Multifunctional acoustic metasurface based on an array of Helmholtz resonators

We demonstrate multifunctional acoustic metasurfaces that can simultaneously realize the same functionality or multiple different functionalities at multiple tunable frequencies. The fundamental physical mechanism is based on designing a supercell of Helmholtz resonators with multiple resonances operating at different frequencies. We theoretically, numerically, and experimentally demonstrate the achievement of multiple functionalities by the proposed designed metastructure, which produces extraordinary reflection at different angles and different acoustic focusing localizations under the same normal incidence. Our finding paves the way towards multifunctional compact acoustic devices and can lead to pragmatic contemporary applications such as multiple beam shaping, or functional devices with special dispersion properties.

Figure 1

(a) 2D schematic diagram of the supercell of a multifunctional acoustic metasurface. A supercell consists of three cavities with different depths. (b) The effective circuit model of the proposed supercell of the metasurface.

Figure 2

(a–c) The simulated (sim.) and analytical [ana., calculated by Eq. (5)] phase response diagrams for $f_1=1340\mathrm{Hz}$, $f_2=2040\mathrm{Hz}$, and $f_3=3000\mathrm{Hz}$, respectively. (d) The simulated (sim.) and analytical [ana., calculated by Eq. (6)] relationship between the height of the cavity and the targeted frequencies with $w_n=2\mathrm{mm}$. The targeted frequencies can be chosen within about 900—3000 Hz. The insets show the acoustic pressure amplitude distribution of the eigenmodes at the three targeted frequencies, indicating that each resonance is coupled with only one cavity, respectively. (e) The reflectance of the supercell with different $w_n$ values for different frequencies. The loss is induced by the thermal-viscous effect in the cavities.

Figure 3

(a) The phase responses for achromatic $-{45}^{\circ }$ extraordinary reflection at the three frequencies. Linear phase distributions ${\varphi }_n=\sqrt{2}{k}_{n}x/2$ are applied on the interface. (b) The simulated results for achromatic $-{45}^{\circ }$ extraordinary reflection at the three frequencies. (c,d) The corresponding results for achromatic acoustic focusing at (0 m, 0.6 m). Hyperboloidal phase responses ${\varphi }_n=k_n\left(\sqrt{x^2+0.36}-0.6\right)$ are applied on the interface. The arrows indicate the incidence/reflection directions and the focusing positions.

Figure 4

(a) The different phase responses of MAM at the three frequencies: ${\varphi }_1=\sqrt{2}{k}_{1}x/2$, ${\varphi }_2=k_2\left(\sqrt{x^2+1}-1\right)$, and ${\varphi }_3=-\sqrt{2}{k}_{3}x/2$. (b) The simulated results of MAM at the three frequencies, for $-{45}^{\circ }$ extraordinary reflection, acoustic focusing at coordinates $\left(0\mathrm{m},1\mathrm{m}\right)$ and ${45}^{\circ }$ extraordinary reflection. (c) The different phase responses of another MAM at the three frequencies: ${\varphi }_1=k_1\left[\sqrt{{\left(x+0.33\right)}^2+0.36}-0.686\right]$, ${\varphi }_2=k_2\left[\sqrt{x^2+0.36}-0.36\right]$, and ${\varphi }_3=k_3[\sqrt{{\left(x-0.33\right)}^2+0.36}-0.686]$. (d) Acoustic focusing with different focal positions [$\left(-0.33\mathrm{m},0.6\mathrm{m}\right)$, $\left(0\mathrm{m},0.6\mathrm{m}\right)$, and $\left(0.33\mathrm{m},0.6\mathrm{m}\right)$] at the three frequencies. The arrows indicate the incidence/reflection directions and the focusing positions.

Figure 5

(a) The sample of the MAM for acoustic focusing with different focal positions [$\left(1.67\mathrm{m},0.6\mathrm{m}\right)$, $\left(2\mathrm{m},0.6\mathrm{m}\right)$, and $\left(2.33\mathrm{m},0.6\mathrm{m}\right)$] at 1340, 2040, 3000 Hz, respectively. (b) The simulated and experimental acoustic pressure distributions of the acoustic focusing at the three frequencies. The measured results of the acoustic pressure fields at the given region marked in the figure are shown in the inset. (c) The simulated and the measured results of the acoustic pressure amplitude distributions at the line of $y=0.6\mathrm{m}$.