Tunable near zero acoustic metasurface based on acoustic split ring resonators

In this paper we present an acoustic metasurface based on a matrix consisting of unit cells with effective mass density of Lorentzian type, each one consisting of a thin elastic membrane placed in a short tube coaxial with an acoustic duct. The effective density of a single unit cell is developed as a function of its geometrical parameters and the material parameters of the membrane. An infinite metasurface constructed by imposing periodic boundary conditions on a matrix of unit cells is shown to exhibit frequency selectivity, with transmission possible only in a narrow band of frequencies where the effective density is close to zero. Since one of the properties of a zero refractive index surface is that the output angle is equal to zero regardless of the incident angle, the obtained surface can be used to convert spherical acoustic waves to plane waves. An acoustic surface with different unit cells, with their effective densities tailored so as to achieve a GRIN profile corresponding to an acoustic lens, has also been analyzed. Finally, we demonstrate the possibility of controlling effective densities of such a structure by applying appropriate DC voltage bias to membranes made of piezoelectric material. In this way the behavior of the surface can be easily tuned
without any structural changes.