Impedance is an important issue in the design of acoustic lenses because mismatched impedance is detrimental to real focusing applications. Here, we report two designs of acoustic lenses that focus acoustic waves in water and air, respectively. They are tailored by acoustic meta-surfaces, which are rigid thin plates decorated with periodically distributed sub-wavelength slits. Their respective building blocks are constructed from the coiling-up spaces in water and the layered structures in air. Analytic analysis based on coupled-mode theory and transfer matrix reveals that the impedances of the lenses are matched to those of the background media. With these impedance-matched acoustic lenses, we demonstrate the acoustic focusing effect by finite-element simulations.
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