  This paper describes a new kind of acoustic metasurface with multiply
resonant units, which have previously been used to induce multiple resonances
and effectively produce negative mass density and bulk/shear moduli. The
proposed acoustic metasurface can be constructed using real materials and does
not rely on an ideal rigid material. Therefore, it can work well in a water
background. The thickness of the acoustic metasurface is about two orders of
magnitude smaller than the acoustic wavelength in water. The design of a unit
group is proposed to avoid the phase discretization becoming too fine in such a
long-wavelength condition. We demonstrate that the proposed acoustic
metasurface achieves good performance in anomalous reflection, focusing, and
carpet cloaking.
