Flat acoustic lens by acoustic grating with curled slits

• Expression of transmission coefficient of an acoustic grating with curled slits.
• Non-dispersive and tunable effective medium parameters for the acoustic grating.
• A flat acoustic focusing lens with gradient index by using the acoustic grating.

We design a flat sub-wavelength lens that can focus acoustic wave. We analytically study the transmission through an acoustic grating with curled slits, which can serve as a material with tunable impedance and refractive index for acoustic waves. The effective parameters rely on the geometry of the slits and are independent of frequency. A flat acoustic focusing lens by such acoustic grating with gradient effective refractive index is designed. The focusing effect is clearly observed in simulations and well predicted by the theory. We demonstrate that despite the large impedance mismatch between the acoustic lens and the matrix, the intensity at the focal point is still high due to Fabry–Perot resonance.