Continuous-phase-transformation acoustic metasurface

•Continuous-phase-transformation acoustic metasurfaces (CPTAMs) with filling media are proposed.•The relationships between the modulation of the CPTAM and its structural parameters are derived.•CPTAMs can focus with sub-wavelength, small focus aberration, and almost no sidelobe.•The curved metasurfaces can theoretically achieve continuous deflection angle focusing.•The aperiodic metasurfaces can achieve focusing with continuous frequency. Acoustic metasurfaces are artificial structures, one of whose functions is to achieve plane wave focusing due to the phase gradient transformation of specific structural units. However, previous periodic acoustic metasurfaces for plane wave focusing have drawbacks such as discrete operating frequency, large focus aberration, obvious sidelobes, etc. Here, we propose periodic folded, periodic curved, aperiodic folded, and aperiodic curved acoustic metasurfaces with filling medium, which use continuous-phase-transformation to realize the control of acoustic waves. The results show that, all four acoustic metasurfaces can achieve sub-wavelength focusing, with small focus aberrations and almost no sidelobes. Furthermore, the periodic and aperiodic curved metasurfaces use continuous deflection angles to achieve more efficient focusing than that of the periodic and aperiodic folded metasurfaces; aperiodic folded and curved metasurfaces can focus for the continuous operating frequency which is different from the discrete operating frequency in the previous periodic metasurfaces. The continuous-phase-transformation acoustic metasurface (CPTAM) proposed in this paper will have a wide range of applications in non-destructive testing, medical imaging, engineering technology, etc.