Three-Dimensional Axisymmetric Cloak Based on the Cancellation of Acoustic Scattering from a Sphere

This Letter presents the design, fabrication, and experimental characterization of a directional three-dimensional acoustic cloak for airborne sound. The cloak consists of 60 concentric acoustically rigid tori surrounding the cloaked object, a sphere of radius 4 cm. The major radii and positions of the tori along the symmetry axis are determined using the condition of complete cancellation of the acoustic field scattered from the sphere. They are obtained through an optimization technique that combines genetic algorithm and simulated annealing. The scattering cross section of the sphere with the cloak, which is the magnitude that is minimized, is calculated using the method of fundamental solutions. The low-loss fabricated cloak shows a reduction of the 90% of the sphere scattering cross section at the frequency of 8.55 kHz.

Figure 1

(a) Schematic representation of the 3D designed cloak. The cloak consists of 60 concentric tori surrounding the central spherical object. (b) Photograph of the cloak taken after its fabrication. It is made in plastic with a central sphere of radius 4 cm. The total length of the sample ($\mathrm{\text{object}}+\mathrm{\text{cloak}}$) along the $z$ axis is 17 cm. (c),(d) Photographs taken inside the anechoic room.

Figure 2

(a) Map of the total pressure (real part in arbitrary units) obtained from the scattering of an incident plane wave with frequency 8.62 kHz with a rigid sphere with radius 4 cm. (b) Map corresponding to the sphere surrounded by the designed cloak. Both maps are calculated using a multiple scattering approach based on the method of fundamental solutions. The rectangle defined by the dashed lines represents the area scanned by the experimental setup.

Figure 3

Pressure maps measured at 8.55 kHz, the operational frequency of the fabricated cloak. Maps on the left (right) represent the real part of the total pressure on the horizontal (vertical) plane. (a) Free space, (b) bare sphere, (c) $\mathrm{\text{sphere}}+\mathrm{\text{cloak}}$.

Figure 4

Upper panels: Plot of the averaged visibility ($\gamma$) as a function of the frequency. The experimental results with and without the cloak are marked by red circles and blue squares, respectively. The reference visibility (${\gamma }_0$) when there is no object is marked by black triangles. The lines represent the simulations. Lower panels: The purple diamonds plot the ratio between the averaged visibility of the sphere with the cloak (${\gamma }_c$) and without cloak (${\gamma }_{\mathrm{sph}}$). Both are shifted by the reference visibility. The black lines represent the ratio between the scattering cross sections of the sphere with and without cloak, ${\sigma }_c/{\sigma }_{\mathrm{sph}}$, obtained from simulations. Full (empty) symbols define data on the horizontal (vertical) plane.