Multifunctional Waterborne Acoustic Metagratings: From Extraordinary Transmission to Total and Abnormal Reflection

Wavelength-thick multifunctional metagratings for waterborne sound are highly desirable in various application scenarios, such as human health monitoring and ocean exploration. In this article, we present a class of metagratings with which distinct and switchable wave manipulation functionalities, such as extraordinary transmission, total reflection, and abnormal reflection can be achieved through a single acoustic grating. Simultaneous and high-efficiency control over both reflected and transmitted waves is achieved through a systematic design approach in which wave diffraction theory, effective medium theory, and intelligent optimization algorithms are concurrently utilized. Switching between different functionalities can be achieved simply by changing the operation frequency, or by changing the incident angles. Robust and perfect wave-front manipulation effects are obtained over a wide range of incident angles and operation frequencies. Our work not only provides a design paradigm of planar acoustic devices for multiple manipulation purposes, but also presents a feasible solution for the development of integrated acoustic devices for distinct underwater applications.

Figure 1

A schematic drawing of a multifunctional acoustic metagrating in which different functionalities, such as ET, TR, and AR, can be simultaneously achieved with the same grating at different incident angles. (a) The metagrating is composed of two different acoustic media sandwiching a 1D grating. The sound velocities in the upper and lower media are $v_0$ and $v_1$, respectively, with $v_1>v_0$, and d is the period of the 1D grating, with W and H representing the width and height of each cylinder. (b) Diffraction orders for a metagrating with $v_1=1.33v_0$ and $d=1\mathrm{m}$ at various incident angles ${\theta }_{\mathrm{in}}$ and frequencies. Solid vertical lines mark the critical angle $|{\theta }_{\mathrm{TR}}|={48.75}^{\circ }$ for TR, where $T_0=0$ as long as $|{\theta }_{\mathrm{in}}|>|{\theta }_{\mathrm{TR}}|$. The dashed and dotted curves mark the emerging conditions of $R_{\pm 1}$ and $T_{\pm 1}$ diffraction orders, respectively. Different colors are used to show that different diffraction orders are available in corresponding regions. (c) An enlarged view of (b) for the frequency range $750\mathrm{Hz}\le f_0\le 850\mathrm{Hz}$ and incident angle range ${\theta }_{\mathrm{in}}>0^{\circ }$, where multiple functionalities are numerically demonstrated.

Figure 2

A realistic design of the multifunctional metagrating. (a) The metagrating consists of a 1D grating sandwiched by two media, with the upper medium being water, and the lower medium being an acoustic crystal composed of a square array of silicon cylinders immersed in water with a filling ratio $f=0.7$, corresponding to an effective sound velocity $v_{\mathrm{eff}}=v_1=1.33v_0$. The grating is a 1D array of aluminum cylinders with width W = 54.25 cm and height H = 40 cm. (b) The diffraction efficiency spectra for $R_0$, $R_{-1}$, and $T_0$, as functions of ${\theta }_{\mathrm{in}}$ at the working frequency of 800 Hz. (c)–(f) show the total pressure fields when a plane wave is incident from above on the grating with different incident angles: (c) ${\theta }_{\mathrm{in}}=0^{\circ }$, (d) ${\theta }_{\mathrm{in}}={30}^{\circ }$, (e) ${\theta }_{\mathrm{in}}={55}^{\circ }$, and (f) ${\theta }_{\mathrm{in}}={68.63}^{\circ }$, respectively. White arrows indicate the propagation directions of the incident and diffracted waves.

Figure 3

Comparison of the wave manipulation effects between the optimized and unoptimized metagratings. (a) corresponds to the optimized aluminum cylinders presented in Fig. 2, where perfect ET and AR functionalities are achieved at ${\theta }_{\mathrm{in}}={20}^{\circ }$ and ${70}^{\circ }$, respectively. In (b), the geometrical parameters of aluminum cylinders are changed to W = 90 cm and H = 40 cm. In (c) and (d), the aluminum cylinders are replaced by rubber and epoxy cylinders, respectively. In all panels, the total acoustic pressure field and the first Cauchy stress invariant are plotted in the water background and solid cylinders, respectively. White arrows indicate the propagation directions of the incident and diffracted waves.

Figure 4

Diffraction efficiencies of $T_0$, $R_0$, and $R_{-1}$ at different operation frequencies and incident angles. (a)–(c) are 3D graphs of $T_0$, $R_0$ and $R_{-1}$, respectively. The light blue (d), light red (e), and light green (f) cross sections show the diffraction efficiency spectra of $R_0$, $R_{-1}$, and $T_0$ at different incident angles: (d) ${\theta }_{\mathrm{in}}={30}^{\circ }$, (e) ${\theta }_{\mathrm{in}}={55}^{\circ }$, (f) ${\theta }_{\mathrm{in}}={70}^{\circ }$. Yellow stars mark the position of working frequency. (g)–(i) are the 2D versions or top-views of (a)–(c), respectively, with three dotted lines denoting three different values of ${\theta }_{\mathrm{in}}$. Please note the high consistency between (g)–(i) and Fig. 1.

Figure 5

Diffraction behaviors when a plane wave impinges on the metagrating from below. (a) Diffraction efficiency spectra as functions of ${\theta }_{\mathrm{in}}$ at the working frequency. (b)–(e) show the total pressure fields when a plane wave is incident with (b) ${\theta }_{\mathrm{in}}=0^{\circ }$, (c) ${\theta }_{\mathrm{in}}={30}^{\circ }$, (d) ${\theta }_{\mathrm{in}}={55}^{\circ }$, and (e) ${\theta }_{\mathrm{in}}={68.63}^{\circ }$.

Figure 6

Another multifunctional metagrating. (a) The upper medium is an acoustic crystal composed of a square array of rubber cylinders immersed in water with a filling ratio $f=0.35$, corresponding to an effective sound velocity $v_{\mathrm{eff}}=745\mathrm{m/s}=v_0/2$. The lower medium is water. The sandwiched grating is a 1D array of rubber cylinders with width W = 28 cm and height H = 39.07 cm. (b) Diffraction efficiency spectra as functions of ${\theta }_{\mathrm{in}}$ at the working frequency of 900 Hz. (c)–(e) represent the total pressure fields when a Gaussian beam is incident with different angles: (c) ${\theta }_{\mathrm{in}}={15}^{\circ }$, (d) ${\theta }_{\mathrm{in}}={35}^{\circ }$, (e) ${\theta }_{\mathrm{in}}={55.87}^{\circ }$.

Figure 7

Multifunctional metagratings composed of a 1D array of iron (a1)–(a5) and silicon (b1)–(b5) cylinders, respectively. (a1) and (a2) show the unit cell structure and corresponding diffraction efficiency spectra of the metagrating, respectively. (a3)–(a5) show the total pressure fields when a plane wave is incident from above with different incident angles: (a3) ${\theta }_{\mathrm{in}}={20}^{\circ }$, (a4) ${\theta }_{\mathrm{in}}={55}^{\circ }$, and (a5) ${\theta }_{\mathrm{in}}={70}^{\circ }$. (b1)–(b5) are the same as (a1)–(a5), except that iron cylinders are replaced by silicon ones.

Figure 8

Multifunctional metagratings consisting of circular, elliptical, and triangular aluminum cylinders. (a1) and (a2) show the unit cell structure and corresponding diffraction efficiency spectra of the metagrating, respectively. (a3)–(a5) show the total pressure fields when a plane wave is incident from above with different incident angles: (a3) ${\theta }_{\mathrm{in}}={20}^{\circ }$, (a4) ${\theta }_{\mathrm{in}}={55}^{\circ }$, and (a5) ${\theta }_{\mathrm{in}}={70}^{\circ }$. (b1)–(b5) and (c1)–(c5) are the same as (a1)–(a5), except that circular cylinders are replaced by elliptical and triangular ones, respectively.

Figure 9

Acoustic impedance matching through parameter optimization.

Figure 10

(a) The frequency-filtering functionality of the metagrating, where incident waves with different frequencies ($f_1$, $f_2$, and $f_3$) exhibit different behaviors at distinct incident angles (${\theta }_1$, ${\theta }_2$, and ${\theta }_3$). (b) An additional functionality, i.e., AT can be realized if we go to a higher working frequency (e.g., 850–990 Hz in Fig. 1 of the main text) of the metagrating, which offers more flexibility for the control of transmitted wave fronts. Here SR means specular reflection.