Acoustic metasurface by layered concentric structures

Metasurface-based acoustic wave-front manipulation with broad bandwidth and low transmission loss shows great significance in high-intensity applications such as ultrasonic therapy, acoustic tweezers, and haptics. By taking advantage of the helical-structured metamaterials and their concentrically layered arrangement, we present a systematic strategy to construct two-dimensional transmissive acoustic metasurfaces that possess matched impedance to the background medium and simple governing parameters. As a proof of concept, a concentrically layered circular metalens supporting conversion from spherical wave to plane wave is designed and experimentally demonstrated. It is capable of operating in more than one octave band with high transmission. This work could inspire more intriguing and flexible designs in three-dimensional wave control, which may enhance the practicality of acoustic metasurfaces.

Figure 1

Cylindrical layered metasurface. The metasurface is constructed by a series of concentric circular layers with a uniform thickness $a$ and different effective indices.

Figure 2

Unit cell with uniform helix angle. (a) Construction of a cylindrical layered unit cell. The yellow arrow indicates the traveling path of sound wave. The height $h$ is 50 mm. The thickness of the blade is 0.8 mm. The inner and outer radius $r_{i-1}$ and $r_i$, are 20 and 30 mm, respectively. (b) Schematic illustration of the formation of the blades by winding straight lines around a cylinder. $\theta$ is the complement angle of the helix. (c) Retrieved effective parameters and (d) transmission properties of a typical unit cell. The scatters and lines are simulation and theoretical results, respectively. The unit cell's governing parameter $l=83\mathrm{mm}$.

Figure 3

Impedance-matched unit cell. (a) Schematic illustration of the formation of the blades by winding cubic Hermite splines around a cylinder. (b) Schematic illustration of wave propagation in the unit cell. $h$, $r_{i-1}$, and $r_i$ are same as that of the unit cell in Fig. 2. (c) Distribution of the effective impedance ratio along the $z$ axis. From . i to v, relating parameters $l$ of the unit cell are 40, 50, 60, 80, and 100 mm, respectively. (d) Refractive index as a function a $l$. The solid line is obtained from Eq. (8). The scatters denote the retrieved effective index of the unit cells in (c).

Figure 4

Broadband performance of the gradient unit cells. (a) Transmission coefficients of the truncated unit cells. The values of $h_i$ to $h_{iv}$ are 50, 34, 26, and 18 mm, respectively. Structures ii to iv are obtained by cutting down the same length at both ends of the original unit cell. (b) Broadband phase delays for different unit cells. From i to iv, governing parameters $l$ are 40, 60, 80, and 100 mm, respectively. (c),(d) Comparison of the overall transmission coefficients of the uniform and gradient unit cells. The governing parameter $l=80\mathrm{mm}$ in (c) and $l=100\mathrm{mm}$ in (d), respectively. (c) and (d) share the same legend.

Figure 5

Fabricated broadband wave-front converter sample. (a) Photograph of the sample. It has 19 layers, and the thickness of each layer is 10 mm. (b) Designed index profile for the spherical to plane wave transformation. The yellow box shows the cross-sectional surface of the sample along its diameter. The red line with legend theory represents the required distribution of index obtained from Eq. (13). The black dots represent the discrete indices for each layer.

Figure 6

Measurement of the lens. (a) illustrates the experiment setup and measured region. The metasurface-based wave-front convertor is a plate with a diameter of 380 mm and thickness of 50 mm. The loudspeaker is located at the center of the lens 200 mm to its back surface along the $x$ axis. The tested region (yellow) are $140\times 400\mathrm{m}{\mathrm{m}}^2$ and $290\times 400\mathrm{m}{\mathrm{m}}^2$. The nearest distance between the microphone and the surface of the lens is 10 mm. The data of surface $A^{\prime }$ is obtained in the absence of the metasurface. (b)–(d) illustrate the normalized pressure field at three frequencies, respectively. All three subfigures share the same normalization range. (e) Energy transmission coefficient of the lens.

Figure 7

Measured sound pressure fields of the wave-front converter at other frequencies. (a)–(f) Experimental results at some representative frequencies from 3500 to 6500 Hz. The normalization of the data is based on same scale.

Figure 8

Retrieved effective refractive index of the uniform spiraling units. (a) The real part of the effective indices. The solid lines represent the lossless cases, and the dotted markers denote the results with the inherent thermal and viscous losses being taken into account. (b) The imaginary part of the effective indices. The magenta solid line indicates the superposition of four colored lines corresponding to the lossless cases.

Figure 9

Energy transmission coefficients of lossy gradient spiraling unit cells with different $l$. (a) $l=40\mathrm{mm}$, (b) $l=60\mathrm{mm}$, (c) $l=80\mathrm{mm}$, and (d) $l=100\mathrm{mm}$.

Figure 10

The boundary layers of a gradient spiraling unit cell. (a) Schematic diagram of the cross-section area used in the simulations. The gradient tube is one channel of the impedance-matched unit cell shown in Fig. 3. The red rectangle is the intersection between r-z plane and the gradient tube on its middle position. The dotted straight line is positioned at the center of the rectangle. (b) Local velocity maps of the cross-sectional rectangle in (a) at distinct frequencies. The results are normalized separately at each frequency. The horizontal and vertical coordinates are in the global coordinate system. (c) Distributions of local velocity along the white dotted line shown in (a).