Programming Reflected and Transmitted Sound Behaviors Based on Motor-Driven Digital Metasurface
基于电机驱动的数字元面编程反射和传播声音行为
Abstract 摘要
Acoustic metasurfaces have shown indispensable abilities for wave control with subwavelength resolution and enabled exotic sound functions unavailable using naturally occurring materials. To further improve the utilization of sound field resources and enhance the coverage of acoustic signals, full-space acoustic metasurfaces hold great potential for independent tailoring of reflected and transmitted waves. However, achieving dynamic manipulation of the full sound field in a programmable fashion has remained inaccessible until now. Here, a computer-controlled motor-driven acoustic metasurface is proposed and designed to program the reflected and transmitted sound behaviors without crosstalk. The metasurface elements consist of a stationary cuboid and a rotatable lid connecting with an individually programmable micromotor. Eight distinct resonant substructures with specific wave responses are integrated inherently in the cuboid, and the lid can be rotated automatically to select one of them at a time, and therefore, the proposed metasurface enables 2-bit phase adjustment. For ever-changing coding instructions, the metasurface can choose to modulate reflected or transmitted waves in real time. To show the capabilities of the presented programmable acoustic metasurface, two typical functions are demonstrated: dynamic acoustic focusing and variable acoustic holograms in both reflection and transmission modes.
声学元表面已显示出不可或缺的亚波长分辨率波控制能力，并实现了天然材料无法实现的奇特声音功能。为了进一步提高声场资源的利用率，增强声学信号的覆盖范围，全空间声学元表面在独立定制反射波和透射波方面具有巨大潜力。然而，以可编程的方式实现对全声场的动态操控，迄今为止仍无法实现。在此，我们提出并设计了一种计算机控制的电机驱动声学元表面，可对反射声和透射声的行为进行编程，而不会产生串扰。元表面元件由一个固定的立方体和一个可旋转的盖子组成，盖子与一个可单独编程的微电机相连。立方体中固有八个具有特定波响应的共振子结构，盖子可自动旋转，每次选择其中一个，因此，所提议的元表面可实现 2 位相位调整。对于不断变化的编码指令，元面可以选择实时调制反射波或传输波。为了展示所提出的可编程声学元表面的能力，我们演示了两种典型功能：动态声学聚焦和反射与透射模式下的可变声学全息图。
1 Introduction 1 引言
Acoustic waves are the forms of matter motion and energy transfer in nature. Achieving precise and flexible sound manipulation has been a long-standing fundamental problem in wave physics. Acoustic metamaterials,[1] consisting of subwavelength artificial meta-atom arrays, are capable of realizing extraordinary and unusual sound properties unattainable in naturally occurring materials, such as negative mass density and negative bulk modulus,[2-5] which, in turn, show unprecedented potential for wave control. In contrast to bulky metamaterials, acoustic metasurfaces,[6] as a class of planar platforms, have aroused considerable attention due to their low profile and high integration. By locally controlling phase shifts between adjacent meta-atoms, metasurfaces can steer waves toward desired propagation directions based on Fermat's principle, thus spawning a series of exotic wave phenomena, including anomalous deflection,[7] acoustic bending,[8] splitting,[9] and diffusion,[10] and opening up new opportunities for sound-matter interactions.
声波是自然界中物质运动和能量传递的形式。实现精确而灵活的声波操纵是波物理学中一个长期存在的基本问题。由亚波长人工超原子阵列组成的声学超材料，1 能够实现天然材料无法实现的非同寻常的声音特性、例如负质量密度和负体积模量，2-5 这反过来又显示出前所未有的波控制潜力。与体积庞大的超材料相比，声学超表面6 作为一类平面平台，因其低矮的外形和高集成度而备受关注。通过局部控制相邻元原子之间的相移，元表面可以根据费马原理将波导向所需的传播方向，从而产生一系列奇特的波现象，包括反常偏转、7 声弯曲、8 分裂、9 和扩散、10 并为声音与物质的相互作用提供了新的机会。
Traditional reflection-type and transmission-type acoustic metasurfaces mainly focus on sound manipulation in half space, and have been applied in architectural acoustics[11] and medical treatment.[12] To achieve high-capacity versatile information processing and expand the utilization of field resources, full-space metasurfaces, as an emerging class of platform with abundant physical properties and high integration, have been used for omnidirectional communications.[13] In acoustics, there are also some successful explorations in the manipulation of 2D and 3D full sound fields.[14, 15] However, passive acoustic metasurfaces with fixed geometries are unable to manipulate sound waves dynamically. To this end, many efforts have been devoted to developing active acoustic metasurfaces with variable sound properties under external stimuli ranging from mechanical actuations[16-22] to electronic factors.[11, 23-27] In this regard, a few tunable full-space metasurfaces with manually adjustable acoustic functionalities have also been investigated.[28, 29] To further achieve high-speed modulation, programming the reflected and transmitted sound waves via a single platform is highly desired, but there are still many challenges in its implementation.
传统的反射型和透射型声学元表面主要针对半空间的声音操纵，并已应用于建筑声学11 和医疗领域。12 为了实现大容量的多功能信息处理，扩大现场资源的利用率，全空间元表面作为一类具有丰富物理特性和高集成度的新兴平台，已被用于全向通信。13 在声学领域，对二维和三维全声场的处理也有一些成功的探索。14, 15 然而，具有固定几何形状的被动声学元表面无法动态操控声波。为此，许多人致力于开发在外部刺激（从机械驱动16-22 到电子因素）作用下具有可变声特性的有源声学元表面。11, 23-27 在这方面，还研究了一些具有手动调节声学功能的可调全空间元表面。28, 29 为了进一步实现高速调制，人们非常希望通过单一平台对反射声波和发射声波进行编程，但在实现过程中仍面临许多挑战。
In this work, we propose, design, and demonstrate a computer-controlled motor-driven programmable acoustic metasurface to modulate the reflected and transmitted sound behaviors dynamically and independently. First, we design and realize a programmable acoustic metasurface element that consists of a stationary cuboid and a rotatable lid. There are totally eight predesigned subresonators integrated in the cuboid, in which four selectable subresonators are used for the reflection mode to provide different reflection phases, and the remaining four subresonators are used for the transmission mode to produce essential transmission phases. The lid is rotated to select one of eight subresonators at a time. Therefore, the reflected or transmitted waves can be manipulated dynamically by rotating the lids that are driven by a micromotor array. All the micromotors are inserted into the elements, and each meta-element can be programmed individually by a single micromotor, as shown in Figure 1. To show the performances of the metasurface, we demonstrate numerically and experimentally two typical functions: dynamic acoustic focusing and acoustic holography. For the focusing function, focus numbers, intensities, and positions can be adjusted accurately in real time in both reflection and transmission modes. For the holographic function, multiple complex sound images are displayed alternatively in both reflection and transmission modes. These novel functionalities are expected to accelerate the development of acoustic imaging technology in the fields of medical diagnosis and nondestructive detection.
在这项工作中，我们提出、设计并演示了一种由计算机控制的电机驱动的可编程声学元面，可动态、独立地调节反射声和透射声的行为。首先，我们设计并实现了一个可编程声学元面元件，它由一个固定的立方体和一个可旋转的盖子组成。立方体中集成了八个预先设计的子谐振器，其中四个可选子谐振器用于反射模式，提供不同的反射相位，其余四个子谐振器用于传输模式，产生基本的传输相位。旋转盖子可以一次选择八个子谐振器中的一个。因此，通过旋转由微电机阵列驱动的盖子，可以动态地操纵反射波或透射波。如图1所示，所有微电机都插入元件中，每个元元件都可由单个微电机单独编程。为了展示元表面的性能，我们通过数值和实验演示了两种典型功能：动态声聚焦和声全息。就聚焦功能而言，在反射和透射模式下，聚焦数、强度和位置都可以实时精确调整。至于全息功能，则可在反射和透射模式下交替显示多个复杂的声音图像。这些新功能有望加速声成像技术在医疗诊断和无损检测领域的发展。
所提出的计算控制电机驱动声学元表面用于对反射声和透射声行为进行编程。编码指令从指令发射器发送到微电机阵列驱动器，最后再发送到不同的微电机。每个元件都可以独立编程。由于编码序列是动态变化的，因此可以在反射和透射模式下实现不同的功能，如动态声聚焦和全息。
2 Results 2 项成果
2.1 Design and Analysis of the Acoustic Metasurface Element
2.1 声学元表面元件的设计与分析
To modulate the reflection and transmission phases independently, we propose and design an acoustic metasurface element that is composed of a cuboid and a rotatable lid. The cuboid consists of eight individual fan-shaped cavities, each of which contains a resonant sub-unit for providing specific reflection or transmission responses, and the rotatable lid is connected with a shaft driven by a micro-stepper motor. These eight cavities can be divided into two groups, one of which includes four cavities working in the reflection mode, and the remaining four cavities working in the transmission mode. In the design, all the indispensable geometric substructures for controlling the reflected and transmitted waves are processed in advance, and therefore, the phase delay and operation mode can be tuned freely by rotating the top lid under the control of micro-stepper motor, which has the advantages of high accuracy and low crosstalk. The fan-shaped hole in the rotatable lid is used to choose the operation mode and change phase delay. As the lid rotates, the corresponding cavity matching well with the fan-shaped hole can provide predefined reflection or transmission responses, while the remaining seven cavities will not interact with the incident waves.
为了独立调节反射和透射相位，我们提出并设计了一种由一个立方体和一个可旋转盖子组成的声学元表面元件。长方体由八个独立的扇形空腔组成，每个空腔都包含一个谐振子单元，用于提供特定的反射或透射响应。这八个腔体可分为两组，其中一组包括四个工作在反射模式的腔体，其余四个工作在传输模式的腔体。在设计中，所有用于控制反射波和透射波的不可或缺的几何子结构都已预先处理好，因此，在微型步进电机的控制下，通过旋转顶盖可以自由调节相位延迟和工作模式，具有精度高、串扰小的优点。可旋转顶盖上的扇形孔用于选择工作模式和改变相位延迟。当顶盖旋转时，与扇形孔匹配良好的相应空腔可提供预定的反射或透射响应，而其余七个空腔则不会与入射波发生相互作用。
The baffle between adjacent cavities can be regarded as a sound rigid boundary and thus avoids undesired inter-channel crosstalk, thereby obtaining high reflection or transmission amplitude. In addition, there is a hole in the center of the cuboid, ensuring smooth and friction-free rotation of the shaft. Meanwhile, the wall between the central hole and the eight fan-shaped cavities eliminates unwanted scattered waves caused by the interaction between the incident waves and the micro-stepper motor, further improving the efficiency of metasurface elements working in both reflection and transmission modes. Also, the bottom of each element contains a rectangular hole for wiring, which can eliminate the interference of wires on the transmitted waves. The metasurface element is illustrated in an enlarged view of Figure 2a.
相邻腔体之间的挡板可被视为声刚性边界，从而避免了不希望出现的通道间串扰，从而获得较高的反射或传输振幅。此外，长方体的中心有一个孔，可确保轴平稳无摩擦地旋转。同时，中心孔和八个扇形空腔之间的壁消除了入射波与微型步进电机之间的相互作用所产生的不必要的散射波，进一步提高了元表面元件在反射和透射模式下的工作效率。此外，每个元件的底部都有一个用于布线的矩形孔，可以消除导线对透射波的干扰。图2a 的放大图展示了元表面元件。
a) 元件的剖面图和立方体的俯视图。 b) 制作的元面的正视图和背视图。 c,d) 模拟反射相位 (c) 和振幅 (d) 与 d 的函数关系。f,g) 当 w2= 10 mm、和 w2 当 w1= 5.6 毫米。h) 当 w1= 5.6 mm 和 w2= 12.2 mm。i,j) 在反射模式 (i) 和透射模式 (j) 下不同编码状态下元件的模拟相位和振幅。
Next, we investigate the reflection and transmission properties of the designed metasurface element at the working frequency of 4000 Hz using a numerical simulation method. For resonant metasurface elements, the majority of incident wave energy can be effectively coupled into a resonant cavity near the resonant frequency. By fine-tuning the geometric dimensions of the resonant substructure, the resonant frequency can be designed, enabling precise phase control. For the reflection mode, the bottoms of the cavities are sealed, and the sound speed can be modulated by changing the depth d for reflection phase control. The simulated curves of reflection phase and amplitude as a function of d are illustrated in Figure 2c,d. When d is tuned from 12 to 25 mm, we observe that the phase shifts can cover nearly the 2π range and the reflection amplitudes are almost 1. Figure 2e shows the simulated model and the scattered sound pressure field when d = 17 mm. We can see clearly that the incident waves can enter the cavity matching well with the fan-shaped hole and eventually are reflected due to impedance mismatch. Therefore, this ingenious design method can avoid undesired inter-channel interference and program the reflected and transmitted sound waves without crosstalk. The geometric parameters are optimized as, the side length and height of the element are a = 36 mm and h = 30 mm, respectively, the thickness and radius of the rotatable lid are t = 2 mm and r1 = 17.5 mm, respectively, and the radii of the fan-shaped holes are r2 = 11.5 mm.
接下来，我们使用数值模拟方法研究了所设计的元表面元件在 4000 Hz 工作频率下的反射和透射特性。对于谐振元表面元件，大部分入射波能都能在谐振频率附近有效地耦合到谐振腔中。通过微调谐振子结构的几何尺寸，可以设计谐振频率，从而实现精确的相位控制。对于反射模式，腔体底部是密封的，通过改变深度d来调制声速，从而实现反射相位控制。反射相位和振幅随 d 变化的模拟曲线如图 2c,d 所示。当d从 12 mm 调整到 25 mm 时，我们观察到相移几乎可以覆盖 2π 的范围，反射幅度几乎为 1。图 2e 显示了 d = 17 mm 时的模拟模型和散射声压场。我们可以清楚地看到，入射波可以进入与扇形孔匹配良好的空腔，最终由于阻抗失配而被反射。因此，这种巧妙的设计方法可以避免不必要的信道间干扰，并对反射声波和发射声波进行无串音编程。几何参数优化为：元件的边长和高度分别为 a = 36 mm 和 h = 30 mm、旋转盖的厚度和半径分别为 t = 2 毫米和 r1 = 17。5 毫米，扇形孔的半径分别为 r2 = 11.5 毫米。
For the transmission mode, two cascaded Helmholtz resonators in each cavity are used to change the transmission phase. As sketched in Figure 2f,g, the transmission phase shifts can exceed 3π/2 by choosing different combinations of w1 and w2. Figure 2h shows the simulated model and the total acoustic pressure field when w1 = 5.6 mm and w2 = 12.2 mm, where most of the incident energy can be transmitted through the selected cavity. It is observed that the reflection and transmission properties of the element are related to the size of the substructure in the fan-shaped cavity.
对于传输模式，每个腔体中的两个级联亥姆霍兹谐振器用于改变传输相位。如图 2f,g 所示，通过选择 w1 和 w2 的不同组合，传输相移可超过 3π/2。图2h显示了 w1 = 5.6 mm 和 w2 = 12.2 mm 时的模拟模型和总声压场，其中大部分入射能量可通过选定的空腔传输。据观察，元件的反射和透射特性与扇形空腔中子结构的大小有关。
We also investigate the impact of visco-thermal acoustic losses on the reflection and transmission properties, as drawn with open circles in Figure 2c,d,f,g. The phase responses are almost identical with and without losses. The reflection amplitudes with losses are greater than 0.87, and the transmission amplitudes with losses decrease slightly at resonance compared with their counterparts without losses. The reason is that the smallest slit in the cavity is nearly 5.1 mm, which is ≈160 times as thick as the boundary layer. Therefore, the thermoviscous effects are negligible.
我们还研究了粘热声波损耗对反射和透射特性的影响，如图2c,d,f,g中的圆圈所示。有损耗和无损耗时的相位响应几乎相同。有损耗时的反射幅度大于 0.87，有损耗时的传输幅度在共振时比无损耗时略有下降。原因是空腔中最小的狭缝接近 5.1 毫米，是边界层厚度的 ≈ 160 倍。因此，热粘效应可以忽略不计。
For the reflection and transmission modes, the element can achieve discrete phase shifts covering the full 3π/2 span, and thus we choose 2-bit encoding to represent the metasurface element,[30] namely “00”, “01”, “10”, and “11”. For the reflection mode, four coding states correspond to the elements with geometric parameters d being equal to 23.3, 18.1, 17.6, and 17 mm, respectively; for the transmission mode, four coding states correspond to the elements with geometric parameters w1 and w2 being selected as 3.6 and 10.6, 3.5 and 10.1, 5.9 and 10.8, 5.6 mm and 12.2 mm. The discrete phases and amplitudes of different coding states for the reflection mode are illustrated in Figure 2i, and the results of the transmission mode are shown in Figure 2j. It is observed that the phase difference between adjacent coding states is ≈π/2 for each operation mode, and the reflection amplitudes reach almost 1 and the transmission ones are greater than or equal to 0.75. The influences of the actual motion and size of the motor on the reflection and transmission performances can be ignored, see more details in Note S1 (Supporting Information).
对于反射和透射模式，元件可以实现覆盖整个 3π/2 跨度的离散相移，因此我们选择 2 位编码来表示元表面元件，30 即 "00"、"01"、"10 "和 "11"。对于反射模式，四个编码状态分别对应于几何参数d等于 23.3、18.1、17.6和17毫米；对于传输模式，四个编码状态对应于几何参数w1 和w2 分别选为3.6 和 10.6、3.5 和 10.1、5.9 和 10.8、5.6 毫米和 12.2 毫米。图2i显示了反射模式不同编码状态的离散相位和振幅，图2j显示了传输模式的结果。可以看出，在每种工作模式下，相邻编码状态之间的相位差均为≈π/2，反射振幅几乎达到 1，透射振幅大于或等于 0.75。电机的实际运动和尺寸对反射和透射性能的影响可以忽略不计，更多详情请参见注S1（佐证资料）。
2.2 Programmable Manipulation of Reflected and Transmitted Sound Waves
2.2 可编程控制反射声波和透射声波
To verify the dynamic manipulation of the reflected and transmitted sound waves, we design and realize a programmable acoustic metasurface based on the above-mentioned elements. The whole metasurface consists of 100 elements that can be driven by 100 independent micromotors controlled by a computer. The manipulation of sound behavior and the operation mode can be changed by rotating the lid of each element. All lids are driven by a programmable micro-stepper motor array, in which each motor is connected to a motor driver, as shown in Figure 1. Hence, such a metasurface can be programmed flexibly, thus performing abundant functionalities according to the input coding instructions. We will demonstrate two typical acoustic functions based on the programmable metasurface, namely dynamic acoustic focusing and acoustic holography in both reflection and transmission modes.
为了验证对反射声波和透射声波的动态控制，我们在上述元件的基础上设计并实现了一个可编程的声学元表面。整个元表面由 100 个元件组成，可由计算机控制的 100 个独立微电机驱动。通过旋转每个元件的盖子，可以改变声音行为和操作模式。如图1所示，所有盖子都由可编程微型步进电机阵列驱动，其中每个电机都连接到一个电机驱动器。因此，这种元表面可以灵活编程，从而根据输入的编码指令实现丰富的功能。我们将展示两种基于可编程元表面的典型声学功能，即动态声聚焦和反射与透射模式下的声全息。
首先，我们展示了动态声聚焦功能，其中焦点的强度、数量和位置可根据需要进行更改。元表面所需的调制相位分布可表示为
其中，α 表示 j-th 焦点的振幅权重，λ 为波长，（xj、yj, zj) 是第 j 个焦点的坐标。对于每个焦点，元表面的离散相位轮廓可用编码序列表示。
For the reflection mode, we present two different kinds of focusing patterns: two focal points along y-axis and two focal points along x-axis. In the first case, we calculate the corresponding coding sequence, as illustrated in Figure 3b. When a plane wave impinges normally on the metasurface, the simulated result is shown in Figure 3c. We can observe that two predesigned focal points with different intensities along the y-axis appear in the focal plane at a distance of 107 mm from the front of the metasurface. In the second case, as the coding sequence changes, the original two focal points disappear completely, and two focal points along the x-axis are generated in the same focal plane. The coding pattern and the simulated results are illustrated in Figure 3d,e.
对于反射模式，我们提出了两种不同的聚焦模式：沿 y 轴的两个焦点和沿 x 轴的两个焦点。在第一种情况下，我们计算相应的编码序列，如 Figure3b 所示。当平面波正常撞击元表面时，模拟结果如图3c所示。我们可以观察到，在距离元表面前端 107 mm 的焦平面上出现了两个预先设计的、沿 y 轴具有不同强度的焦点。在第二种情况下，随着编码序列的变化，原来的两个焦点完全消失，而在同一焦平面上产生了沿 x 轴的两个焦点。编码模式和模拟结果如图3d,e所示。
a) 反射场中的测量装置照片。b,c) α12: α22 = 1: 0.在反射模式下，z = 107 毫米处为 75。d,e) α12 时两个焦点的编码模式 (d) 以及相应的模拟和测量声强分布 (e)：α22 = 1: 1，z = 107 mm 时的反射模式。g,h) 两个焦点的编码模式（g）以及相应的模拟和测量声强分布（h），α12: α22 = 1: 0.i,j) 编码模式 (i) 以及 z = -135 mm 处单个焦点的相应模拟和测量声强分布 (j)。 k-n) 沿 (c)、(e)、(h) 和 (j) 中虚线的模拟和测量焦点强度分布。
For the transmission mode, we present another set of focusing patterns. In the first case, we converge the incident waves at the predefined positions, resulting in two focal points with different intensities. The coding sequence is illustrated in Figure 3g, and the simulated result is shown in Figure 3h. We observe that two focal points with different intensities are generated at (120, 240, and −110 mm) and (240, 120, and −110 mm). In the second case, by switching the coding sequence, the wave is concentrated in a single focal point at (180, 180, and −125 mm), and the coding pattern and the simulated result are shown in Figure 3i,j.
对于透射模式，我们提出了另一套聚焦模式。在第一种情况下，我们将入射波汇聚到预定位置，形成两个强度不同的焦点。编码序列如图 3g 所示，模拟结果如图 3h 所示。我们观察到，在（120、240 和 -110 mm）和（240、120 和 -110 mm）处产生了两个强度不同的焦点。在第二种情况下，通过切换编码序列，波集中在（180、180 和 -125 mm）处的一个焦点上，编码模式和模拟结果如图 3i,j所示。
We fabricate the programmable acoustic metasurface consisting of 10 × 10 individually programmable elements, as shown in Figure 2b. A two-phase four-wire micro-stepper motor is inserted into the element, which is connected to a motor driver (TMC2009) by XH2.54 terminal wires. There are totally four single-chip microcomputers (STC15W4K56S4) used to control the micromotor array, and each single-chip microcomputer is mounted on a control circuit board and used to drive twenty-five micromotors independently at the same time. The operation conditions of the motors allow one circle per 4 s. For a single operation mode, the maximum rotation angle is 3π/4 for switching the coding states, and the required responding time is 1.5 s. To further improve the control speed of the metasurface, it is a feasible method for each micromotor to rotate in both clockwise and anticlockwise directions.
我们制作的可编程声学元表面由 10 × 10 个单独的可编程元件组成，如图2b所示。元件中插入了一个两相四线微型步进电机，该电机通过 XH2.54 端子线与电机驱动器（TMC2009）相连。共有四台单片微型计算机（STC15W4K56S4）用于控制微电机阵列，每台单片微型计算机安装在一块控制电路板上，用于同时独立驱动 25 个微电机。电机的运行条件允许每 4 秒钟转一圈。在单一运行模式下，编码状态切换的最大旋转角度为 3π/4，所需的响应时间为 1.5 秒钟。为了进一步提高元表面的控制速度，让每个微电机同时沿顺时针和逆时针方向旋转是一种可行的方法。
We verify dynamic acoustic focusing in an acoustic anechoic environment, and the measured environments for reflection and transmission fields are illustrated in Figure 3a,f, respectively. For both reflection and transmission modes, the preset focal points can be observed clearly in the measured focal planes, which are consistent well with the corresponding simulated results, as shown in Figure 3c,e,h,j.
我们在消声环境中验证了动态声聚焦，反射场和透射场的测量环境分别如图 3a,f 所示。如图3c,e,h,j所示，对于反射和透射模式，在测量的焦平面上都能清晰地观察到预设的焦点，这与相应的模拟结果十分吻合。
To further investigate the focusing effects quantitatively, we calculate the focal intensity distributions along the dashed lines through the focal points shown in Figure 3c,e,h,j. For the two sets of experimental results in the reflection mode, the normalized measured intensity ratios of the two focal points are ≈1:0.75 and 1:1, respectively, which agree well with the simulated results, as shown in Figure 3k,l. For the transmission mode, in the first case, the normalized measured intensity ratio of the two focal points is 1:0.5, showing good agreement with the simulated one, as shown in Figure 3m. In the second case, there is only one focal point and the simulated and measured results are illustrated in Figure 3n, which indicates that most of the transmission energy is concentrated close to the center of the focal plane. It is noted that we observe some tiny discrepancies between the experiments and the simulations, which are mainly attributed to fabrication tolerance. The rotation errors of motors can be ignored, as analyzed in Note S2 (Supporting Information). Hence, such a programmable acoustic metasurface can not only adjust focus numbers, focus positions, and focus intensities but also choose to converge reflected or transmitted sound waves as required.
为了进一步定量研究聚焦效应，我们计算了沿虚线穿过图3c,e,h,j所示焦点的焦点强度分布。如图3k,l所示，在反射模式下的两组实验结果中，两个焦点的归一化测量强度比分别为≈1:0.75 和 1:1，与模拟结果十分吻合。对于透射模式，在第一种情况下，两个焦点的归一化测量强度比为 1:0.5，与模拟结果非常吻合，如图3m所示。在第二种情况下，只有一个焦点，模拟和测量结果如图3n所示，这表明大部分传输能量都集中在焦平面中心附近。值得注意的是，我们观察到实验和模拟之间存在一些微小的差异，这主要归因于制造公差。正如注S2（佐证资料）中分析的那样，电机的旋转误差可以忽略不计。因此，这种可编程的声学元表面不仅可以调整聚焦数、聚焦位置和聚焦强度，还可以根据需要选择汇聚反射或透射声波。
In the second example, we consider a more complex scene, dynamic acoustic holography. To improve the quality of sound images, an improved weighted Gerchberg-Saxton algorithm is introduced. In this case, we verify the holography functions based on the programmable acoustic metasurface. For the reflection mode, we select two different letters, namely “C” and “J”, and for the transmission mode, we select two different symbols, namely “?” and “!”. The target images and their corresponding optimized coding sequences are shown in Figure 4a,b,e,f. The letter “C” can be identified clearly in the simulated acoustic intensity distributions, where the imaging planes are 207, 217, and 227 mm away from the metasurface, as shown in Figure 4c. In contrast to conventional metasurfaces with continuous phase modulation, the elements in the design contain four coding states in both reflection and transmission modes. This metasurface with 2-bit phase modulation capability is naturally robust, and thus the target images can be distinctly displayed within a certain spatial range. Figure 4c also shows the measured acoustic intensity distribution at z = 217 mm, in which the letter “C” is legible. In addition, the simulated acoustic intensity distributions of the letter “J” at z = 147, 157, and 167 mm away from the sample and the corresponding experimental result at z = 157 mm are depicted in Figure 4d.
在第二个例子中，我们考虑了一个更为复杂的场景--动态声全息。为了提高声音图像的质量，我们引入了一种改进的加权 Gerchberg-Saxton 算法。在这种情况下，我们根据可编程声学元面来验证全息功能。对于反射模式，我们选择了两个不同的字母，即 "C "和 "J"；对于传输模式，我们选择了两个不同的符号，即"? "和"!"。目标图像及其相应的优化编码序列如 Figure4a,b,e,f 所示。如图4c所示，在成像平面距离元表面 207、217 和 227 毫米的模拟声强分布中，可以清楚地识别出字母 "C"。与采用连续相位调制的传统元表面相比，该设计中的元件在反射和透射模式下都包含四种编码状态。这种具有 2 位相位调制能力的元表面具有天然的鲁棒性，因此可以在一定的空间范围内清晰地显示目标图像。图4c还显示了z = 217 毫米处的测量声强分布，其中字母 "C "清晰可辨。此外，图 z = 147、157 和 167 mm 处字母 "J "的模拟声强分布以及 z = 157 mm 处的相应实验结果如图 4d 所示。
a,b) 反射模式下的目标图像以及字母 "C"（a）和 "J"（b）的相应编码模式。 c,d) 模拟和测量的字母 "C"（c）和 "J"（d）的声强分布。"g,h）符号"？"（g）和"！"（h）的模拟和测量声强分布。i-l）结果图像与字母 "C"（i）和 "J"（j）以及符号"？"（k）和"！"（l）的相应目标图像之间的相关性。
为了对全息图像进行定量评估，我们计算了两幅图像之间的相关系数，其表达式为
其中，Huv 和 Tuv 是全息图像和目标图像的数据矩阵、
In contrast to previously reported approaches for reconfigurable acoustic holograms using medium-sound-speed modulation[32] and microbubble arrays,[33] the current motor-driven programmable metasurface enables dynamic acoustic imaging in both reflection and transmission modes, which can be observed intuitively in Video S1 (Supporting Information). Other functionalities, such as dynamic acoustic vortex and beam scanning, have been realized using reflection-type programmable acoustic metasurface.[27] Furthermore, these functionalities can also be implemented in full space, see Note S4 (Supporting Information). Besides these exciting functionalities implemented using the full-space programmable acoustic metasurface, other potential applications, such as on-demand acoustic energy harvesting[34] and personalized indoor sound field customization,[19, 35] can also be unlocked with this dynamic design.
与之前报道的利用中声速调制32 和微气泡阵列实现可重构声全息图的方法不同、33 目前由电机驱动的可编程元表面可在反射和透射模式下进行动态声学成像，这可以在视频S1（辅助信息）中直观地观察到。27 此外，这些功能还可以在全空间实现，见注释 S4 （佐证资料）。除了利用全空间可编程声学元表面实现这些令人兴奋的功能外，还有其他潜在的应用，如按需声学能量采集34 和个性化室内声场定制、19, 35 也可以通过这种动态设计来解锁。
To better illustrate the performances of the presented programmable acoustic metasurface, we compare the key characteristics of the current work with other reported metasurfaces, as summarized in Table 1. It can be found that the proposed metasurface can program sound behaviors with good performances in both reflection and transmission modes. Although the number of controllable phase states is fixed, the current 2-bit programmable acoustic metasurface has realized diverse functionalities in full space. With the development of precision processing technology and high-precision electronically tunable devices, we can achieve efficient wave manipulation and carry out more complex functions by integrating more optional resonant cavities into the same component to build high-bits programmable acoustic metasurfaces. To further regulate the reflection and transmission phases continuously, we can integrate multiple advanced electronic components into the same element.
为了更好地说明所提出的可编程声学元表面的性能，我们将当前工作的主要特点与其他已报道的元表面进行了比较，如表1所示。可以发现，所提出的元表面能在反射和透射模式下都具有良好的声学特性。虽然可控相位的数量是固定的，但目前的 2 位可编程声学元表面已经实现了全空间的多种功能。随着精密加工技术和高精度电子可调谐器件的发展，我们可以通过将更多可选谐振腔集成到同一元件中来实现高效的波操纵，并实现更复杂的功能，从而构建高比特可编程声学元表面。为了进一步连续调节反射和透射相位，我们可以在同一元件中集成多个先进的电子元件。
表 1。与之前报道的可编程声学元表面的比较。
| Refs. 参考文献 | Operation condition 运行状况 | Discretized phase 离散化阶段 | Element amplitude 元件振幅 | Control mechanism 控制机制 |
|---|---|---|---|---|
| [11] | 3D transmission field 三维传输场 | 1-bit encoding 1 位编码 | >0.4 | Electromagnet 电磁铁 |
| [18] | 2D transmission field 二维传输场 | Continuous 连续 | >0.8 | Pump 泵 |
| [19] | 3D reflection field 三维反射场 | 1-bit encoding 1 位编码 | >0.77 | Motor 电机 |
| [21] | 2D reflection field 二维反射场 | 1-bit encoding 1 位编码 | >0.9 | Electromagnet 电磁铁 |
| [27] | 3D reflection field 三维反射场 | Continuous 连续 | Not reported 未报告 | Electromagnet 电磁铁 |
| This work 这项工作 | 3D reflection and transmission fields 三维反射和透射场 |
2-bit encoding 2 位编码 | ≈1 (reflection);>0.75 (transmission) ≈1（反射）；>0.75（透射） |
Motor 电机 |
It is noted that full-space metasurfaces capable of simultaneously manipulating the reflected and transmitted waves have been investigated in acoustics[14, 15, 28] and electromagnetics.[13, 36-39] Due to the scalar nature of sound waves, this work presented a switchable full-space programmable acoustic metasurface to further improve the efficiency of the metasurface. Additionally, to program micromotors wirelessly and independently, we can use the radio frequency module NRF24L01 to send and receive coding information.[40
据悉，能够同时操纵反射波和透射波的全空间元曲面已在声学14, 15, 28 和电磁学中得到研究。13, 36-39 由于声波的标量性质，这项工作提出了一种可切换的全空间可编程声学元面，以进一步提高元面的效率。此外，为了对微电机进行无线独立编程，我们可以使用射频模块 NRF24L01 来发送和接收编码信息。]
3 Conclusion 3 结论
We proposed, designed, and demonstrated a computer-controlled motor-driven acoustic metasurface capable of programming the reflected and transmitted sound behaviors dynamically and independently. The proposed metasurface consists of 100 individually accessible and digitally programmable elements, which can choose to operate in a reflection field or transmission field dynamically. Each element is programmed using just a single micro-stepper motor. Based on this metasurface, we verified two typical applications, dynamic acoustic focusing and dynamic acoustic holography. For the first application, we can realize variable focus numbers, adjustable focus positions, and controllable focus intensities in both reflection and transmission modes. For the second application, we can realize different acoustic holograms in both reflection and transmission modes. This work opens up a promising avenue toward dynamic manipulation of multi-dimensional sound fields via a single programmable acoustic metasurface, which may enable self-adaptive tuning for intelligent customization of sound fields in the near future.
我们提出、设计并演示了一种计算机控制的电机驱动声学元面，它能够动态、独立地对反射声和透射声行为进行编程。所提议的元表面由 100 个可单独访问和数字编程的元件组成，这些元件可动态选择在反射场或透射场中工作。每个元件只需使用一个微型步进电机即可编程。基于这个元表面，我们验证了动态声聚焦和动态声全息这两个典型应用。对于第一种应用，我们可以在反射和透射模式下实现可变聚焦数、可调聚焦位置和可控聚焦强度。对于第二种应用，我们可以在反射和透射模式下实现不同的声全息图。这项工作为通过单个可编程声学元表面实现多维声场的动态操控开辟了一条前景广阔的道路，在不久的将来，它可能会实现自适应调谐，从而实现声场的智能定制。
4 Experimental Section 4 实验部分
Numerical Simulation 数值模拟
Full-wave simulations were conducted using the finite element method based on COMSOL Multiphysics software. The background medium was air with the mass density and sound speed being 1.21 kg m−3 and 343 m s−1, respectively. For the simulated element shown in Figure 2a, the base material of the cuboid, shaft, and lid is photosensitive resin with the mass density and sound speed being 1300 kg m−3 and 716 m s−1, respectively. These components of the element can be regarded as acoustically rigid. The lid is attached closely to the cuboid, and therefore, the incident waves cannot enter the central hole of the element and interact with the micromotor. In such a view, the micromotors were ignored in simulations.
使用基于 COMSOL Multiphysics 软件的有限元法进行了全波模拟。背景介质为空气，其质量密度和声速分别为 1.21 kg m-3 和 343 m s-1 。对于图2a所示的模拟元件，长方体、轴和盖的基体材料是光敏树脂，其质量密度和声速分别为 1300 kg m-3 和 716 m s-1 。该元件的这些组成部分可视为声学刚体。盖子紧贴在立方体上，因此入射波无法进入元件的中心孔与微电机相互作用。因此，在模拟中忽略了微电机。
Sample Fabrication 样品制作
The sample was fabricated by 3D-printing technology. The cuboid array, the middle shafts, and the rotatable lids were processed separately. The radius and height of the shaft were 2 and 27 mm, respectively. The shaft was used to transmit the torque required for the rotation of the lid. On one side of the shaft, there was a circular hole with a radius of 1 mm and a depth of 3 mm used to connect with the micromotor. The other side of the shaft and the lid were fixed together by glue. A circular hole with a radius of 2.5 mm in the center of the cuboid was used to ensure smooth rotation of the shaft. The circular hole was connected with a square hole with a side length of 6.1 mm at the bottom of the cuboid. The square hole allowed the micromotor to be inserted stably into the cuboid. The micromotor is mainly composed of a top shaft, which has a height of 3 mm and a radius of 1 mm, and a cylindrical base, which has a height of 12.5 mm and a radius of 3 mm. To achieve independent control of each micromotor, a rectangular channel with a length of 36 mm and a width of 8 mm is embedded 1 mm away from the bottom of the cuboid and used for wiring. For each micromotor, four wires were used to connect the micromotor with the driver module, and the diameter of each wire was 0.6 mm.
样品是通过三维打印技术制作的。长方体阵列、中轴和可旋转盖子是分别加工的。轴的半径和高度分别为 2 毫米和 27 毫米。轴用于传递旋转盖子所需的扭矩。轴的一侧有一个半径为 1 毫米、深度为 3 毫米的圆孔，用于连接微电机。轴的另一侧和盖子用胶水固定在一起。长方体中心有一个半径为 2.5 毫米的圆孔，用于确保轴的平稳旋转。圆孔与长方体底部边长为 6.1 毫米的方孔相连。方孔可使微电机稳定地插入长方体中。微电机主要由高度为 3 毫米、半径为 1 毫米的顶轴和高度为 12.5 毫米、半径为 3 毫米的圆柱形底座组成。为了实现对每个微电机的独立控制，在离立方体底部 1 毫米处嵌入了一个长 36 毫米、宽 8 毫米的矩形通道，用于布线。每个微电机使用四根导线连接微电机和驱动模块，每根导线的直径为 0.6 毫米。
Experimental Setup 实验装置
The control circuit board of the micromotor array was powered by a direct current (DC) power supply with a voltage of 8.8 V and connected to a computer via a USB interface. A USB 3.0 cable was used to transmit the command. The coding instructions were transmitted to the single-chip microcomputer and then sent to different micromotor drivers for individual programming of each motor, see Note S5 (Supporting Information). During measurements, a planar speaker (Panphonics SSHP60×20) was used as a sound source to generate a plane wave incidence. A quarter-inch microphone (MPA416, BSWA) was mounted on a moving stage driven by a stepper motor to scan the acoustic pressure fields at a step size of 10 mm. The scanning areas were 360 mm × 360 mm and parallel to the sample. For the reflection mode, with and without sample to obtain the total field and incident field were measured twice, respectively, during which other configurations remained unchanged, and finally the target field distribution was obtained by subtracting the incident field from the total field. For the transmission mode, the measured total field was the target field distribution. All the measured data were sampled by the acquisition card (NI 4431) and analyzed by the computer.
微电机阵列的控制电路板由电压为 8.8 V 的直流电源供电，并通过 USB 接口与计算机相连。使用 USB 3.0 电缆传输指令。编码指令被传输到单芯片微电脑，然后发送到不同的微电机驱动器，对每个电机进行单独编程，参见注S5（佐证资料）。测量时，使用平面扬声器（Panphonics SSHP60×20）作为声源，以产生平面波入射。四分之一英寸传声器（MPA416，BSWA）安装在由步进电机驱动的移动台上，以 10 毫米的步长扫描声压场。扫描区域为 360 毫米 × 360 毫米，与样品平行。对于反射模式，分别测量两次有样品和无样品的总场和入射场，期间其他配置保持不变，最后从总场中减去入射场，得到目标场分布。对于透射模式，测得的总场就是目标场分布。所有测量数据均由采集卡（NI 4431）进行采样，并由计算机进行分析。
Acknowledgements 致谢
This work was supported by the National Natural Science Foundation of China (U23B2015 and 62288101), the Fundamental Research Funds for the Central Universities (2242023K5002), and the 111 Project (111-2-05).
本研究得到了国家自然科学基金（U23B2015 和 62288101）、中央高校基本科研业务费（2242023K5002）和 111 项目（111-2-05）的资助。
Conflict of Interest 利益冲突
The authors declare no conflict of interest.
作者声明没有利益冲突。
Supporting Information 辅助信息
| Filename 文件名 | Description 说明 |
|---|---|
| adfm202411403-sup-0001-SuppMat.docx3 MB | Supporting Information 辅助信息 |
| adfm202411403-sup-0002-VideoS1.mp414.4 MB | Supplemental Video 1 补充视频 1 |
Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.
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