Objective
We are attempting to develop acoustic metamaterials that demonstrate exotic material properties such as negative dynamic modulus and mass density with manageable loss levels. 

Background
Analogous to electromagnetic metamaterials, unprecedented mechanical properties can be obtained by engineering far sub-wavelength artificial “atoms” of acoustic media. 

Negative modulus has recently been demonstrated in an ultrasonic metamaterial that constitutes an array of Helmholtz resonators in a fluid channel.  Helmholtz resonators consist of a cavity in a rigid material connected to the fluid matrix through a much narrower throat. A unit cell of such a construct is shown in Figure 1(a). The fluid in the throat acts approximately as a mass, whereas the compressible fluid in the cavity performs the function of a spring. Sub-wavelength Helmholtz resonators radiate in a hemispherical pattern but can also be, in effect, monopoles in narrow one- and two-dimensional waveguides, where the shadow region does not exist.

By developing an analogous acoustic metamaterial with negative mass density, we will be able to demonstrate acoustic superlens, hyperlens and potentially nearly perfect lenses.  In addition, the development of negative mass density is a key precursor to developing acoustic cloaking and entirely new surface wave modes.

Results
We designed an ultrasonic metamaterial with negative stiffness. Experimental evidence (Figure 1b) has been presented asserting that a one-dimensional chain of Helmholtz resonators has a negative group velocity due to negative modulus. Negative material responses can give rise to new surface states. We present than an acoustic metamaterial with negative mass density can support new surface states. We offer the microscopic picture of these new surface states in the form of particle trajectories as shown in Figure 2.

Figure 1. (a) Cross-section view of a Helmholtz resonator. A cavity is carved out of a rigid material (gray) and connected to the outside via a neck.  Forces applied to the neck area S drives neck fluid approximately as a mass into the cavity which compresses like a spring.  The inset illustrates the analogy between a Helmholtz resonator and a LC circuit.  (b) 1-D chain of Helmholtz resonators which results in negative modulus at resonance, which is shown in (c).

Figure 2. Schematic of the surface state at an interface separating two semi-infinite media. Medium I (green) is considered to have positive material properties (mass density ρ and bulk modulus B); whereas medium II (yellow) is taken as an acoustic metamaterial with generic material properties. (a) Schematic of the pressure profile of surface bound states (shown in red). The motion trajectory of the material points is an ellipse (shown in blue); the elliptical rotation of the particles near the interface is same in both the media (shown clock-wise). The eccentricity of the ellipses depends on the wave vector of the surface state with major axes parallel to the interface. (b) The pattern of the displacements of the surface wave is illustrated (top view). Schematic shows that the displacements in y and z directions are 900 out of phase, with slipping at the interface.

References:
1. N. Fang, D. J. Xi, J. Y. Xu, M. Ambati, W. Srituravanich, C. Sun, X. Zhang, Nature Materials 5 (6), 452 (2006). view pdf