Acoustic Beam Splitting and Cloaking Based on a Compressibility-Near-Zero Medium

We report an artificial acoustic compressibility-near-zero medium made of a phononic crystal composed of epoxy blocks arranged in a square lattice. Its anisotropic effective density leads to a linear cross in its isofrequency contour in the vicinity of the Brillouin zone center, as its effective compressibility approaches zero. When a Gaussian beam is normally incident on the phononic crystal, a splitting effect is achieved at the frequency of the crossing point. Based on such a beam-splitting effect, an acoustic cloaking of an irregular-shaped object embedded in the phononic crystal is demonstrated both theoretically and experimentally. Such an anisotropic zero-index material offers a potential method to control acoustic waves.

Figure 1

Band structure and IFCs of the two-dimensional PC. (a) Band structure of the PC with lattice constant $a=27\mathrm{mm}$. The host medium (gray) is air. The blue rectangles with length $18.9\mathrm{mm}$ and width $5.4\mathrm{mm}$ are epoxy blocks. The horizontal dotted line represents the frequency of the eigenstate at the $\mathrm{\Gamma }$ point of the second band. (b)–(d) The IFCs near the Brillouin zone center at (b) $6.07,$ (c) $6.125,$ and (d) $6.18\mathrm{kHz}$. The black solid lines and red dotted lines in (b)–(d) are obtained from comsol simulation and the effective parameters, respectively.

Figure 2

Effective parameters of the two-dimensional PC. (a) The normalized effective compressibility of the PC. (b) The x component (solid blue line) and y component (dotted red line) of normalized effective mass density. The vertical dashed lines in (a), (b) represent the frequency $6.125\mathrm{kHz}$.

Figure 3

Beam splitting and directional propagation in the CNZM at $6.18\mathrm{kHz}$. (a) The acoustic pressure-field distribution when a Gaussian beam is normally incident on the PC. (b) The acoustic pressure-field distribution when a point source is placed at the center of PC. All boundaries of the simulated regions in (a), (b) are set as scattering boundaries.

Figure 4

An acoustic cloaking based on the beam-splitting effect. (a) The normalized acoustic pressure-field distributions when a point source is placed at the bottom of our PC with $24\times 16$ unit cells. The right and left side of the PC are blocked by sound-hard boundaries. An N-shaped sound-hard object (white) is hidden in the PC. The yellow-shaded area indicates the range of location of objects. (b) The experimental setup. (c), (d) Experimental results (c) without and (d) with the sound-hard object.