Adjustable folding structure unit and tunable acoustic coding metasurface

Abstract

The invention discloses an adjustable folding structure unit and a tunable acoustic coding metasurface in the technical field of acoustic metamaterials, and the adjustable folding structure unit adopts a labyrinth structure and comprises a sound wave inlet, a sound wave outlet and a labyrinth channel formed by at least eight transverse plates. Sound waves enter the labyrinth channel from the sound wave inlet and then propagate to the sound wave outlet along a preset path; the tunable acoustic coding metasurface comprises a plurality of adjustable folding structure units arranged according to a coding sequence, the acoustic wave phase difference reaches pi by adjusting the length of at least one movable transverse plate in the labyrinth channel, and coding units can be generated. The sound beam splitting is directionally controlled by adjusting the sorting mode of the coding sequence; the sound focusing is directionally controlled by adjusting the sorting mode of the coding sequence and the number of the adjustable folding structure units. According to the invention, flexible and efficient directional control of sound beam splitting and sound focusing is realized, and the problems of insufficient reconfigurability, narrow frequency band, too high system complexity and high cost of an acoustic coding metasurface are solved.

Description

Technical Field

[0001] The invention relates to an adjustable folding structure unit and a tunable acoustic coding metasurface, belonging to the technical field of acoustic metamaterials. Background Art

[0002] Acoustic metasurface is an important component of acoustic metamaterials. It can be regarded as a two-dimensional metamaterial with a thickness less than the working wavelength. It can achieve arbitrary control of sound waves on a sub-wavelength scale and exhibit a variety of interesting functions, such as sound focusing, sound imaging, sound invisibility, etc. With the demand for the practical application of acoustic artificial metamaterials, acoustic metasurface structures that can achieve active control of sound waves are becoming an increasingly important research direction.

[0003] Traditionally, most passive metasurfaces are designed with fixed-shape units, such as spatial curled structures and Helmholtz resonators. Although they have great potential in acoustic wave manipulation, their shapes are fixed. Once manufactured, the acoustic response generated by these passive metasurfaces cannot be tuned, and the sound field is difficult to change, so the actual impact is very limited. Therefore, we need an actively adjustable acoustic metasurface that can actively and flexibly realize the required sound field manipulation according to our needs.

[0004] In recent years, digitally programmable metasurfaces, also known as coded metasurfaces, have attracted much attention due to their excellent reconstruction capabilities. Since the concept of digitally coded metasurfaces was first proposed in 2014, research in this field has developed rapidly in electromagnetic waves and gradually expanded to the field of acoustics. Subsequently, the concept of acoustically coded metasurfaces was introduced to achieve functions such as directional scattering and focusing of the sound field. However, these designs generally have the problem of insufficient reconfigurability, which limits their application in actively controlling the sound field.

[0005] Inspired by the coded metasurface, a new type of Schroeder diffuser was designed, whose thickness was greatly reduced, but active regulation was still not achieved. On the other hand, although the emergence of active coded metasurfaces can regulate the local reverberant sound field, its key materials are sensitive to tension, and durability becomes a challenge during repeated regulation.

[0006] In addition, researchers have developed reconfigurable acoustic lenses that demonstrate excellent focusing performance, but this is accompanied by complex system hardware, large size, and high cost. In general, most of the current encodeable acoustic metasurfaces are still in a passive state, and their reconfigurability needs to be improved. Although a few active encodeable metasurfaces have good reconstruction capabilities, they still rely on complex active control transducer arrays, and their working mechanism is similar to the expensive active phased array technology.

[0007] The information disclosed in this background technology section is only intended to enhance the understanding of the overall background of the invention and should not be regarded as an acknowledgement or any form of suggestion that the information constitutes the prior art already known to ordinary technicians in this field. Summary of the invention

[0008] The technical problem to be solved by the present invention is: how to overcome the problems of insufficient reconfigurability, narrow frequency band, excessive system complexity and high cost of acoustic coding metasurface, while achieving flexible and efficient directional manipulation of acoustic beam splitting and acoustic focusing.

[0009] In order to solve the above technical problems, the present invention is implemented by adopting the following technical solutions.

[0010] In a first aspect, the present invention provides an adjustable foldable structural unit, wherein the adjustable foldable structural unit adopts a labyrinth structure, including a sound wave inlet, a sound wave outlet, and a labyrinth channel formed by at least eight horizontal plates, wherein the sound wave enters the labyrinth channel from the sound wave inlet and propagates along a preset path to the sound wave outlet;

[0011] By adjusting the length of at least one movable horizontal plate in the maze channel to change the propagation distance of the sound wave, the phase delay of the sound wave is controlled so that the phase difference of the sound wave reaches π at the target frequency, and the coding unit 0 or 1 can be generated.

[0012] Furthermore, a cavity is provided inside the adjustable folding structure unit, and at least eight horizontal plates are provided in the cavity, including:

[0013] The bottom horizontal plate is fixed to the lowest end of the cavity and is provided with a bottom slit as an entrance for sound waves;

[0014] Two top transverse plates, including a first top transverse plate and a second top transverse plate, are located at the top of the cavity and are opposite to the bottom transverse plate, and a top slit is provided between the first top transverse plate and the second top transverse plate as a sound wave outlet;

[0015] a left transverse plate, located at the leftmost end of the cavity, connected to the first top transverse plate and the bottom transverse plate respectively;

[0016] a right transverse plate, located at the rightmost end of the cavity and opposite to the left transverse plate, and connected to the second top transverse plate and the bottom transverse plate respectively;

[0017] At least one movable horizontal plate, which passes through the left horizontal plate and is connected to and controlled by an external push-pull mechanism to extend or retract the movable horizontal plate;

[0018] At least two fixed horizontal plates, respectively located above and below the movable horizontal plate, fixed to the inner surface of the right horizontal plate;

[0019] Among them, at least 2mm air channels are left between the movable horizontal board, the fixed horizontal board, the left horizontal board, the right horizontal board, the bottom horizontal board and the top horizontal board.

[0020] Furthermore, the external push-pull mechanism is connected to the movable horizontal plate through a through hole opened on the side of the adjustable folding structure unit.

[0021] In a second aspect, the present invention provides a tunable acoustic coding metasurface, comprising a plurality of adjustable folded structural units as described in the first aspect, wherein the plurality of adjustable folded structural units are arranged in a coding sequence;

[0022] The coding sequence is used to define the position and coding unit of each adjustable folded structural unit in the tunable acoustic coding metasurface;

[0023] By adjusting the length of at least one movable horizontal plate in the maze channel of each adjustable folding structure unit to change the propagation distance of the sound wave, the phase difference of the sound wave reaches π at the target frequency, and a coding unit corresponding to the coding sequence can be generated.

[0024] Furthermore, the acoustic beam is directionally manipulated by adjusting the order of the coding sequence.

[0025] Furthermore, the method for directionally manipulating the acoustic beam splitting by adjusting the order of the coding sequence comprises:

[0026] vertically incident a plane wave onto the tunable acoustic coding metasurface;

[0027] Using the tunable acoustic coding metasurface, encoding and modulating the plane wave according to a coding sequence, and calculating the far-field acoustic field distribution of the plane wave using a far-field function;

[0028] According to the far-field acoustic field distribution of the plane wave, the length of at least one movable horizontal plate in each adjustable folded structural unit maze channel on the tunable acoustic coding metasurface is adjusted to generate a coding unit 0 or 1 to form a new coding sequence;

[0029] The acoustic beamlets are directionally steered according to the new coding sequence.

[0030] Further, when the coding sequence is all coding unit 0 or all coding unit 1, the far field function is expressed as:

[0031] (1);

[0032] In the formula, Indicates the far-field sound field distribution formed when the coding sequence is all coding unit 0 or all coding unit 1, represents the far-field elevation angle, represents the far-field direction angle, C1 is a constant, representing the amplitude factor related to the sound field characteristics when the coding sequence is all coding unit 0 or all coding unit 1, represents the cosine function, represents the sine function, Indicates taking the absolute value, , No special meaning, , , represents the sound wave vector of air, represents the length of the adjustable folding structural unit;

[0033] When the coding units 0 and 1 in the coding sequence are arranged alternately, and the coding sequence is 0101... / 0101..., ' / ' is a line break character, indicating a line break, and the far field function is expressed as:

[0034] (2);

[0035] In the formula, represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are arranged alternately, C2 is a constant, representing the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are arranged alternately and the coding sequence is 0101... / 0101...;

[0036] When the coding units 0 and 1 in the coding sequence are periodically arranged alternately, and the coding sequence is 0101... / 1010..., the far field function is expressed as:

[0037] (3);

[0038] In the formula, It represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are periodically alternately arranged. C3 is a constant, which represents the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are periodically alternately arranged and the coding sequence is 0101... / 1010...

[0039] Furthermore, the acoustic focusing is directionally manipulated by adjusting the ordering of the coding sequence and the number of adjustable folding structural units.

[0040] Furthermore, the method for directionally manipulating acoustic focusing by adjusting the ordering of the coding sequence and the number of adjustable folding structural units includes:

[0041] Adjusting the length of at least one movable horizontal plate in the maze channel of the adjustable folding structure unit at the center position of the tunable acoustic coding metasurface to generate a coding unit 1;

[0042] The length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the coding super-tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1;

[0043] At the target frequency, the width of each region of the tunable acoustic coding metasurface and the number of adjustable folded structural units are adjusted to directionally manipulate the acoustic focusing at different focal positions.

[0044] Furthermore, the length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1, wherein when the sound is focused, when the focus is set on the central axis of the tunable acoustic coding metasurface, the calculation formula of the distance from the central axis of the tunable acoustic coding metasurface to different coding areas is expressed as:

[0045] (4);

[0046] In the formula, x ±（i+1） represents the distance between the i+1th coding region on the left or the i+1th coding region on the right of the center of the tunable acoustic coding metasurface and the focal abscissa, λ represents the wavelength of the acoustic wave, where λ=c / f, c represents the speed of sound in air, f represents the target frequency, and f y The ordinate of the focus, where the subscript y has no actual physical meaning, and x ±i It shows the distance between the i-th coding region on the left side of the center position of the tunable acoustic coding metasurface or the i-th coding region on the right side and the horizontal coordinate of the focus.

[0047] Compared with the prior art, the present invention has the following beneficial effects:

[0048] The adjustable folding structural unit proposed in the present invention realizes efficient regulation of the phase of the sound wave through an innovative maze structure design. The adjustable folding structural unit flexibly changes the propagation path of the sound wave in the maze channel by adjusting the length of the movable horizontal plate, thereby accurately controlling the phase delay of the sound wave. When the phase difference of the sound wave reaches π at the target frequency, the coding unit 0 or 1 can be stably generated, providing a reliable basis for sound wave coding.

[0049] Based on the above-mentioned adjustable folding structural unit, the tunable acoustic coding metasurface constructed by the present invention realizes flexible and efficient directional manipulation of sound beam splitting and sound focusing through the orderly arrangement of multiple adjustable folding structural units. Through the definition of the coding sequence, the position and coding unit of each adjustable folding structural unit in the tunable acoustic coding metasurface can be accurately controlled, and then a sound wave field matching the coding sequence can be generated at the target frequency. Not only does it overcome the problem of poor reconfigurability in the prior art, but it also reduces costs by reducing the use of complex systems, while maintaining a high degree of control accuracy and flexibility. The application of the tunable acoustic coding metasurface provided by the present invention will greatly expand the application field of sound wave control in the future and promote the development of acoustic technology. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of a schematic diagram of an adjustable folding structure unit regulating the phase of an acoustic wave provided by an embodiment of the present invention;

[0051] Figure 2 is a schematic diagram of a tunable acoustic coding metasurface structure provided by an embodiment of the present invention;

[0052] Figure 3 It is a schematic diagram of the principle of phase regulation of a two-dimensional folding structure of an adjustable folding structure unit provided in an embodiment of the present invention;

[0053] Figure 4 It is a schematic diagram of the relationship between the phase of the adjustable folding structure unit provided by the embodiment of the present invention and the incident frequency (f) and the length (l3) of the movable horizontal plate;

[0054] Figure 5 It is a schematic diagram of the relationship between the phase and normalized amplitude of the adjustable folded structure unit at a target frequency of 2 kHz and the length (l3) of the movable cross plate provided by an embodiment of the present invention;

[0055] Figure 6 is a schematic diagram of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is all “0”;

[0056] Figure 7 is a schematic diagram of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is "01 / 01";

[0057] Figure 8 is a schematic diagram of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is "01 / 10";

[0058] Fig. 9 is a schematic diagram of far-field radiation of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is all “0”;

[0059] Fig.10 is a schematic diagram of far-field radiation of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is “01 / 01”;

[0060] Fig.11 is a schematic diagram of far-field radiation of a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is “01 / 10”;

[0061] Fig.12 It is a schematic diagram of the amplitude simulation in the xy plane at 17 cm above the tunable acoustic coding metasurface when the coding sequence provided by the embodiment of the present invention is all "0";

[0062] Fig.13 It is a schematic diagram of the xy plane amplitude simulation at 17 cm above the tunable acoustic coding metasurface when the coding sequence provided by the embodiment of the present invention is "01 / 01";

[0063] Fig.14 It is a schematic diagram of the xy plane amplitude simulation at 17 cm above the tunable acoustic coding metasurface when the coding sequence provided by the embodiment of the present invention is "01 / 10";

[0064] Fig.15 It is a schematic diagram of the xy plane amplitude experiment at 17 cm above the tunable acoustic coding metasurface when the coding sequence provided by the embodiment of the present invention is all "0";

[0065] Fig.16 It is a schematic diagram of an xy plane amplitude experiment at 17 cm above a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is "01 / 01";

[0066] Fig.17 It is a schematic diagram of an xy plane amplitude experiment at 17 cm above a tunable acoustic coding metasurface when the coding sequence provided by an embodiment of the present invention is "01 / 110";

[0067] Fig.18 It is a principle diagram of adjustable acoustic focusing after the sound wave passes through the acoustic coding lens provided by an embodiment of the present invention;

[0068] Fig.19 Schematic diagram of the simulated sound intensity distribution when the frequency is f1=2kHz and the focus is (fx, fy) = (0mm, 180mm) provided by an embodiment of the present invention;

[0069] Fig. 20 Schematic diagram of the simulated sound intensity distribution when the frequency is f2=2.4kHz and the focus is (fx, fy) = (140mm, 320mm) provided by an embodiment of the present invention;

[0070] Fig.21The frequency is f1 = 2kHz, the focus is (fx, fy) = (0mm, 180mm) and the sound intensity distribution is measured experimentally according to the embodiment of the present invention. The experimental measurement area is Fig.19 Schematic diagram of the red frame area;

[0071] Fig. 22 The frequency of the present invention is f2 = 2.4kHz, the focus is (fx, fy) = (140mm, 320mm) and the sound intensity distribution is measured experimentally. The experimental measurement area is Fig. 20 Schematic diagram of the red frame area;

[0072] Fig.23 Schematic diagram of normalized sound intensity distribution along the lines “I” and “II” provided by an embodiment of the present invention, which is simulated and experimentally measured;

[0073] Fig.24 It is a schematic diagram of normalized sound intensity distribution of simulation and experimental measurement along the lines “III” and “IV” provided by an embodiment of the present invention.

[0074] Figure markings: 1-adjustable folding structural unit; 2-cavity; 3-bottom horizontal plate; 4-fixed horizontal plate; 5-left horizontal plate; 6-right horizontal plate; 7-movable horizontal plate; 8-bottom slit; 9-top slit; 10-through hole; 11-first top horizontal plate; 12-second top horizontal plate; 13-air channel. DETAILED DESCRIPTION

[0075] The technical solution of the present invention is described in detail below through the accompanying drawings and specific embodiments. It should be understood that the embodiments of the present invention and the specific features in the embodiments are detailed descriptions of the technical solution of the present invention, rather than limitations on the technical solution of the present invention. The embodiments of the present invention and the technical features in the embodiments may be combined with each other unless there is a conflict.

[0076] Example 1

[0077] This embodiment introduces an adjustable folding structure unit, such as Figure 1 As shown, the adjustable folding structure unit 1 adopts a labyrinth structure, including a sound wave inlet, a sound wave outlet, and a labyrinth passage formed by at least eight horizontal plates. Figure 3 As shown, after the sound wave enters the maze channel from the sound wave entrance M, it propagates along the preset path to the sound wave exit N; by adjusting the length of at least one horizontal board in the maze channel, the propagation distance of the sound wave is changed, and the phase delay of the sound wave is controlled so that the sound wave phase difference reaches π at the target frequency, generating a coding unit 0 or 1.

[0078] The phase delay expression of the sound wave is φ = kL1, where φ represents the transmission phase, k represents the sound wave vector of the air, and L1 represents the propagation distance of the sound wave. According to the phase delay expression of the sound wave, adjusting the propagation distance L1 of the sound wave can effectively control the phase delay of the sound wave. Therefore, as long as at least one horizontal plate in the adjustable folding structure unit can be flexibly moved, the propagation distance L1 of the sound wave can be changed, thereby actively controlling the transmission phase φ of the adjustable folding structure unit, and then generating the coding unit 0 or 1 as required.

[0079] like Figure 2 As shown, a cavity 2 is provided inside the adjustable folding structure unit 1, and at least eight horizontal plates are provided in the cavity 2, including:

[0080] The bottom horizontal plate 3 is fixed to the lowest end of the cavity 2 and is provided with a bottom slit 8 as an entrance for sound waves;

[0081] Two top transverse plates, including a first top transverse plate 11 and a second top transverse plate 12, are located at the top of the cavity 2 and are opposite to the bottom transverse plate 3. A top slit 9 is provided between the first top transverse plate 11 and the second top transverse plate 12 as a sound wave outlet;

[0082] The left transverse plate 5 is located at the leftmost end of the cavity 2 and is connected to the first top transverse plate 11 and the bottom transverse plate 3 respectively;

[0083] The right transverse plate 6 is located at the rightmost end of the cavity 2 and is opposite to the left transverse plate 3, and is connected to the second top transverse plate 12 and the bottom transverse plate 3 respectively;

[0084] At least one movable horizontal plate 7 passes through the left horizontal plate 5 and is connected and controlled by an external push-pull mechanism to extend or retract the movable horizontal plate 7;

[0085] At least two fixed transverse plates 4, respectively located above and below the movable transverse plate 7, fixed to the inner surface of the right transverse plate 6;

[0086] An air passage 13 of at least 2 mm is left between the movable horizontal plate 7, the fixed horizontal plate 4, the left horizontal plate 5, the right horizontal plate 6, the bottom horizontal plate 3 and the top horizontal plate.

[0087] The adjustable folding structure unit 1 has a length and width of 70 mm, a thickness of 18 mm, and a wall thickness of 5 mm; the cavity 2 has a length and width of 60 mm, and a height of 8 mm; wherein the thickness of the transverse plate is 2 mm, the length of the bottom transverse plate 3, the left transverse plate 5, the right transverse plate 6 and the fixed transverse plate 4 are 50 mm, the length of the first top transverse plate 11 and the second top transverse plate 12 are 25 mm, the length of the movable transverse plate 7 is a variable l3, and the width of the bottom slit 8 and the top slit 9 are 10 mm.

[0088] The external push-pull mechanism is connected to the movable transverse plate 7 via a through hole 10 provided on the side of the adjustable folding structure unit 1 .

[0089] In this embodiment, the external push-pull mechanism is a handle with a length of 20 mm.

[0090] In order to select appropriate 0 and 1 coding units, this embodiment constructs Figure 5 The simulation model shown studies the relationship between the transmission phase φ of the sound wave of the adjustable folded structure unit 1 in the continuous frequency domain f and the length l3 of the movable horizontal plate 7, wherein the length l3 of the movable horizontal plate 7 ranges from 0 to 20 mm. In particular, this embodiment focuses on the frequency range of 1.5 kHz to 2.5 kHz to comprehensively analyze and understand the influence of the continuous frequency domain on the transmission phase of the sound wave, thereby providing a scientific basis for the optimization of the encoding unit.

[0091] In the above simulation environment, this embodiment sets the propagation medium of sound as air, the speed of sound v is 343m / s, and the density ρ is 1.21kg / m³. In view of the significant impedance difference between solid and air, this embodiment simplifies the solid part of the adjustable folding structure unit 1 into a rigid material, and uses a rigid boundary to simulate its solid structure during modeling, while the rest of the model is completely filled with air.

[0092] In order to simulate the actual sound field environment, this embodiment sets two cubic background sound field areas at the upper and lower sides of the adjustable folding structure unit 1, respectively. The upper area has a size of 10cm×10cm×20cm, and the lower area has a size of 10cm×10cm×5cm. In order to introduce periodic sound waves and simulate the sound wave incident situation, this embodiment applies continuous boundary conditions to the two pairs of side boundaries of the background sound field, and adds plane wave radiation as boundary conditions to the upper and lower side boundaries, respectively. The lower side boundary is specially set with an incident pressure field to simulate the incident source of the sound wave.

[0093] In order to accurately measure and analyze the transmission phase φ, this embodiment sets an observation point A at a position 10 cm away from the upper surface of the adjustable folding structure unit 1. Through this observation point, the phase change after the sound wave passes through the adjustable folding structure unit 1 under different movable horizontal plate 7 length l3 conditions can be calculated and obtained, and the transmission phase can be calculated.

[0094] The relationship between the transmission phase φ of the acoustic wave of the adjustable folded structural unit 1 in the continuous frequency domain f and the length l3 of the movable horizontal plate 7 is as follows: Figure 4 shown.

[0095] Depend on Figure 4It can be seen that at frequencies of 1.7 kHz and above, the transmission phase change almost covers the span of π, which meets the phase requirements of the 0 and 1 coding units of the tunable acoustic coding metasurface. Therefore, this embodiment selects 2 kHz as the target frequency. The relationship between the phase φ of the adjustable folded structure unit and the length l3 of the movable cross plate at the target frequency of 2 kHz is calculated, as shown in Figure 7 shown.

[0096] Since the 0 and 1 coding units not only have a relative phase difference of 180°, but also should have similar amplitudes, this implementation calculates the relationship between the amplitude of the adjustable folded structure unit and the length of the movable cross plate (l3) after normalization at the target frequency of 2 kHz, as shown in Figure 8 As shown. Figure 8 It can be seen that when the length l3 of the movable horizontal plate 7 is 7 mm and 19 mm respectively, the requirements of the 0 and 1 coding units are met.

[0097] The adjustable folding structural unit provided by the present invention has strong reconfigurability. The tunable acoustic coding metasurface formed by the adjustable folding structural unit can realize active and flexible sound field control according to needs. Based on theoretical and experimental results, it is confirmed that only the coding method of the adjustable folding structural unit is needed to achieve a variety of sound control effects such as sound beam splitting and sound focusing. The adjustable folding structural unit proposed by the present invention provides a feasible idea for the design of multifunctional programmable metasurfaces, and is expected to be applied to the fields of digital lenses, acoustic communications, etc.

[0098] Example 2

[0099] Based on the same inventive concept as Example 1, this example introduces a tunable acoustic coding metasurface, such as Figure 2 As shown, the tunable acoustic coding metasurface includes a plurality of adjustable folded structural units as described in Example 1. Each adjustable folded structural unit of the tunable acoustic coding metasurface can be flexibly switched between coding units 0 or 1 as needed to achieve directional steering of acoustic beam splitting.

[0100] The tunable acoustic coding metasurface provided by the present invention comprises a plurality of adjustable folding structural units 1 as described in Example 1, 4. The plurality of adjustable folding structural units are arranged according to a coding sequence;

[0101] The coding sequence is used to define the position and coding unit of each adjustable folded structural unit in the tunable acoustic coding metasurface;

[0102] By adjusting the length of at least one movable horizontal plate in each adjustable folding structure unit maze channel to change the propagation distance of the sound wave, the sound wave phase difference reaches π at the target frequency, and a coding unit corresponding to the coding sequence can be generated. The present invention directionally manipulates the acoustic beam by adjusting the order of the coding sequence, wherein the method for directionally manipulating the acoustic beam by adjusting the order of the coding sequence includes:

[0103] vertically incident a plane wave onto the tunable acoustic coding metasurface;

[0104] Using the tunable acoustic coding metasurface, encoding and modulating the plane wave according to a coding sequence, and calculating the far-field acoustic field distribution of the plane wave using a far-field function;

[0105] According to the far-field acoustic field distribution of the plane wave, the length of at least one movable horizontal plate in each adjustable folded structural unit maze channel on the tunable acoustic coding metasurface is adjusted to generate a coding unit 0 or 1 to form a new coding sequence;

[0106] The acoustic beamlets are directionally steered according to the new coding sequence.

[0107] This embodiment verifies the effect of directional control of acoustic beam splitting by tunable acoustic coding metasurface through comprehensive numerical simulation and experimental means. The tunable acoustic coding metasurface under the coding sequence of all 0s, all 1s and repeated sequence 0101... / 0101... shows one-dimensional characteristics. The first diffraction order of the two-dimensional periodic structure of the coding sequence 0101... / 1010... does not appear in the zero order, which simplifies the complexity of experiments and simulations.

[0108] In view of the experimental conditions and various practical factors, this embodiment constructs a tunable acoustic coding metasurface sample consisting of 2×2 adjustable folded structural unit cells with a size of 140mm×140mm×18mm.

[0109] During the experiment, the tunable acoustic coding metasurface was placed horizontally on the xy two-dimensional plane, and six speakers with a diameter of 10.5 cm were linearly arranged 30 cm below the tunable acoustic coding metasurface as plane wave sound sources. The above speakers were synchronously driven by a multi-function signal generator to generate sound waves at a frequency of 2 kHz, ensuring that all sound waves had the same initial phase and amplitude.

[0110] In order to accurately measure the sound field distribution, this embodiment uses a microphone mounted on a 3D stepper motor to scan point by point on the xy two-dimensional plane 17 cm above the tunable acoustic coding metasurface, and the scanning step length is set to 2 cm. In addition, porous sound-absorbing foam is arranged around the experimental device to simulate an echo-free anechoic environment as much as possible.

[0111] When the coding sequence is all coding unit 0 or all coding unit 1, Figure 6 As shown, the far-field function is expressed as:

[0112] (1);

[0113] In the formula, Indicates the far-field sound field distribution formed when the coding sequence is all coding unit 0 or all coding unit 1, represents the far-field elevation angle, Indicates that the far-field direction angle C1 is a constant, and indicates the amplitude factor related to the sound field characteristics when the coding sequence is all coding unit 0 or all coding unit 1, represents the cosine function, represents the sine function, Indicates taking the absolute value, , No special meaning, , , represents the sound wave number of air, Represents the length of the adjustable folding structural unit.

[0114] To achieve maximum scattering, ∣ c o s [ ( ψ 1 + ψ 2 ] / 2 ∣ = 1 , ∣ c o s [ ( ψ 1 − ψ 2 ] / 2 ∣ = 1 , =0, the plane wave will be scattered as a single main beam propagating along the incident direction. When the coding sequence is all “0”, the far-field radiation of the tunable acoustic coding metasurface can be obtained. Fig. 9 shown.

[0115] When the coding units 0 and 1 in the coding sequence are arranged alternately, and the coding sequence is 0101... / 0101..., ' / ' is a line break character, indicating a line break, such as Figure 7 As shown, the far-field function is expressed as:

[0116] (2);

[0117] In the formula, It represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are arranged alternately with each other. C2 is a constant, which represents the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are arranged alternately with each other and the coding sequence is 0101... / 0101...

[0118] When the elevation and azimuth angles of the plane wave are , 𝜑=90°, 270°, where arcsin represents the inverse sine function. The plane wave will generate scattered beams in the directions of (θ, 90°) and (θ, 270°), forming two symmetrical radiation branches, such as Fig.10 shown.

[0119] When the coding units 0 and 1 in the coding sequence are periodically arranged alternately, and the coding sequence is 0101... / 1010..., Figure 8 As shown, the far-field function is expressed as:

[0120] (3);

[0121] In the formula, It represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are periodically alternately arranged. C3 is a constant, which represents the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are periodically alternately arranged and the coding sequence is 0101... / 1010...

[0122] When the elevation and azimuth angles of the scattered beam are , 𝜑=45°, 135°, 225°, 315°. It can be seen that the plane wave will generate scattered beams in the four directions of (θ, 45°), (θ, 135°), (θ, 225°) and (θ, 315°), forming four symmetrical radiation branches, as shown in Fig.11 shown.

[0123] Further, Figure 12-17 The acoustic wave amplitude distribution in the xy two-dimensional plane 17 cm above the tunable acoustic coding metasurface under different coding sequences obtained through simulation and experimental measurement is shown.

[0124] Fig.12 The schematic diagram of the xy plane amplitude simulation at 17 cm above the tunable acoustic coding metasurface when the coding sequence is all "0" is shown. In the figure, there is a place with high sound pressure intensity and a concentrated transmission beam, which is consistent with the theoretical analysis, proving the effectiveness of the "00 / 00" tunable acoustic coding metasurface designed by the present invention.

[0125] Fig.13 The schematic diagram of the xy plane amplitude simulation at 17 cm above the tunable acoustic coding metasurface with the coding sequence of "01 / 01" is shown. In the figure, there are two places with large sound pressure intensity and two symmetrical transmission beams, which are consistent with the theoretical analysis, proving the effectiveness of the "01 / 01" tunable acoustic coding metasurface designed by the present invention.

[0126] Fig.14The schematic diagram of the xy plane amplitude simulation at 17 cm above the tunable acoustic coding metasurface with the coding sequence of "01 / 10" is shown. In the figure, there are four places with high sound pressure intensity and four symmetrical transmission beams, which are consistent with the theoretical analysis, proving the effectiveness of the "01 / 01" tunable acoustic coding metasurface designed by the present invention.

[0127] Fig.15 The experimentally measured amplitude diagram in the xy plane 17 cm above the tunable acoustic coding metasurface with the coding sequence of "00 / 00" is shown, which is close to the simulation diagram, proving the effectiveness of the "00 / 00" tunable acoustic coding metasurface designed by the present invention.

[0128] Fig.16 The experimentally measured amplitude diagram in the xy plane 17 cm above the tunable acoustic coding metasurface with the coding sequence of "01 / 01" is shown, which is close to the simulation diagram, proving the effectiveness of the "01 / 01" tunable acoustic coding metasurface designed by the present invention.

[0129] Fig.17 The experimentally measured amplitude diagram in the xy plane 17 cm above the tunable acoustic coding metasurface with the coding sequence of "01 / 10" is shown, which is close to the simulation diagram, proving the effectiveness of the "01 / 10" tunable acoustic coding metasurface designed by the present invention.

[0130] The observation results show that there is a high degree of consistency between the numerical simulation and the experimental data, which strongly verifies Figure 12-17 The tunable coding metasurface designed by the present invention can effectively manipulate the beam splitting effect of the transmitted acoustic wave on a metasurface, proving the effectiveness of the design of the present invention. The slight difference between the two can be attributed to the precision error in the sample manufacturing process and the acoustic energy loss that is difficult to completely avoid in the experimental environment.

[0131] In addition, this embodiment further studies the application of tunable acoustic coding metasurfaces and designs a reconfigurable acoustic coding lens using 12 adjustable folded structural units. By adjusting the length of the movable cross plate 7, the coding sequence of the acoustic coding lens can be flexibly controlled to achieve acoustic focusing with adjustable focus at a target frequency of 1.7-2.5kHz.

[0132] Fig.18 Schematic diagram of adjustable acoustic focusing after sound waves pass through a coded metasurface lens.

[0133] The tunable acoustic coding metasurface contains two types of subunits: coding unit "0" and coding unit "1". Adjacent intervals are filled with different coding units to ensure that the phase difference between adjacent intervals is 180°. In order to produce constructive interference at the focus, the path difference between two adjacent continuous areas satisfies , where l ±（i+1） represents the distance between the i+1th adjustable folded structure unit on the left or the i+1th adjustable folded structure unit on the right of the center of the tunable acoustic coding metasurface and the focus, l ±i It represents the distance between the i-th adjustable folded structure unit on the left side or the i-th adjustable folded structure unit on the right side of the center position of the tunable acoustic coding metasurface and the focus.

[0134] The present invention directionally manipulates acoustic focusing by adjusting the order of the coding sequence and the number of adjustable folded structural units, wherein the method for directionally manipulating acoustic focusing by adjusting the order of the coding sequence and the number of adjustable folded structural units comprises:

[0135] Adjusting the length of at least one movable horizontal plate in the maze channel of the adjustable folding structure unit at the center position of the tunable acoustic coding metasurface to generate a coding unit 1;

[0136] The length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the coding super-tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1;

[0137] At the target frequency, the width of each region of the tunable acoustic coding metasurface and the number of adjustable folded structural units are adjusted to directionally manipulate the acoustic focusing at different focal positions.

[0138] The length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1, wherein when the sound is focused, when the focus is set on the central axis of the tunable acoustic coding metasurface, the calculation formula of the distance from the central axis of the tunable acoustic coding metasurface to different coding areas is expressed as:

[0139] (4);

[0140] In the formula, x ±（i+1） represents the distance between the i+1th coding region on the left or the i+1th coding region on the right of the center of the tunable acoustic coding metasurface and the focal abscissa, λ represents the wavelength of the acoustic wave, where λ=c / f, c represents the speed of sound in air, f represents the target frequency, and f y The ordinate of the focus, where the subscript y has no actual physical meaning, and x ±i It shows the distance of the i-th coding region to the left of the center position of the tunable acoustic coding metasurface or the distance of the i-th coding region to the right of the focal point abscissa.

[0141] It can be seen from formula (4) that, when the working frequency f and the focus are constant, by adjusting the length of the movable horizontal plate 7 and generating a coding unit 0 or 1 to form a coding sequence, it is possible to achieve acoustic focusing at any given point.

[0142] In this embodiment, the focusing frequency f1=2kHz, the wavelength λ=c / f1, the wavelength λ is 170mm, and the focal coordinate (f x ,f y )=(0,180mm) lens to carry out experiments and specifically demonstrate the coding process of determining each tunable acoustic coding metasurface area.

[0143] According to f1=2kHz, wavelength λ=170mm, focal coordinates (f x ,f y )= (0,180mm) and formula (4), the parameters of the continuous area are x0=0mm, x1=196mm, x2=302mm, x3=398mm, x4=491mm. Since the side length of the adjustable folding structure unit in this embodiment is L=70mm, the number of adjustable folding structure units from the focal point horizontal coordinate to the edge of the lens is 2-2-1-1, and the coding sequence is "010,011,110,010" to meet the focusing requirements.

[0144] Similarly, the target frequency is calculated to be f2=2.4kHz, and the focal coordinate (f x ,f y )=(140mm,310mm) The coding sequence of the lens is "101,001,111,110".

[0145] In order to verify the effectiveness of the acoustic coding lens, this example uses 3D printing technology to manufacture a metasurface composed of 12 identical adjustable folding structural units. The material is polylactic acid PLA, the sound speed is 2000m / s, and the density is 1.180 kg / m 3 .

[0146] The experimental device of this embodiment adopts a planar waveguide system with a waveguide height of 8 cm and sound-absorbing sponges placed around it to reduce wave reflection. Planar sound waves are generated by a row of speakers, and the sound field is measured by a microphone and connected to an oscilloscope to read the data. At the target frequencies of 2 kHz and 2.4 kHz, the focal points are (0, 180) and (140, 320), respectively. The experimental simulation sound intensity distribution and experimental results are shown in Figure 2. Figure 19-22 shown.

[0147] Fig.19A schematic diagram of the sound intensity simulated and measured by an acoustic coding lens with a frequency of f1=2kHz and a focus of (fx, fy) = (0mm, 180mm) is shown. In the figure, the sound intensity is the largest at the coordinates (0mm, 180mm), which proves the effectiveness of the acoustic coding lens designed in the present invention.

[0148] Fig. 20 The sound intensity diagram of the acoustic coding lens simulated and measured with a frequency of f2=2.4kHz and a focus of (fx, fy) = (140mm, 320mm) is shown. In the diagram, the sound intensity is the largest at the coordinates (140mm, 320mm), which proves the effectiveness of the acoustic coding lens designed in the present invention.

[0149] Fig.21 The sound intensity diagram of the acoustic coding lens experiment with a frequency of f1=2kHz and a focus of (fx, fy) = (0mm, 180mm) is shown. The experimental measurement area is Fig.19 In the red frame area, the sound intensity is maximum at the coordinates (0mm, 180mm) in the figure, which is close to the simulation diagram, proving the effectiveness of the acoustic coding lens designed in the present invention.

[0150] Fig. 22 The sound intensity diagram of the acoustic coding lens experiment with a frequency of f1=2.4kHz and a focus of (fx, fy) = (140mm, 320mm) is shown. The experimental measurement area is Fig. 20 In the red frame area, the sound intensity is maximum at the coordinates (140mm, 320mm) in the figure, which is close to the simulation figure, proving the effectiveness of the acoustic coding lens designed in the present invention.

[0151] To further analyze the focusing performance, the sound intensity distribution along lines “I”, “II”, “III” and “IV” are shown in Fig.23 , Fig.24 As shown. The half-width at half maximum of the focusing area is 0.58λ and 0.85λ respectively, showing the excellent focusing performance of the designed acoustic coding lens. The experimental results show that the designed acoustic coding lens can achieve precise focusing in a wider frequency band, and the focus can not only be moved on the axis, but also adjusted in the entire working plane. It should be noted that the focusing range of the lens is affected by the number of adjustable folding structural units. Increasing the number of adjustable folding structural units will expand the focus position range, while reducing it will narrow the focusing range.

[0152] Both simulation and experimental results show that the acoustic coding lens based on the tunable acoustic coding metasurface has good working performance in the target frequency range of 1.7~2.5kHz. This invention provides a feasible idea for the design of broadband multifunctional programmable metasurfaces, which will have broad application prospects in research work such as noise control, acoustic wave processing, and acoustic imaging.

[0153] In summary, the adjustable folding structure unit proposed in the present invention realizes efficient regulation of the phase of the sound wave through an innovative maze structure design. The adjustable folding structure unit flexibly changes the propagation path of the sound wave in the maze channel by adjusting the length of the movable horizontal plate, thereby accurately controlling the phase delay of the sound wave. When the phase difference of the sound wave reaches π at the target frequency, the coding unit 0 or 1 can be stably generated, providing a reliable basis for sound wave coding.

[0154] Based on the above-mentioned adjustable folding structural unit, the tunable acoustic coding metasurface constructed by the present invention realizes flexible and efficient directional manipulation of sound beam splitting and sound focusing through the orderly arrangement of multiple adjustable folding structural units. Through the definition of the coding sequence, the position and coding unit of each adjustable folding structural unit in the tunable acoustic coding metasurface can be accurately controlled, and then a sound wave field matching the coding sequence can be generated at the target frequency. Not only does it overcome the problem of poor reconfigurability in the prior art, but it also reduces costs by reducing the use of complex systems, while maintaining a high degree of control accuracy and flexibility. The application of the tunable acoustic coding metasurface provided by the present invention will greatly expand the application field of sound wave control in the future and promote the development of acoustic technology.

[0155] It will be appreciated by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0156] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0157] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0158] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0159] The embodiments of the present invention are described above in conjunction with the accompanying drawings, but the present invention is not limited to the above-mentioned specific implementation methods. The above-mentioned specific implementation methods are merely illustrative and not restrictive. Under the enlightenment of the present invention, ordinary technicians in this field can also make many forms without departing from the scope of protection of the purpose of the present invention and the claims, which all fall within the protection of the present invention.

Claims

1. An adjustable folding structural unit, characterized in that: The adjustable folding structural unit adopts a maze structure, including a sound wave inlet, a sound wave outlet, and a maze channel formed by at least eight horizontal plates. After the sound wave enters the maze channel from the sound wave inlet, it propagates along a preset path to the sound wave outlet; By adjusting the length of at least one movable horizontal plate in the maze channel to change the propagation distance of the sound wave, the phase delay of the sound wave is controlled so that the phase difference of the sound wave reaches π at the target frequency, and the coding unit 0 or 1 can be generated.

2. The adjustable foldable structural unit according to claim 1, characterized in that: The adjustable foldable structural unit has a cavity inside, and at least eight transverse plates are arranged in the cavity, including: The bottom horizontal plate is fixed to the lowest end of the cavity and is provided with a bottom slit as an entrance for sound waves; Two top transverse plates, including a first top transverse plate and a second top transverse plate, are located at the top of the cavity and are opposite to the bottom transverse plate, and a top slit is provided between the first top transverse plate and the second top transverse plate as a sound wave outlet; a left transverse plate, located at the leftmost end of the cavity, connected to the first top transverse plate and the bottom transverse plate respectively; a right transverse plate, located at the rightmost end of the cavity and opposite to the left transverse plate, and connected to the second top transverse plate and the bottom transverse plate respectively; At least one movable horizontal plate, which passes through the left horizontal plate and is connected to and controlled by an external push-pull mechanism to extend or retract the movable horizontal plate; At least two fixed horizontal plates, respectively located above and below the movable horizontal plate, fixed to the inner surface of the right horizontal plate; Among them, at least 2mm air channels are left between the movable horizontal board, the fixed horizontal board, the left horizontal board, the right horizontal board, the bottom horizontal board and the top horizontal board.

3. The adjustable foldable structural unit according to claim 2, characterized in that: The external push-pull mechanism is connected to the movable horizontal plate through a through hole opened on the side of the adjustable folding structure unit.

4. A tunable acoustic coding metasurface, characterized in that: comprising a plurality of adjustable folding structural units as claimed in claim 1, wherein the plurality of adjustable folding structural units are arranged according to a coding sequence; The coding sequence is used to define the position and coding unit of each adjustable folded structural unit in the tunable acoustic coding metasurface; By adjusting the length of at least one movable horizontal plate in the maze channel of each adjustable folding structure unit to change the propagation distance of the sound wave, the phase difference of the sound wave reaches π at the target frequency, and a coding unit corresponding to the coding sequence can be generated.

5. The tunable acoustic coding metasurface according to claim 4, characterized in that: The acoustic beam is directionally steered by adjusting the ordering of the coding sequence.

6. The tunable acoustic coding metasurface according to claim 5, characterized in that: The method for directionally manipulating the acoustic beam by adjusting the order of the coding sequence comprises: vertically incident a plane wave onto the tunable acoustic coding metasurface; Using the tunable acoustic coding metasurface, encoding and modulating the plane wave according to a coding sequence, and calculating the far-field acoustic field distribution of the plane wave using a far-field function; According to the far-field acoustic field distribution of the plane wave, the length of at least one movable horizontal plate in each adjustable folded structural unit maze channel on the tunable acoustic coding metasurface is adjusted to generate a coding unit 0 or 1 to form a new coding sequence; The acoustic beamlets are directionally steered according to the new coding sequence.

7. The tunable acoustic coding metasurface according to claim 6, characterized in that: When the coding sequence is all coding unit 0 or all coding unit 1, the far field function is expressed as: （1）； In the formula, Indicates the far-field sound field distribution formed when the coding sequence is all coding unit 0 or all coding unit 1, represents the far-field elevation angle, represents the far field direction angle, C1 is a constant, representing the amplitude factor related to the sound field characteristics when the coding sequence is all coding unit 0 or all coding unit 1, represents the cosine function, represents the sine function, Indicates taking the absolute value, , No special meaning, , , represents the sound wave vector of air, represents the length of the adjustable folding structural unit; When the coding units 0 and 1 in the coding sequence are arranged alternately, and the coding sequence is 0101... / 0101..., ' / ' is a line break character, indicating a line break, and the far field function is expressed as: （2）； In the formula, represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are arranged alternately, C2 is a constant, representing the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are arranged alternately and the coding sequence is 0101... / 0101...; When the coding units 0 and 1 in the coding sequence are periodically arranged alternately, and the coding sequence is 0101... / 1010..., the far field function is expressed as: （3）； In the formula, It represents the far-field sound field distribution formed when the coding units 0 and 1 in the coding sequence are periodically alternately arranged. C3 is a constant, which represents the amplitude factor related to the sound field characteristics when the coding units 0 and 1 in the coding sequence are periodically alternately arranged and the coding sequence is 0101... / 1010...

8. The tunable acoustic coding metasurface according to claim 4, characterized in that: Acoustic focusing can be directionally manipulated by adjusting the ordering of the coding sequences and the number of adjustable folding structural units.

9. The tunable acoustic coding metasurface according to claim 7, characterized in that: The method for directionally manipulating acoustic focusing by adjusting the ordering of the coding sequence and the number of adjustable folding structural units comprises: Adjusting the length of at least one movable horizontal plate in the maze channel of the adjustable folding structure unit at the center position of the tunable acoustic coding metasurface to generate a coding unit 1; The length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the coding super-tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1; At the target frequency, the width of each region of the tunable acoustic coding metasurface and the number of adjustable folded structural units are adjusted to directionally manipulate the acoustic focusing at different focal positions.

10. The tunable acoustic coding metasurface according to claim 9, characterized in that: The length of at least one movable horizontal plate in the maze channel of the adjustable folded structure unit on both sides of the center position of the tunable acoustic coding metasurface is adjusted in sequence to alternately generate coding units 0 and 1, wherein when the sound is focused, when the focus is set on the central axis of the tunable acoustic coding metasurface, the calculation formula of the distance from the central axis of the tunable acoustic coding metasurface to different coding areas is expressed as: （4）； In the formula, x ±（i+1） represents the distance between the i+1th coding region on the left or the i+1th coding region on the right of the center of the tunable acoustic coding metasurface and the focal abscissa, λ represents the wavelength of the acoustic wave, where λ=c / f, c represents the speed of sound in air, f represents the target frequency, and f y The ordinate of the focus, where the subscript y has no actual physical meaning, and x ±i It shows the distance of the i-th coding region to the left of the center position of the tunable acoustic coding metasurface or the distance of the i-th coding region to the right of the focal point abscissa.

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