Reconfigurable curved metasurface for acoustic cloaking and illusion

A severe limitation of current acoustic metasurfaces remains in their modest tunability to meet multifrequency requirements and alterable functionalities on demand. Here, a reconfigurable curved acoustic metasurface for acoustic cloaking and illusion is reported. The structure is composed of an array of tunable helical units to break this limitation and realize continuously versatile sound manipulations. We theoretically, numerically and experimentally investigate the channel length represented by the helical depth, which is used to achieve full 2π phase shift continuously over the frequency range from 2 to 7 kHz. As pragmatic examples, we present by full-wave numerical simulations the concept of a curved metasurface for the continuously tunable acoustic multifunction, including broadband carpet cloaking and ground illusion at a wide working band. Then, we experimentally demonstrate these functionalities by showing an excellent effect to restore the disturbed reflective field from a cloaked object or to mimic an arbitrary shaped ground.

Figure 1

A 3D schematic view and working principle of an arc metasurface carpet cloak based on a tunable matched helical unit. (a) The schematic diagram of the generalized Snell's law for the wavefront restoration of the curved metasurface with infinite length in $y$-axis direction. It will be used to mimic two types of surfaces, including flat and arbitrary shaped ground. (b) Schematic view of a cross section of the metasurface cloak with distributed helical units. The metasurface is an arc-shaped plate with radius of $R=0.9\mathrm{m}$ and the arc central angle of 60°. Thirty-one helical units are uniformly arranged on its surface with step of 2°. (c) The cylindrical unit of the tunable cloak. The depth of the helical channel $h$ is the tunable parameter of the system by rotating a matched screw into a helical channel from bottom to top and allows the acoustical phase response to be continuously controlled. (d) The cylindrical geometric details of the helical channel and matched screw.

Figure 2

Theoretical, numerical and experimental phase shift response to the frequency domain and the helical depth for the tunable cylindrical unit. (a) The schematic of the (i) analytical structure, (ii) simulated model and (iii) measured acoustic impedance tube. (b) The corresponding phase shift of the tunable unit. [(c) and (d)] The cut lines of (b) at the frequencies of 2.2 and 6.1 kHz showing the variation of the phase degree with the helical depth.

Figure 3

Full-wave simulated scattering acoustic pressure fields for carpet cloaking. The reflected fields in the $xz$ plane in three cases: (i) on a flat ground, (ii) on an uncloaked object (arc-shaped bump) and (iii) on the object with the cloak exposed to the normally incident plane wave at frequency of 2.2 (a) or 6.1 kHz (b). The white dashed boxes indicate the regions within which the measurement will be performed in the next experimental section.

Figure 4

The simulated scattering pressure fields for oblique incidence. The reflected fields in the $xz$ plane in three cases: (i) on a flat ground, (ii) on an uncloaked object (arc-shaped bump) and (iii) on the object with the cloak exposed to the 30° (top), 45° (middle), and 60° (bottom) impinging acoustic waves at the target frequency of 2.2 (a) or 6.1 kHz (b). The black dashed lines and arrows set in (b)(iii) indicate the incident plane wavefronts and directions and also apply in (a)(iii). For all cases in (a)(iii) and (b)(iii), the angle of reflection from the object with the cloak is designed to be equal to the incident angle like a specular reflection.

Figure 5

Full-wave simulated scattering acoustic pressure fields for ground illusion. The reflected fields of (i) a curved arbitrary ground and (ii) the ground illusion with the cloak exposed to the normally incident plane waves at the frequencies of 2.2 [(a) and (b)] and 6.1 kHz [(c) and (d)]. The illusion ground is a convex shape in (a) and (c), as well as a concave shape in (b) and (d). The black dashed lines indicate the positions where the measurement will be performed in the next experimental section.

Figure 6

The details of the experimental setup. (a) Schematic diagram of the measurement. Photographs of the fabricated helical channel and matched screw (b), the cylindrical unit sample (c), the manufactured components of the 31 units and the surface arc-shaped frame (d), the assembled metasurface (e), the steel sheet to imitate a flat ground (f), the loudspeaker array (g), and the experimental waveguide system (h).

Figure 7

Experimental measurements of the real part of the reflected acoustic field in the white dashed box regions shown in Fig. 3. The reflected sound fields of (i) the flat ground, (ii) the uncloaked object, and (iii) the object with cloak exposed to the normally impinging waves at the frequencies of 2.2 (a) and 6.1 kHz (b).

Figure 8

The transverse reflected amplitude at a far-field observation with a distance of 0.8 m to the flat ground by cutting black dashed lines shown in Fig. 5. The reflected pressure amplitude of the arbitrarily curved ground exposed to the normally incident plane waves at the frequencies of 2.2 [(a) and (b)] and 6.1 kHz [(c) and (d)]. The illusion performances are shown in (a) and (c) with the convex ground, as well as in (b) and (d) with the concave ground.

Figure 9

The discrete and fitted results of the equivalent parameter associated with the incident frequency. (a) The mean deviation of the phase shifts varying with the equivalent parameter at different frequencies: 2, 4, 6, and 8 kHz; (b) the numerical fitting for the equivalent parameter varying with the changing frequencies.

Figure 10

Full-wave simulated scattering acoustic pressure fields for carpet cloaking at higher frequencies. The reflected fields in the $xz$ plane for the curved metasurface cloak exposed to the normally incident plane wave at the frequencies of 6.5 (a), 7.0 (b), 7.5 (c), 8.0 (d), 9.0 (e), and 10 kHz (f). The transverse reflected wavefront phase at a far-field observation with a distance of 0.8 m from the ground by cutting black dashed lines shown in (a)−(f).

Figure 11

Thermoviscous loss effects. The phase shift and reflected amplitude of the tunable unit with and without loss at the frequencies of 2.2 (a) and 6.1 kHz (b). The solid and dashed lines represent the results for the loss-free and thermoviscous cases, respectively. (c) Acoustic pressure field distributions of the ground illusion at the frequency of 6.1 kHz for (i) loss-free case and (ii) thermoviscous case. (d) The reflected pressure amplitudes along the dashed lines in (c) with the observation transverse line locating at $z=0.8\mathrm{m}$.

Figure 12

Full-wave simulated scattering acoustic pressure fields for the 3D carpet cloak. (a) Schematic view of a 3D metasurface cloak and its cross section with distributed unit lattice. [(b) and (c)] The reflected fields in the $xz$ and $yz$ planes in three cases: (i) on a flat ground, (ii) on an uncloaked object (spherical-shaped bump), and (iii) on the object with the cloak exposed to the normally incident plane waves at frequencies of 2.2 (b) and 6.1 kHz (c).

Figure 13

A schematic representation of self-feedback real-time tunable mechanisms for the programmable acoustic metasurface. The illustration at the bottom right shows the structure connective components of the tunable broadband mechanical control system.