller than the normal speed of sound. The transparency occurs for the locally resonant frequency so much close to the Bragg one that both the local-resonance-induced bandgap and the Bragg one heavily overlap with each other. The phenomenon seems an acoustical analog of the well-known electromagnetically induced transparency by quantum interference. Different from the Fano-like interference explanation, we also provide a mechanism for the transparency window phenomenon which makes it possible to extend the phenomenon in general.

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It is revealed that the Fano-like interference leads to the extraordinary acoustic transmission through a slab metamaterial of thickness much smaller than the wavelength, with each unit cell consisting of a Helmholtz resonator and a narrow subwavelength slit. More importantly, both the theoretical analysis and experimental measurement show that the angle-independent acoustical transparency can be realized by grafting a Helmholtz resonator and a quarter-wave resonator to the wall of a narrow subwavelength slit in each unit cell of a slit array. The observed phenomenon results from the interferences between the waves propagating in the slit, those re-radiated by the Helmholtz resonator, and those re-radiated by the quarter-wave resonator. The proposed design may find its applications in designing angle-independent acoustical filters and controlling the phase of the transmitted waves.

Nonlinear amplitude-frequency response of an acoustic Helmholtz resonator is investigated by incorporating linear damping, nonlinear damping, and nonlinear restoration. Method of multiple time scale is used for theoretical analysis, and a reasonable explanation of an experiment observation, i.e., the downward shift of resonance frequency, is given. We also discuss the response of two-frequency driving, and find that amplitude-frequency response depends on the phase difference of the driving. In addition, the response amplitude of two-frequency driving can increase approximately 10% as compared with the single frequency driving at a certain phase difference for the parameters we choose to simulate.

Simultaneous temporal and spatial focusing of a pulse is of significance for detection and imaging.Here, an achromatic reflected metalens is designed using hybrid resonance and anti-resonance. The theoretical result demonstrates that the anti-resonance provides an extra degree of freedom to control local phases of reflected waves, yielding an achromatic lens of thickness equal to one half of central wavelength. To overcome the shortcoming of traditional approach to design lenses (neglecting the intercell coupling), a boundary integral method is proposed to alleviate the focus deviation over a broadband. The achromatic feature of designed lens is then verified in the frequency range from 2800 to 5600 Hz by an experiment. Owing to a very weak frequency dependence of focal point and a high reflected focusing efficiency over a broadband, a highly directional and long-distance acoustic probing scheme (the mainlobe width about 8 0 ) is proposed with the aid of achromatic reflected metalens and being confirmed by another experiment, where a signal processing method using triple sensors separated by a subwavelength interval is adopted to eliminate the interferences between incident waves and reflected waves. Our result may find its application in a long-distance underwater acoustic probing.

Monochromatic sound source localization becomes difficult in enclosed space. According to the reciprocity theorem, a self-consistent method of source localization in enclosed space, referred to as the flux projection beamforming, is proposed, only using the measurement of the sound pressure and normal velocity on the closed boundary at a single frequency. Its validity is examined both by experiment and simulation.