CN114543980B - Acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion - Google Patents

Abstract

The invention discloses a method for modulating sound wave phase and reconstructing a sound field based on near-field orbital angular momentum conversion, and belongs to the field of acoustic signal processing and sound field regulation. The invention realizes the orbital angular momentum conversion by utilizing the near-field coupling interaction between the evanescent acoustic vortex generated by the loudspeaker array in the rigid cylindrical waveguide tube and the acoustic vortex super-structure surface, and obtains the continuous modulation of the transmission sound wave transmission phase by rotating the loudspeaker array or the acoustic vortex super-structure surface. And obtaining the hologram complex amplitude distribution of the target acoustic image by using a point source algorithm, and correspondingly adjusting the driving voltage amplitude of the loudspeaker array at different pixel points and the rotation angle of the loudspeaker array or the acoustic vortex super-structure surface to reconstruct the target acoustic image. The method can break through the limitation of the self cut-off frequency of the waveguide tube on the minimum inner diameter of the pipeline, reduce the transverse size of the pixel point of the device with the acoustic geometric phase sound field reconstruction function to the size of the sub-wavelength, improve the information storage density of the device and effectively inhibit the adverse effect of high-order diffraction.

Description

Acoustic Phase Modulation and Acoustic Field Reconstruction Method Based on Near-field Orbital Angular Momentum Conversion

technical field

The invention relates to sound wave transmission phase modulation and free space sound field reconstruction, and belongs to the field of acoustic signal processing and sound field control.

Background technique

Acoustic field reconstruction and complex three-dimensional acoustic field regulation have a wide range of applications in the fields of particle manipulation, ultrasound imaging, medical diagnosis and virtual reality. At present, there are mainly two mature technical means to obtain complex three-dimensional sound fields in the laboratory and commercially: one is to use the integrated speaker array, and realize the amplitude and the driving voltage of the speaker at different pixel positions through electronic circuit design and computer programming. The point-by-point control of the phase, and then adjust the amplitude and phase of the sound field radiated by the speaker, and reconstruct the target sound field, which belongs to the active sound field control technology; the other is based on computer-made holograms, using appropriate physical models and algorithms to solve The spatial distribution function of the transmission and reflection coefficient of the acoustic holographic dry plate corresponding to the target acoustic field is obtained, and then the acoustic holographic dry plate that meets the requirements is prepared by designing a suitable pixel structure and combining mature 3D rapid prototyping technology, and finally reproduced under the irradiation of plane acoustic waves. Constructing the target sound field is a passive sound field control technology. However, the active sound field control technology based on a large-area integrated speaker array requires many signal channels to be controlled, the system composition is complex, the cost is high, and the sound pressure of the sound field obtained is limited, which limits its application in the fields of virtual display and particle manipulation. On the other hand, the passive sound field reconstruction technology based on the acoustic holographic dry plate is limited by the structural material and processing size, and the available working band is relatively limited.

In recent years, represented by metamaterials and metasurfaces, sound field reconstruction and sound field regulation schemes based on acoustic artificial structures have attracted extensive attention from academia and industry. Acoustic artificial structures have extremely high design flexibility and controllability. As an important research branch of metamaterials and metasurfaces, the core task of acoustic field regulation based on acoustic metasurfaces is to design Distributed acoustic holographic dry plate. At present, there are two main design schemes for the design of pixel units composed of acoustic holographic dry plates: one is a resonant artificial structure designed using structural resonance characteristics, such as the classic Helmholtz resonator structure (Helmholtz resonator); the other is based on Design of acoustic wave propagation phase control based on equivalent medium theory, such as space-folded thin curved acoustic waveguide structure (coiling-up spacestructure). The above scheme shows the following three defects in the actual implementation process: first, once the geometric parameters of the artificial acoustic structure are determined, its acoustic response characteristics cannot be changed, and it is difficult to apply to the scene of dynamically programmable sound field reconstruction; second, based on In the control of sound field scattering characteristics in the design of artificial acoustic structures, the phase and amplitude of the transflective sound field are often interrelated and cannot be adjusted independently, which will have a certain impact on the quality of the reconstructed sound field; third, most pixels based on geometric structure parameter optimization The working mechanism and principle of unit acoustic structure design methods are often not clear, and it usually needs to consume huge computing resources to determine the appropriate structural parameters. Therefore, how to propose a new technical solution to allow the artificial acoustic structure to achieve adjustable acoustic phase shift control through some simple and controllable methods, and the practical application and promotion of the sound field reconstruction and sound field control technology based on the acoustic artificial structure very important.

Contents of the invention

One of the objectives of the present invention is to provide an adjustable acoustic wave phase modulation method based on near-field orbital angular momentum conversion. Acoustic orbital angular momentum is a new degree of freedom independent of the amplitude and phase of the acoustic pressure field. In the process of converting between different orbital angular momentums through artificial acoustic structures, it is only necessary to rotate the artificial acoustic structures to obtain precise controllable and The modulated acoustic transmission is phase modulated, ie the acoustic geometric phase. The generation and adjustment process of the acoustic geometric phase has nothing to do with the specific form of the artificial acoustic structure, but only depends on the orbital angular momentum conversion process and rotation operation that the artificial acoustic structure can support. Therefore, the implementation of the acoustic wave phase modulation method based on orbital angular momentum conversion is simple and convenient, the design scheme of artificial structures is flexible and diverse, and the appropriate structural form can be selected for different working bands, which can improve the flexibility of acoustic wave transmission phase adjustment And improve the freedom of sound field control.

On this basis, one of the objectives of the present invention is to provide a sound field reconstruction method based on near-field orbital angular momentum conversion. Acoustic orbital angular momentum conversion is realized based on the near-field coupling interaction between the evanescent acoustic vortex sound source generated by the microspeaker array and the acoustic vortex metasurface, which can break through the limit of the waveguide's own cut-off frequency on the minimum inner diameter of the pipe, and significantly reduce the acoustic The geometric phase sound field reconstructs the lateral size of the pixel of the functional device to the sub-wavelength size, improves the information storage density of the device, effectively suppresses the adverse effects of high-order diffraction, and provides a sub-wavelength pixel, large viewing angle, and large information capacity. Sound field reconstruction method. In addition, the reconfigurable feature based on the pixel phase can significantly expand the sound field reconstruction method and expand different sound field reconstruction application scenarios, such as dynamically programmable sound field reconstruction and acoustic signal encryption.

The purpose of the present invention is achieved through the following technical solutions:

The adjustable acoustic wave phase modulation method based on near-field orbital angular momentum conversion disclosed by the present invention comprises the following steps:

Step 1: Place the loudspeaker array into a rigid cylindrical waveguide to generate high-quality evanescent acoustic vortices.

可以写成一系列不同加权系数声学涡旋本征波导模式的和，如式(1)所示：The evanescent acoustic vortex is a special form of the eigenmode of the acoustic vortex in a rigid cylindrical waveguide with a radius R. Typically, the acoustic field in a rigid cylindrical waveguide

It can be written as the sum of a series of acoustic vortex eigenwaveguide modes with different weighting coefficients, as shown in formula (1):

z为圆柱波导内的空间坐标；P_m,n为第(m,n)阶本征波导模式

的加权系数(即振幅)，j为虚数单位；J_m(k_m,nr)为第m阶柱贝塞尔函数；α_m,n是方程dJ_m(k_m,nr)/d(k_m,nr)|_r＝R＝J_m′(α_m,n)＝0第n阶根，故k_m,n＝α_m,n/R；

是轴向波矢大小，k₀为自由空间声波波矢量大小；

描述声学涡旋所携带的轨道角动量，其中m为拓扑荷数，又称TC(topological charge)。where r,

z is the spatial coordinate in the cylindrical waveguide; P _m,n is the (m,n)th order eigenwaveguide mode

The weighting coefficient (i.e. amplitude) of , j is the imaginary unit; J _m (k _m,n r) is the m-th order column Bessel function; α _m,n is the equation dJ _m (k _m,n r)/d( k _m,n r)| _r＝R ＝J _m ′(α _m,n )＝0th order root, so k _m,n ＝α _m,n /R;

is the axial wave vector size, k ₀ is the free space acoustic wave vector size;

Describe the orbital angular momentum carried by the acoustic vortex, where m is the topological charge, also known as TC (topological charge).

When k _m,n >k ₀ , the axial wave vector k _z is a pure imaginary number, and the vortex sound field decays exponentially along the +z axis, which is a typical evanescent field. At this time, the eigenmode of the acoustic vortex cannot propagate in the waveguide, that is, the evanescent acoustic vortex.

In order to obtain the evanescent acoustic vortex, preferably, the radius of the rigid cylindrical waveguide satisfies R<α _m,n /k ₀ , n=0.

扬声器阵列不同微型扬声器的驱动电压大小相等。In order to obtain high-quality evanescent acoustic vortex, it is preferred to use M×N micro-speakers to form a speaker array, where M=|m| is the topological charge (TC) of the evanescent acoustic vortex, and N is the speaker drive The phase discrete order of the voltage, the phase difference of the adjacent loudspeaker driving voltage is

The drive voltages for different microspeakers in the speaker array are equal.

In order to optimize and enhance the integration of the loudspeaker array, preferably, the topological charge size M of the evanescent acoustic vortex can be 1, 2 and 3, and the corresponding micro-speaker driving voltage phase discrete order N is 4, 3 and 3, The phase differences of the driving voltages of adjacent loudspeakers are 90°, 120° and 120° respectively.

In order to facilitate the installation of the speaker array, preferably, the micro-speakers in the speaker array are arranged at equal intervals along the angular direction, and the angular interval between adjacent speakers is

如式(2)所示：Preferably, in the subsequent steps, the evanescent vortex only has a unique topological charge, and the evanescent vortex produced by the loudspeaker array

As shown in formula (2):

Step 2: Design an acoustic vortex metasurface with specific topological charges.

The acoustic vortex metasurface has a settable topological charge. For the incident acoustic vortex, an additional orbital angular momentum increment can be introduced to change the topological charge of the transmitted acoustic vortex to realize the conversion of acoustic orbital angular momentum.

将上述扇形圆柱子单元按照透射声场相位大小，沿逆时针方向递增(拓扑荷数为K)或递减(拓扑荷数为-K)的方式周期排列，组成声学涡旋超构表面。The design method of the acoustic vortex metasurface: the cylindrical acoustic vortex metasurface with radius R is composed of K×L fan-shaped cylindrical subunits, where K is the topological charge of the acoustic vortex metasurface, and L is Subunits transmit discrete orders of phase in the sound field. By selecting a suitable acoustic structure and optimizing the geometric parameters, each fan-shaped cylinder has a specific phase and amplitude modulation coefficient of the transmitted acoustic field. The ideal subunit transmission amplitude is 1, and the transmission phase difference between two adjacent subunits is

According to the phase size of the transmitted sound field, the fan-shaped cylindrical subunits are arranged periodically in the counterclockwise direction in a manner of increasing (topological charge is K) or decreasing (topological charge is -K) to form an acoustic vortex metasurface.

Preferably, the number of fan-shaped cylindrical subunits is L≥4.

Preferably, the phase and amplitude of the sound field transmitted by the fan-shaped cylindrical subunit are as close to ideal values as possible.

Preferably, the magnitude K of the topological charge of the acoustic vortex metasurface is equal to the magnitude M of the topological charge of the evanescent acoustic vortex.

Step 3: Use the acoustic vortex metasurface of step 2 and the evanescent acoustic vortex of step 1 to realize the orbital angular momentum conversion process through near-field coupling interaction, and rotate the acoustic vortex metasurface to obtain the acoustic wave transmission phase from -180° to 180° continuous adjustment.

In the field of micro-nano optics, the conversion of photon spin angular momentum can be used to obtain the geometric phase related to the in-plane spatial orientation of micro-nano structural units, which can be realized by designing each micro-nano structural unit to rotate in a two-dimensional plane. Functions for complex light field shaping. It is known that the acoustic vortex can carry a specific orbital angular momentum. Therefore, based on the principle of momentum conservation, the idea of using spin angular momentum conversion in micro-nano optics to obtain geometric phase is extended to acoustics, and the acoustic orbital angular momentum is independent of the sound pressure. The degree of freedom of the field amplitude and phase is used to control the phase of the acoustic wave transmission by using the orbital angular momentum conversion process. This phase is also called the acoustic geometric phase.

In order to simplify the analysis, the evanescent acoustic vortex described in formula (2) is denoted as |m>. In step 2, the process of coupling the evanescent acoustic vortex sound field energy into a plane acoustic wave |0> by the acoustic vortex metasurface can be expressed as formula (3):

为声学涡旋超构表面的透射算符，θ_i为声学涡旋超构表面的初始角度。沿+z轴方向，将产生倏逝声学涡旋的扬声器阵列沿逆时针方向旋转

得到新的声场分布

此时旋转前后的坐标系之间满足r′＝r，

z′＝z。因此，旋转前后的涡旋声场满足式(4)：In formula (3),

is the transmission operator of the acoustic vortex metasurface, θ _i is the initial angle of the acoustic vortex metasurface. Along the +z axis, the loudspeaker array that creates the evanescent acoustic vortex is rotated counterclockwise

Get new sound field distribution

At this time, r′=r is satisfied between the coordinate systems before and after rotation,

z'=z. Therefore, the vortex sound field before and after rotation satisfies formula (4):

则式(3)变为：Simultaneously rotate the evanescent acoustic vortex and the acoustic vortex metasurface counterclockwise, the rotation angle is

Then formula (3) becomes:

Combining formula (3) and formula (5), we get:

即声学几何相位。根据运动的相对性，固定声学涡旋超构表面，沿逆时针方向将倏逝声学涡旋旋转

等价于固定倏逝声学涡旋超构表面，沿顺时针方向将声学涡旋超构表面

则此时透射平面声波所携带的相位调制为

由于透射平面声波信号的相移大小与扬声器阵列或编码超构表面旋转角度大小具有线性关系，因此能够显著提升声波相位调控的精度。Therefore, the transmission coefficient of the rotating acoustic vortex metasurface will get an additional phase

That is, the acoustic geometric phase. According to the relativity of motion, the acoustic vortex metasurface is fixed, and the evanescent acoustic vortex is rotated counterclockwise

Equivalent to a fixed evanescent acoustic vortex metasurface, moving the acoustic vortex metasurface clockwise

Then the phase modulation carried by the transmitted plane acoustic wave is

Since the phase shift of the transmitted plane acoustic wave signal has a linear relationship with the rotation angle of the loudspeaker array or the encoding metasurface, the accuracy of the acoustic wave phase regulation can be significantly improved.

Define the distance between the loudspeaker array that produces the evanescent acoustic vortex and the acoustic vortex metasurface as d, from formula (2), we can see that the expression of the amplitude of the sound field incident and coupled to the acoustic vortex metasurface at this time for:

When the interval d is larger, the average intensity of the acoustic field energy coupled into the acoustic vortex metasurface is lower, and the amplitude of the outgoing plane acoustic wave signal is also smaller.

In order to ensure the amplitude of the plane acoustic wave signal generated based on orbital angular momentum conversion, preferably, the distance between the loudspeaker and the acoustic vortex metasurface is below one working wavelength.

Step 4: The present invention also discloses a sound field reconstruction method based on orbital angular momentum conversion, which is realized based on the adjustable sound wave transmission phase modulation method based on near-field coupling acoustic orbital angular momentum conversion.

Acoustic orbital angular momentum is a degree of freedom independent of the amplitude and phase of the acoustic pressure field. The adjustable acoustic wave transmission phase regulation method based on orbital angular momentum conversion improves the dimension of sound field regulation. It only needs one-time design and does not need to readjust the acoustic artificial structure. Geometric parameters, by rotating the loudspeaker array or the metasurface of the acoustic vortex to generate the evanescent acoustic vortex, the pixel phase encoding of the sound field reconstruction function device is realized, which simplifies and reduces the complexity and difficulty of the realization of the sound field reconstruction function device.

In order to reduce the geometric size of the pixels of the sound field reconstruction function device and improve the pixel density and information storage capacity, the present invention uses the evanescent acoustic vortex sound source generated based on the micro-speaker array and the acoustic vortex metasurface through near-field coupling. The interaction achieves an acoustic orbital angular momentum transfer. In this method, the evanescent acoustic vortex can break through the limit of the waveguide's own cut-off frequency on the minimum inner diameter of the pipe, which can significantly reduce the lateral size of the pixel of the acoustic geometric phase sound field reconstruction function device to the sub-wavelength size, and improve the information storage density of the device. , effectively suppress the adverse effects of high-order diffraction, and improve the sound field quality and resolution of the reconstructed sound field.

The acoustic wave phase control method based on near-field acoustic orbital angular momentum conversion can perform phase independent and reconfigurable control at the pixel level. At this time, the transmission end of the waveguide is equivalent to an acoustic point source. According to the form of the sound field in the target space, combined with the point source The algorithm inversely solves the spatial phase and amplitude distribution of the acoustic hologram, adjusts the rotation angle of the encoded metasurface at different spatial positions correspondingly, and reconstructs the target sound field.

The steps of obtaining the target sound field hologram and reconstructing the target sound field by the point source algorithm are as follows:

假设声学全息平面位于z＝0，包含K′×L′个像素点，则声学全息平面上(k′,l′)像素点的声场为目标声学图像上所有点源沿-z方向辐射出的球面声波的叠加：1) It is known that the target acoustic image plane is located at z=Z _d , contains M′×N′ pixels, and each pixel is equivalently treated as an acoustic point source, (m′,n′) pixel P(X _{m ′} , Y _n′ , Z _d ), the amplitude and phase of A _{m′, n′} and

Assuming that the acoustic holographic plane is located at z=0 and contains K'×L' pixels, the sound field of the (k',l') pixel on the acoustic holographic plane is the radiation from all point sources on the target acoustic image along the -z direction Superposition of spherical acoustic waves:

为目标声学图像像素点(m′,n′)与目标声学全息图像素点(k′,l′)之间的距离。则目标全息图(k′,l′)像素点的振幅和相位分别为A_k′,l′＝abs[p(x_k′,y_l′,0)]和

abs和arg分别对应取幅值和取幅角数学算符。In formula (8)

is the distance between the target acoustic image pixel point (m′, n′) and the target acoustic hologram pixel point (k′, l′). Then the amplitude and phase of the target hologram (k′,l′) pixel point are A _k′,l′ =abs[p(x _k′ ,y _l′ ,0)] and

abs and arg correspond to the magnitude and argument mathematical operators, respectively.

There are two schemes for the specific implementation of the hologram: one is the complex amplitude hologram (the amplitude and phase of the pixel are modulated at the same time); the other is the phase hologram (only the phase value of the pixel is modulated), that is, all amplitudes are ignored. The encoded information (A _{k', l'} is a constant), only retains the phase encoding information. The above two hologram implementations can reconstruct the target sound field, but the complex amplitude type hologram can usually obtain better sound field reconstruction quality than the phase type hologram.

2) It is known that the sound wave propagation satisfies time-reversal symmetry, and the superposition of spherical sound waves radiated from the point source along the +z direction obtained by formula (8) can reconstruct the target acoustic image, namely:

为目标声学全息图像素点(k′,l′)与目标声学图像之间任意像素点的距离。A_k′,l′和

为全息图像素点的振幅大小和相位，并且：In formula (9)

is the distance between any pixel point between the target acoustic hologram pixel point (k′, l′) and the target acoustic image. A _k′,l′ and

is the amplitude and phase of the hologram pixel, and:

Among them, m is the topological charge of the evanescent acoustic vortex, θ _k′,l′ is the rotation angle of the loudspeaker array or the metasurface of the acoustic vortex in the (k′,l′)th pixel of the hologram. For the amplitude modulation A _k′,l′ , it can be seen from formula (7) that the amplitude of the sound field of the hologram pixel can be realized by changing the distance between the loudspeaker array and the acoustic vortex metasurface. In addition, it can also be realized by adjusting the driving voltage amplitude of the micro-speakers in the speaker array.

In addition, the reconfigurable feature of the pixel point phase can significantly expand the sound field reconstruction method and expand different sound field reconstruction application scenarios, such as dynamic programmable sound field reconstruction, that is, the micro speaker array is fixed to the stepping motor and other transmission devices, and through the computer The host computer program in the host sends commands to the motion controller to control the stepping motors at the corresponding pixel positions according to the rotation angles of the speaker arrays at different pixel positions obtained by formula (10), realizing the sound field reconstruction function of dynamic programming.

变为

此时重构目标声场P′(X,Y,Z_d)的表达式为：From formula (9), when the topological charge of the evanescent acoustic vortex changes from m to -m, the phase of the hologram pixel also changes from

becomes

At this time, the expression for reconstructing the target sound field P′(X, Y, Z _d ) is:

的点源沿-z方向辐射出的球面声波叠加得到的声场的共轭(强度分布与原目标声学图像相同)，此时重构出的目标声学图像位于z＝-Z_d，是一个虚像。因此，倏逝声学涡旋拓扑荷数的符号也可以对目标重构声场的特性进行操控。Where conj is to take the conjugate (conjugate). The sound field distribution described in formula (11) is composed of the amplitude distribution A _{k′, l′} (x _k′ , y _l′ ) and the phase distribution

The conjugate of the sound field obtained by the superposition of the spherical acoustic waves radiated from the point source along the -z direction (the intensity distribution is the same as the original target acoustic image), and the reconstructed target acoustic image is located at z=-Z _d , which is a virtual image. Therefore, the sign of the topological charge of the evanescent acoustic vortex can also manipulate the characteristics of the target reconstructed sound field.

Consider two acoustic images P ₁ (X,Y,Z _1,d ) (real image) and P ₂ (X,Y,-Z _2,d ) located at z=Z _1,d and z=-Z _2,d (virtual image), the sound fields of the two on the z=0 plane are superimposed to obtain:

p(x _k′ ,y _l′ ,0)=p ₁ (x _k′ ,y _l′ ,0)+p ₂ (x _k′ ,y _l′ ,0) (12)

in:

A_1,m′,n′和

分别为声学图像P₁(X,Y,Z_1,d)的(m′,n′)像素点P₁(X_m′,Y_n′,Z_1,d)的振幅和相位，A_2,m′,n′和

分别为声学图像P₂(X,Y,Z_2,d)的(m′,n′)像素点P₂(X_m′,Y_n′,Z_2,d)的振幅和相位。由式(11)知，当倏逝声学涡旋由m变为-m，则分别在z＝-Z_1,d和z＝Z_2,d获得共轭的目标声学图像conj[P₁(X,Y,Z_1,d)]和conj[P₂(X,Y,-Z_2,d)]。原先的实像P₁变成虚像conj(P₁)，而原来的虚像P₂则变成实像conj(P₂)。因此，通过上述方法设计得到的声学全息图，能够通过改变倏逝声学涡旋的拓扑荷数的符号实现全息图同侧不同声场的重现，提升声学全息图的信息存储容量，并在声学信号加密方面具有应用价值。and

A _1,m′,n′ and

are respectively the amplitude and phase of the (m′,n′) pixel point P ₁ (X _m′ ,Y _n′ ,Z _1,d ) of the acoustic image P ₁ (X,Y,Z _1,d ), A _{2, m',n'} and

are the amplitude and phase of the (m′,n′) pixel point P ₂ (X _m′ , Y _n′ , Z _2,d ) of the acoustic image P ₂ (X, Y, Z _2,d ), respectively. From _formula (11) _, when the evanescent acoustic vortex changes from m to -m, the conjugate target acoustic image conj[P ₁ (X ,Y,Z _1,d )] and conj[P ₂ (X,Y,-Z _2,d )]. The original real image P ₁ becomes the virtual image conj(P ₁ ), and the original virtual image P ₂ becomes the real image conj(P ₂ ). Therefore, the acoustic hologram designed by the above method can realize the reproduction of different sound fields on the same side of the hologram by changing the sign of the topological charge of the evanescent acoustic vortex, and improve the information storage capacity of the acoustic hologram. The encryption aspect has application value.

In order to obtain the best sound field reconstruction effect, preferably, the present invention uses complex amplitude holograms for sound field reconstruction.

In order to minimize the lateral size of the pixels and increase the pixel density of the device, preferably, a speaker array composed of 1×4 micro-speakers is used to generate an evanescent acoustic vortex as a signal source.

In order to facilitate the realization of the dynamic programmable sound field reconstruction function, preferably, the present invention realizes the modulation of the amplitude of the pixel point by changing the driving voltage amplitude of the micro-speaker.

In order to realize acoustic holographic image encryption and large-capacity acoustic information storage, preferably, the topological charge sign of the evanescent acoustic vortex can be realized by switching the sign of the driving voltage phase of the micro-speaker under the condition of keeping the voltage amplitude constant.

Beneficial effect:

1. The present invention discloses a sound wave phase modulation and sound field reconstruction method based on near-field orbital angular momentum conversion, which uses the orbital angular momentum conversion process to obtain the modulation of the acoustic transmission phase. Compared with the method of changing the geometric parameters of artificial acoustic structures, The method of realizing the phase modulation of acoustic transmission by rotating the artificial acoustic structure is simple and intuitive with high control precision.

2. A sound wave phase modulation and sound field reconstruction method based on near-field orbital angular momentum conversion disclosed in the present invention uses the evanescent acoustic vortex sound source generated by the micro-speaker array and the acoustic vortex metasurface to interact with each other through near-field coupling The function realizes the conversion of acoustic orbital angular momentum, significantly reduces the geometric size of pixels to sub-wavelength size, and improves pixel density and information storage capacity.

3. A sound wave phase modulation and sound field reconstruction method based on near-field orbital angular momentum conversion disclosed in the present invention uses a point source algorithm to obtain complex-amplitude holograms of different target acoustic images, and adjusts the amplitude of the speaker drive voltage and the loudspeaker The angle of rotation of the array or the acoustic vortex metasurface to obtain a high-quality reconstruction of the acoustic image of the target.

4. An acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion disclosed in the present invention, through acoustic hologram design and changing the sign of the evanescent acoustic vortex topological charge, reconstructing different acoustic images , compared with the traditional acoustic holographic sound field reconstruction technology, it can realize the encryption of the acoustic signal and improve the information storage capacity.

Description of drawings

Fig. 1 is a schematic diagram of the device principle of the acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion disclosed by the present invention;

Fig. 2 is the flowchart of the sound wave phase modulation and sound field reconstruction method based on near-field orbital angular momentum conversion disclosed by the present invention;

Fig. 3 is a schematic diagram of an acoustic vortex metasurface, wherein: Fig. 3 (a) is a structural schematic diagram of an acoustic vortex metasurface, and Fig. 3 (b) is a structural schematic diagram of a fan-shaped cylindrical subunit;

Fig. 4 is the acoustic response of the fan-shaped cylinder on the acoustic vortex metasurface, wherein: Fig. 4 (a) is the transmission phase curve of different fan-shaped cylinders, and Fig. 4 (b) is the transmission amplitude curve of different fan-shaped cylinders;

5 is a schematic structural diagram of the basic pixel unit of the acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion disclosed by the present invention;

Among them: 1─speaker array, 2─acoustic vortex metasurface, 3─waveguide;

Fig. 6 is a change diagram of the transmission phase of the transmitted acoustic wave as the rotation angle of the vortex metasurface changes;

Fig. 7 is the acoustic field result of the acoustic hologram in the example of the present invention, wherein: Fig. 7 (a) is the schematic diagram of the target acoustic image reconstructed by the acoustic hologram, Fig. 7 (b) is the normalized amplitude of the acoustic hologram, Fig. 7 ( c) is the phase of the acoustic hologram, and Fig. 7(d) is the energy distribution of the sound field of the reconstructed target acoustic image.

Fig. 8 is the result of two different acoustic holographic sound fields based on topological charge switching in the example of the present invention. Among them: Figure 8(a) is a schematic diagram of reconstructing the "heart" sound field when the topological charge of the evanescent acoustic vortex is 1, and Figure 8(b) is when the topological charge of the evanescent acoustic vortex is -1 The schematic diagram of reconstructing the "star" sound field, Fig. 8(c) is the normalized amplitude, phase and intensity distribution of the reconstructed sound field of the acoustic hologram.

detailed description

In order to better illustrate the purpose and advantages of the present invention, the present invention will be further described below in conjunction with the accompanying drawings and examples.

Example 1

As shown in Figure 1, this embodiment discloses a sound wave phase modulation and sound field reconstruction method based on near-field orbital angular momentum conversion, using the evanescent acoustic vortex and acoustic vortex generated by the speaker array in the rigid cylindrical waveguide The near-field coupling interaction of the metasurface realizes the conversion of the orbital angular momentum, and the modulation of the transmission phase of the transmitted acoustic wave is obtained through the rotating speaker array or the acoustic vortex metasurface. Using the point source algorithm, the complex amplitude distribution of the hologram of the target acoustic image is obtained, and the driving voltage amplitude of the speaker array at different pixel points and the rotation angle of the speaker array/acoustic vortex metasurface are correspondingly adjusted to reconstruct the target acoustic image.

As shown in Figure 2, a method for acoustic phase modulation and acoustic field reconstruction based on near-field orbital angular momentum conversion disclosed in this embodiment, the specific implementation steps are as follows:

Step 1: Place the loudspeaker array into a rigid cylindrical waveguide to generate high-quality evanescent acoustic vortices.

Use 4 micro-speakers with a diameter of 10mm, arrange them in a 2×2 square grid array and fix them on a sound-absorbing sponge with a diameter of 40mm, set the distance between the speakers at 15mm, and use a function signal generator to generate 4-way amplitude The same but independent sinusoidal voltage signals drive the microspeaker array synchronously. The frequency of the sinusoidal voltage signal is 2858Hz, and along the counterclockwise direction, the driving electrical signals corresponding to the four microspeakers have 0°, 90°, and 180° in turn. and 270° phase shift.

The loudspeaker array is placed in a rigid acrylic cylindrical waveguide with an inner diameter of 40 mm and a length of 120 mm to generate an evanescent acoustic vortex sound source with a topological charge of 1.

Step 2: Design an acoustic vortex metasurface with a topological charge equal to the topological charge of the evanescent acoustic vortex source.

The medium of the working environment of the acoustic vortex metasurface is air, its density and sound velocity are 1.21kg/m ³ and 343m/s respectively, the frequency f ₀ of the incident sound wave is 2858Hz, and the corresponding wavelength λ ₀ is about 12cm. The material of the acoustic vortex metasurface is photosensitive resin, and other materials with a large difference in acoustic impedance from air can also be selected, such as nylon, ABS plastic, metal, etc.

As shown in Fig. 3(a), preferably, the acoustic vortex metasurface is composed of twelve fan-shaped cylindrical subunits.

As shown in Figure 3(b), as a preference, the fan-shaped cylindrical subunit is composed of a coaxial cylindrical surface with a thickness dR of 15mm and a solid cylinder with a radius r of 3mm at the center, and the height H of the fan-shaped column is 75mm. The columns are separated by connecting plates with a thickness of 1.5 mm and connected to a solid cylinder with a central radius r of the metasurface of 3 mm, so the diameter of the coded metasurface is 40 mm, which coincides with the inner diameter of the transmission pipeline. Each fan-shaped column contains four identical circular resonant cavities along the axial direction. The wall thickness of the circular resonant cavity is 1.5mm, and the width is Adjustment of the sound wave phase.

The twelve fan-shaped cylindrical subunits that make up the vortex metasurface have a transmission amplitude of nearly 1 (as shown in Figure 4(a)) and a transmission phase magnitude of -180° to 150° with a discrete step of 30° (Figure 4(b)). Therefore, a vortex metasurface with a topological charge of 1 or -1 can be obtained by arranging the fan-shaped pillar units counterclockwise or clockwise according to the magnitude of the transmission phase.

Step 3: The acoustic vortex metasurface and the adjacent evanescent acoustic vortex realize the orbital angular momentum conversion process through the near-field coupling interaction, and the rotating acoustic vortex metasurface obtains continuous control of the acoustic wave transmission phase from -180° to 180° .

The loudspeaker array that generates the evanescent acoustic vortex sound source in step 1 and the acoustic vortex metasurface in step 2 are adjacently placed in a rigid acrylic cylindrical waveguide to form a pixel unit, as shown in Figure 5. The coupling interaction between the evanescent acoustic vortex and the acoustic vortex metasurface generates a plane acoustic wave with a topological charge of 0 at the transmission end and continues to propagate forward in the waveguide.

Taking the central symmetry axis in the long axis direction of the cylindrical waveguide as the rotation axis, the acoustic vortex metasurface is rotated clockwise along the sound wave propagation direction or the loudspeaker array is rotated counterclockwise. At this time, the phase change of the transmitted plane acoustic wave is equal to the product of the rotation angle and the topological charge of the evanescent acoustic vortex.

The interaction between the evanescent acoustic vortex sound source with a topological charge of 1 and the acoustic vortex metasurface with a topological charge of 1 is used to obtain phase modulation of acoustic transmission, and the amount of change in the acoustic wave transmission phase is equal to that of the acoustic vortex metasurface Rotation angle, as shown in Figure 6.

Step 4: Using the point source algorithm, the spatial distribution of the normalized amplitude and phase of the pixels of the complex amplitude hologram is obtained.

Select the target acoustic image "lemon", assuming it is located at a position 10λ _{0 in front of the plane of the acoustic hologram, and the spatial geometric size of the acoustic image is 15λ 0 ×} 15λ ₀ , the number of pixels is 100×100, and the size of each pixel is is 0.15λ ₀ , where λ ₀ is the central working wavelength of the acoustic vortex metasurface. The pixel size of the acoustic hologram is set to 0.5λ ₀ , and the number of pixels is 50×50, so the spatial size of the acoustic hologram is 25λ ₀ ×25λ ₀ .

作为独立的声学点源辐射出球面声波，沿-z方向传播到位于原点处的声学全息图平面，其中A_m′,n′和

分别为目标图像像素点的振幅和相位。由于目标声学图像设定为仅具有空间强度分布的二维图像，因此

为0或随机噪声。The (m′,n′)th pixel on the target image

Spherical acoustic waves are radiated as independent acoustic point sources, and propagate along the -z direction to the plane of the acoustic hologram at the origin, where A _m′,n′ and

are the amplitude and phase of the target image pixel, respectively. Since the target acoustic image is set to be a two-dimensional image with only spatial intensity distribution, so

is 0 or random noise.

The phase of the target image pixel

The total sound field obtained by superimposing all pixels of the target image on the (k′,l′)th pixel on the acoustic holographic plane is:

为目标声学图像像素点(m′,n′)与目标声学全息图像素点(k′,l′)之间的距离，像素点个数M′＝N′＝100,目标声学图像和声学全息平面的距离Z_d＝10λ₀。In formula (8)

is the distance between the target acoustic image pixel (m′, n′) and the target acoustic hologram pixel (k′, l′), the number of pixels M′=N′=100, the target acoustic image and the acoustic hologram The distance Z _d =10λ ₀ of the plane.

abs和arg分别对应取幅值和取幅角数学算符。Since sound wave propagation satisfies time-reversal symmetry, the sound field at the acoustic holographic plane obtained by Eq. (8) should be the same as the sound field radiated by the acoustic hologram. Therefore, the amplitude and phase of the target hologram (k′,l′) pixel are respectively A _k′,l′ = abs[p(x _k′ ,y _l′ ,0)] and

abs and arg correspond to the magnitude and argument mathematical operators, respectively.

Step 5: Adjust the driving voltage amplitude of the speaker array and rotate the speaker array or the acoustic vortex metasurface, correspond the normalized amplitude and phase of the pixels with the complex amplitude hologram obtained in step 4, and reconstruct the target sound field .

如果选择固定声学涡旋超构表面不动而旋转扬声器阵列，则扬声器阵列的旋转角度为

Figure 7(a) is a schematic diagram of reconstructing the target acoustic image from the acoustic hologram, and the dotted line box is a partially enlarged image of the acoustic hologram. The spatial orientation realizes the phase modulation of the pixel point, and the rotation angle of the acoustic vortex metasurface of the pixel point is

If you choose to fix the acoustic vortex metasurface and rotate the speaker array, the rotation angle of the speaker array is

Based on the amplitude (Fig. 7(b)) and phase (Fig. 7(c)) information of the complex amplitude hologram obtained in step 4, set the normalized amplitude and phase of different pixels of the acoustic hologram, and finally reconstruct the The energy distribution of the acoustic holographic sound field is shown in Fig. 7(d), and the target acoustic image "lemon" can be clearly identified.

In summary, this example provides an acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion, which is realized by the near-field coupling interaction between the evanescent acoustic vortex and the acoustic vortex metasurface The orbital angular momentum conversion process obtains a continuous controllable modulation of the acoustic transmission phase. Using the point source algorithm, the complex amplitude distribution of the hologram of the target acoustic image is obtained, and the driving voltage amplitude of the speaker array at different pixel points and the rotation angle of the speaker array/acoustic vortex metasurface are correspondingly adjusted to reconstruct the target acoustic image.

Example 2

The acoustic hologram is designed, and the reconstruction of different target acoustic images is realized by switching the sign of the topological charge of the evanescent acoustic vortex.

As shown in Figure 2, this embodiment includes the following steps:

Step 1: Place the loudspeaker array into a rigid cylindrical waveguide to generate high-quality evanescent acoustic vortices.

Use 4 micro-speakers with a diameter of 10mm, arrange them in a 2×2 square grid array and fix them on a sound-absorbing sponge with a diameter of 40mm, set the distance between the speakers at 15mm, and use a function signal generator to generate 4-way amplitude The same but independent sinusoidal voltage signals drive the microspeaker array synchronously. The frequency of the sinusoidal voltage signal is 2858Hz, and along the counterclockwise direction, the driving electrical signals corresponding to the four microspeakers have 0°, 90°, and 180° in turn. and 270° phase shift.

The loudspeaker array is placed in a rigid acrylic cylindrical waveguide with an inner diameter of 40 mm and a length of 120 mm to generate an evanescent acoustic vortex sound source with a topological charge of 1.

Change the initial phase shift of four microspeaker drive voltages from 0°, 90°, 180° and 270° to 0°, -90°, -180° and -270° or 270°, 180°, 90° and 0°, the topological charge of the evanescent acoustic vortex can be switched from 1 to -1.

Step 2: Design an acoustic vortex metasurface with a topological charge equal to the topological charge of the evanescent acoustic vortex source.

The medium of the working environment of the acoustic vortex metasurface is air, its density and sound velocity are 1.21kg/m ³ and 343m/s respectively, the frequency f ₀ of the incident sound wave is 2858Hz, and the corresponding wavelength λ ₀ is about 12cm. The material of the acoustic vortex metasurface is photosensitive resin, and other materials with a large difference in acoustic impedance from air can also be selected, such as nylon, ABS plastic, metal, etc.

As shown in Fig. 3(a), preferably, the acoustic vortex metasurface is composed of twelve fan-shaped cylindrical subunits.

As shown in Figure 3(b), as a preference, the fan-shaped cylindrical subunit is composed of a coaxial cylindrical surface with a thickness dR of 15mm and a solid cylinder with a radius r of 3mm at the center, and the height H of the fan-shaped column is 75mm. The columns are separated by connecting plates with a thickness of 1.5 mm and connected to a solid cylinder with a central radius r of 3 mm on the metasurface. Each fan-shaped column contains four identical circular resonant cavities along the axial direction. The wall thickness of the circular resonant cavity is 1.5mm, and the width is Adjustment of the sound wave phase.

The twelve fan-shaped cylindrical subunits that make up the vortex metasurface have a transmission amplitude of nearly 1 (as shown in Figure 4(a)) and a transmission phase magnitude of -180° to 150° with a discrete step of 30° (Figure 4(b)). Therefore, a vortex metasurface with a topological charge of 1 can be obtained by arranging the fan-shaped pillar units in sequence according to the size of the transmission phase.

Step 3: The acoustic vortex metasurface and the adjacent evanescent acoustic vortex realize the orbital angular momentum conversion process through the near-field coupling interaction, and the rotating acoustic vortex metasurface obtains continuous control of the acoustic wave transmission phase from -180° to 180° .

The loudspeaker array that generates the evanescent acoustic vortex sound source in step 1 and the acoustic vortex metasurface in step 2 are adjacently placed in a rigid acrylic cylindrical waveguide to form a pixel unit, as shown in Figure 5. The evanescent acoustic vortex and the acoustic vortex metasurface generate a plane acoustic wave with zero topological charge at the transmission end through the coupling interaction, and continue to propagate forward in the waveguide.

Taking the central symmetry axis in the long axis direction of the cylindrical waveguide as the rotation axis, the acoustic vortex metasurface is rotated clockwise along the sound wave propagation direction or the loudspeaker array is rotated counterclockwise. At this time, the phase change of the transmitted plane acoustic wave is equal to the product of the rotation angle and the topological charge of the evanescent acoustic vortex.

The interaction between the evanescent acoustic vortex sound source with a topological charge of 1 and the acoustic vortex metasurface with a topological charge of 1 is used to obtain phase modulation of acoustic transmission, and the amount of change in the acoustic wave transmission phase is equal to that of the acoustic vortex metasurface Rotation angle, as shown in Figure 6.

Step 4: Using the point source algorithm, the spatial distribution of the normalized amplitude and phase of the pixels of the complex amplitude hologram is obtained.

Select the "heart" and "star" patterns as the target image, assuming that the plane of the acoustic hologram is located at the origin, the "heart" pattern is located _at the position 10λ0 in front of the plane of the acoustic hologram, and the "star" pattern is located behind the plane of the acoustic hologram 10λ ₀ , and the spatial geometric dimensions of the two acoustic images are both 15λ ₀ ×15λ ₀ , the number of pixels is 100×100, and the size of each pixel is 0.15λ ₀ , where λ ₀ is the The central operating wavelength of the acoustic vortex metasurface. The spatial size of the acoustic hologram is 25λ ₀ ×25λ ₀ , the number of pixels is 50×50, and the pixel size is set to 0.5λ ₀ .

沿-z方向辐射并传播的球面波和“星”型目标声学图像的像素点

沿+z方向辐射并传播的球面波在z＝0平面上的声场叠加得到：Pixels of the acoustic image of the "heart" target

Spherical waves radiating and propagating in the -z direction and pixel points of the acoustic image of the "star" target

The sound field superposition of the spherical wave radiating and propagating along the +z direction on the z=0 plane is obtained:

p(x _k′ ,y _l′ ,0)=p ₁ (x _k′ ,y _l′ ,0)+p ₂ (x _k′ ,y _l′ ,0) (12)

in:

i＝1,2。A_1,m′,n′和

分别为声学图像P₁(X,Y,Z_1,d)的(m′,n′)像素点P₁(X_m′,Y_n′,Z_1,d)的振幅和相位，A_2,m′,n′和

分别为声学图像P₂(X,Y,Z_2,d)的(m′,n′)像素点P₂(X_m′,Y_n′,Z_2,d)的振幅和相位。and

i=1,2. A _1,m′,n′ and

are respectively the amplitude and phase of the (m′,n′) pixel point P ₁ (X _m′ ,Y _n′ ,Z _1,d ) of the acoustic image P ₁ (X,Y,Z _1,d ), A _{2, m',n'} and

are the amplitude and phase of the (m′,n′) pixel point P ₂ (X _m′ , Y _n′ , Z _2,d ) of the acoustic image P ₂ (X, Y, Z _2,d ), respectively.

abs和arg分别对应取幅值和取幅角数学算符。The amplitude and phase of the target hologram (k′,l′) pixel point are respectively A _k′,l′ = abs[p(x _k′ ,y _l′ ,0)] and

abs and arg correspond to the magnitude and argument mathematical operators, respectively.

Step 5: Adjust the driving voltage amplitude of the loudspeaker array and rotate the acoustic vortex metasurface, and correspond the normalized amplitude and phase of the pixel to the complex amplitude hologram obtained in step 4. By changing the topological charge of the evanescent acoustic vortex sound source, different target sound fields are reconstructed.

基于步骤4所得到的复振幅全息图的振幅(见图8(c)(左图))，当倏逝声学涡旋的拓扑荷数为1时(扬声器阵列的4个微型扬声器相对应驱动电信号依次具有0°，90°，180°和270°相移)，全息图像素点的相位如图8(c)(中上)所示。设置好声学全息图不同像素点的归一化振幅和相位，最终重构出的声学全息声场的能量分布如图8(c)(右上)所示，可以清晰地辨认出“心”型目标声学图像。Figure 8(a) is a schematic diagram of reconstructing the acoustic image of a "heart"-shaped target from an acoustic hologram. The dashed box is a partially enlarged image of the acoustic hologram. The textured surface changes its spatial orientation to realize the phase modulation of the pixel point, and the rotation angle of the acoustic vortex metasurface of the pixel point is

Based on the amplitude of the complex amplitude hologram obtained in step 4 (see Fig. 8(c) (left figure)), when the topological charge of the evanescent acoustic vortex is 1 (the four micro-speakers of the speaker array correspond to the driving voltage The signals have phase shifts of 0°, 90°, 180° and 270° in turn), and the phases of the hologram pixels are shown in Fig. 8(c) (top middle). After setting the normalized amplitude and phase of different pixels of the acoustic hologram, the energy distribution of the finally reconstructed acoustic holographic sound field is shown in Figure 8(c) (upper right). image.

基于步骤4所得到的复振幅全息图的振幅(见图8(c)(左图))，当倏逝声学涡旋的拓扑荷数为-1时(扬声器阵列的4个微型扬声器相对应驱动电信号依次具有0°，-90°，-180°和-270°相移)，全息图像素点的相位如图8(c)(中下)所示，该相位分布为图8(c)(中上)的共轭。设置好声学全息图不同像素点的归一化振幅和相位，最终重构出的声学全息声场的能量分布如图8(c)(右下)所示，可以清晰地辨认出“星”型目标声学图像。Figure 8(b) is a schematic diagram of reconstructing the acoustic image of a "star"-shaped target from an acoustic hologram. The dotted box is a partially enlarged image of the acoustic hologram. The surface changes its spatial orientation to realize pixel phase modulation, and the rotation angle of the acoustic vortex metasurface of the pixel is the same as that in Fig. 8(a), which is still

Based on the amplitude of the complex amplitude hologram obtained in step 4 (see Figure 8(c) (left figure)), when the topological charge of the evanescent acoustic vortex is -1 (the four micro-speakers of the speaker array correspond to drive The electrical signal has 0°, -90°, -180° and -270° phase shift in turn), the phase of the hologram pixel point is shown in Fig. 8(c) (middle bottom), and the phase distribution is Fig. 8(c) (middle upper) conjugate. After setting the normalized amplitude and phase of different pixels of the acoustic hologram, the energy distribution of the finally reconstructed acoustic holographic sound field is shown in Figure 8(c) (lower right), and the "star" target can be clearly identified Acoustic image.

In summary, this example provides an acoustic wave phase modulation and acoustic field reconstruction method based on near-field orbital angular momentum conversion, which is realized by the near-field coupling interaction between the evanescent acoustic vortex and the acoustic vortex metasurface The orbital angular momentum conversion process obtains a continuous controllable modulation of the acoustic transmission phase. Then use the point source algorithm to obtain the complex amplitude distribution of the hologram under the superimposition of two target acoustic images, correspondingly adjust the driving voltage amplitude of the loudspeaker array at different pixel points and the rotation angle of the acoustic vortex metasurface, and finally adjust the evanescent The acoustic vortex topological charge (1 or -1) reconstructs different target acoustic images.

The specific description above further elaborates the purpose, technical solution and beneficial effect of the invention. It should be understood that the above description is only a specific embodiment of the present invention and is not used to limit the protection of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims (5)

1. The adjustable sound wave phase modulation method based on near-field orbital angular momentum conversion is characterized by comprising the following steps of: comprises the following steps of (a) preparing a solution,

the method comprises the following steps: placing the speaker array into a rigid cylindrical waveguide to generate a high-quality evanescent acoustic vortex;

the first implementation method of the method is that,

the evanescent acoustic vortex is a special form of an acoustic vortex eigenmode in a rigid cylindrical waveguide with the radius of R; acoustic field in rigid cylindrical waveguides in general

The sum of a series of different weighting factor acoustic vortex eigenwaveguide modes can be written as shown in equation (1):

in the formula, r is a group of a,

z is a spatial coordinate within the cylindrical waveguide; p is _m,n Is an (m, n) th order intrinsic waveguide mode

J is an imaginary number unit; j is a unit of _m (k _m,n r) is a Bssel function of the mth order; alpha (alpha) ("alpha") _m,n Is equation dJ _m (k _m,n r)/d(k _m,n r)| _r＝R ＝J _m ′(α _m,n ) =0 nth root, so k _m,n ＝α _m,n /R；

Is the magnitude of the axial wave vector, k ₀ The vector magnitude of the acoustic wave in free space;

describing orbital angular momentum carried by the acoustic vortices, wherein m is the topological charge number;

when k is _m,n ＞k ₀ Time, axial wave vector k _z The acoustic field is a pure imaginary number, and the field of the vortex sound field is exponentially attenuated along the direction of the + z axis, so that the acoustic field is a typical evanescent field; at the moment, the intrinsic mode of the acoustic vortex cannot be transmitted in the waveguide, namely the acoustic vortex is evanescent;

to obtain evanescent acoustic vortices, the radius of the rigid cylindrical waveguide is such that R < alpha _m,n /k ₀ ，n＝0；

In order to obtain high-quality evanescent acoustic vortices, a loudspeaker array is formed by using M multiplied by N miniature loudspeakers, wherein M = | M | is the topological charge size of the evanescent acoustic vortices, N is the phase discrete order of the loudspeaker driving voltage, and the phase difference of the driving voltages of the adjacent loudspeakers is

The driving voltages of different micro loudspeakers of the loudspeaker array are equal;

in order to optimize and improve the integration degree of the loudspeaker array, the topological charge number M of the evanescent acoustic vortex is 1,2 and 3, the phase discrete order N of the corresponding driving voltage of the micro loudspeaker is 4,3 and 3, and the phase difference of the driving voltages of the adjacent loudspeakers is 90 degrees, 120 degrees and 120 degrees respectively;

in order to facilitate the installation of the loudspeaker array, the micro loudspeakers in the loudspeaker array are arranged at equal intervals along the angular direction, and the angular interval between the adjacent loudspeakers is

In the subsequent steps, the evanescent sound vortex only has unique topological charge number, and the evanescent sound vortex generated by the loudspeaker array has unique topological charge number

As shown in formula (2):

step two: designing an acoustic vortex superstructure surface with a specific topological charge number;

step three: using the acoustic vortex ultrastructural surface in the step two and the evanescent acoustic vortex in the step one to realize an orbital angular momentum conversion process through near field coupling interaction, and rotating the acoustic vortex ultrastructural surface to obtain continuous regulation and control of a sound wave transmission phase from-180 degrees to 180 degrees;

the third step is to realize the method as follows,

in the field of micro-nano optics, a geometric phase related to the in-plane space orientation of the micro-nano structure units can be obtained by utilizing the conversion of photon spin angular momentum, and the function of shaping a complex light field can be realized by designing the rotation orientation of each micro-nano structure unit in a two-dimensional plane; given that an acoustic vortex can carry specific orbital angular momentum, the idea of obtaining a geometric phase by utilizing spin angular momentum conversion in micro-nano optics is popularized to acoustics based on the momentum conservation principle, the acoustic orbital angular momentum is used as a degree of freedom independent of the amplitude and the phase of a sound pressure field, and the regulation and control of a sound wave transmission phase are obtained by utilizing the orbital angular momentum conversion process; this phase is also referred to as the acoustic geometric phase;

to simplify the analysis, the evanescent acoustic vortex described by equation (2) is denoted as | m >; the process of coupling evanescent acoustic vortex sound field energy into a planar sound wave |0> by the acoustic vortex ultrastructure surface in the second step can be expressed as formula (3):

in the formula (3), the reaction mixture is,

transmission operator, theta, for acoustic vortex surfaces _i Is the initial angle of the acoustic vortex superstructure surface; along the + z axis, evanescent acoustics will be generatedVortex speaker array rotating in counter-clockwise direction

Obtaining a new sound field distribution

R' = r is satisfied between the coordinate systems before and after the rotation at this time,

z' = z; therefore, the vortex sound field before and after rotation satisfies equation (4):

simultaneously rotating evanescent acoustic vortex and acoustic vortex super-structure surface along the counterclockwise direction, wherein the rotating angle is

Equation (3) becomes:

combining formula (3) and formula (5), yielding:

therefore, the transmission coefficient of the rotating acoustic vortex ultrastructure surface obtains an additional phase

Namely the acoustic geometric phase; fixing the acoustic vortex metamorphic surface according to the relativity of motion, and rotating the evanescent acoustic vortex in the counterclockwise direction

Rotating the acoustic vortex super-structured surface in a clockwise direction, equivalent to a fixed evanescent acoustic vortex

The phase modulation carried by the transmitted plane acoustic wave at this time is

Because the phase shift of the transmission plane sound wave signal has a linear relation with the rotation angle of the surface of the loudspeaker array or the acoustic vortex superstructure, the precision of sound wave phase regulation can be obviously improved;

defining the distance d between the loudspeaker array generating the evanescent acoustic vortex and the acoustic vortex super-structure surface, and obtaining an expression of the sound field amplitude incident and coupled to the acoustic vortex super-structure surface from equation (2):

when the interval d is larger, the average intensity of the sound field energy coupled into the acoustic vortex ultrastructural surface is lower, and the amplitude of the emergent plane sound wave signal is smaller.

2. The adjustable acoustic wave phase modulation method based on near-field orbital angular momentum conversion according to claim 1, wherein: the second step is realized by the method that,

the acoustic vortex ultrastructure surface has settable topological charge, and the topological charge of the transmission acoustic vortex can be changed by introducing additional orbital angular momentum increment aiming at the incident acoustic vortex so as to realize acoustic orbital angular momentum conversion;

the design method of the acoustic vortex ultrastructural surface comprises the following steps: the cylindrical acoustic vortex ultrastructural surface with the radius of R consists of K multiplied by L fan-shaped cylindrical subunits, wherein K is the topological charge number of the acoustic vortex ultrastructural surface, and L is the transmission sound field phase of the subunitsDiscrete order of (a); by selecting a proper acoustic structure and optimizing geometric parameters, each sector cylinder has a specific phase and amplitude modulation coefficient of a transmission sound field, the transmission amplitude of an ideal subunit is 1, and the transmission phase difference between two adjacent subunits is

And periodically arranging the fan-shaped cylindrical subunits in an increasing or decreasing mode along the counterclockwise direction according to the phase size of the transmission sound field to form an acoustic vortex ultrastructure surface.

3. The adjustable acoustic phase modulation method based on near-field orbital angular momentum conversion according to claim 2, wherein: in the second step of the method, the first step of the method,

the number L of the fan-shaped cylindrical subunits is more than or equal to 4;

the phase and amplitude of the transmission sound field of the fan-shaped cylindrical subunit are as close to ideal values as possible;

the topological charge number K of the acoustic vortex super-structure surface is equal to the topological charge number M of the evanescent acoustic vortex.

4. The adjustable acoustic wave phase modulation method based on near-field orbital angular momentum conversion according to claim 1, wherein: in order to ensure the amplitude of the plane sound wave signal generated based on orbital angular momentum conversion, the distance between the loudspeaker and the surface of the acoustic vortex superstructure is below one working wavelength.

5. An acoustic field reconstruction method based on orbital angular momentum conversion is realized based on the adjustable acoustic wave phase modulation method based on near-field orbital angular momentum conversion according to claim 1,2, 3 or 4, and is characterized in that: the method also comprises a fourth step of,

the acoustic orbital angular momentum is used as a degree of freedom independent of amplitude and phase of a sound pressure field, the dimension of sound field regulation is improved by the adjustable sound wave transmission phase regulation method based on orbital angular momentum conversion, only one-time design is needed, geometric parameters of an acoustic artificial structure do not need to be adjusted again, encoding of pixel point phases of a sound field reconstruction function device is achieved through a loudspeaker array or an acoustic vortex super-structure surface which generates evanescent acoustic vortices in a rotating mode, and complexity and difficulty of realization of the sound field reconstruction function device are simplified and reduced;

in order to reduce the geometric size of pixel points of a sound field reconstruction function device and improve the density and information storage capacity of the pixel points, an evanescent acoustic vortex sound source generated based on a micro loudspeaker array and an acoustic vortex super-structure surface are adopted to realize acoustic orbit angular momentum conversion through near-field coupling interaction; the evanescent acoustic vortex can break through the limitation of the self cut-off frequency of the waveguide tube on the minimum inner diameter of the waveguide tube, can remarkably reduce the transverse dimension of a pixel point of a device with the acoustic geometric phase sound field reconstruction function to the size of a sub-wavelength, improves the information storage density of the device, effectively inhibits the adverse effect of high-order diffraction, and improves the sound field quality and the resolution of a reconstructed sound field;

the acoustic wave phase regulation and control method based on near-field acoustic orbit angular momentum conversion can perform phase independent and reconfigurable regulation and control at pixel point level, at the moment, a waveguide tube transmission end is equivalent to an acoustic point source, the spatial phase and amplitude distribution of an acoustic hologram is inversely solved by combining a point source algorithm according to a target space sound field form, the rotation angles of the coded super-structure surface at different spatial positions are correspondingly adjusted, and a target sound field is reconstructed;

the steps of obtaining the target sound field hologram and reconstructing the target sound field by the point source algorithm are as follows:

1) The target acoustic image plane is known to lie at Z = Z _d The method comprises M 'X N' pixel points, each pixel point is equivalently processed into an acoustic point source, and (M ', N') pixel points P (X) _m′ ,Y _n′ ,Z _d ) Respectively has an amplitude and a phase of A _m′,n′ And

assuming that the acoustic holographic plane is located at z =0 and includes K '× L' pixel points, the sound field of the pixel points on the acoustic holographic plane (K ', L') is the superposition of spherical sound waves radiated from all point sources on the target acoustic image along the-z direction:

in formula (8)

The distance between the target acoustic image pixel point (m ', n') and the target acoustic hologram pixel point (k ', l'); the amplitude and phase of the pixel point of the target hologram (k ', l') are A _k′,l′ ＝abs[p(x _k′ ,y _l′ ,0)]And

abs and arg are taken the amplitude and amplitude mathematical operator of angle correspondingly respectively;

there are two approaches to hologram implementation: one is a complex amplitude type hologram; the other is a phase hologram, i.e. ignoring all amplitude encoded information, A _k′,l′ Only phase encoding information is reserved as a constant; both hologram embodiments can reconstruct a target sound field, however, the complex amplitude type can generally obtain better sound field reconstruction quality than the phase type hologram;

2) Given that the acoustic wave propagation satisfies time reversal symmetry, the spherical acoustic wave radiated from the point source in the + z direction obtained by equation (8) can be superimposed to reconstruct a target acoustic image, that is:

in formula (9)

The distance between a target acoustic hologram pixel point (k ', l') and any pixel point between the target acoustic hologram pixel point and the target acoustic image; a. The _k′,l′ And

being pixel points of hologramsAmplitude magnitude and phase, and:

where m is the topological charge of the evanescent acoustic vortices, θ _k′,l′ The rotation angle of the loudspeaker array or the acoustic vortex superstructure surface in the (k ', l') th pixel point of the hologram; for amplitude modulation A _k′,l′ According to the formula (7), the amplitude of the sound field of the hologram pixel point can be realized by changing the distance between the loudspeaker array and the surface of the acoustic vortex superstructure; besides, the method can be realized by adjusting the driving voltage amplitude of the micro-speakers in the speaker array;

in addition, the reconfigurable characteristic of the pixel point phase can obviously expand the sound field reconfiguration mode and expand different sound field reconfiguration application scenes, for example, dynamic programmable sound field reconfiguration, namely, the micro loudspeaker array is fixed to a transmission device such as a stepping motor, and the rotation angles of the loudspeaker array at different pixel point positions obtained by the formula (10) send instructions to the motion controller through an upper computer program in a computer host to control the stepping motor at the corresponding pixel point position so as to realize the sound field reconfiguration function of dynamic programming;

as can be seen from the equation (9), when the topological charge number of the evanescent acoustic vortex is changed from m to-m, the phase of the hologram pixel point is also changed from m to m

Become-

The target sound field P' (X, Y, Z) is reconstructed at this time _d ) The expression of (c) is:

wherein conj is conjugation; the sound field distribution of formula (11) is represented by an amplitude distribution A _k′,l′ (x _k′ ,y _l′ ) And the phase distribution is

The point source of (1) is the conjugate of the sound field obtained by the superposition of spherical sound waves radiated from the point source along the-Z direction, and the reconstructed target acoustic image is positioned at Z = -Z _d Is a virtual image; therefore, the sign of the topological charge number of the evanescent acoustic vortex can also control the characteristics of a target reconstruction sound field;

consider the position at Z = Z _1,d And Z = -Z _2,d Two acoustic images P of ₁ (X,Y,Z _1,d ) And P ₂ (X,Y,-Z _2,d ) And the superposition of the sound fields of the two on the z =0 plane is obtained as follows:

p(x _k′ ,y _l′ ,0)＝p ₁ (x _k′ ,y _l′ ,0)+p ₂ (x _k′ ,y _l′ ,0) (12)

wherein:

and is provided with

A _1,m′,n′ And

respectively an acoustic image P ₁ (X,Y,Z _1,d ) (m ', n') pixel point P ₁ (X _m′ ,Y _n′ ,Z _1,d ) Amplitude and phase of (A) _2,m′,n′ And

respectively acoustic imagesP ₂ (X,Y,Z _2,d ) (m ', n') pixel point P ₂ (X _m′ ,Y _n′ ,Z _2,d ) Amplitude and phase of (d); when the evanescent acoustic vortex changes from m to-m, the evanescent acoustic vortex is respectively changed from Z = -Z as shown in equation (11) _1,d And Z = Z _2,d Obtaining a conjugated target acoustic image conj [ P ] ₁ (X,Y,Z _1,d )]And conj [ P ] ₂ (X,Y,-Z _2,d )](ii) a Original real image P ₁ Become virtual images conj (P) ₁ ) The original virtual image P ₂ Then it becomes the real image conj (P) ₂ ) (ii) a Therefore, the acoustic hologram designed by the method can realize the reappearance of different sound fields on the same side of the hologram by changing the sign of the topological charge number of the evanescent acoustic vortex, improve the information storage capacity of the acoustic hologram and have application value in the aspect of acoustic signal encryption;

in order to obtain the optimal sound field reconstruction effect, a complex amplitude type hologram is adopted for sound field reconstruction;

in order to reduce the transverse size of pixel points and increase the density of the pixel points of the device to the maximum extent, a loudspeaker array consisting of 1 multiplied by 4 micro loudspeakers is used for generating evanescent acoustic vortex as a signal source;

in order to realize the reconstruction function of the dynamic programmable sound field simply and conveniently, the amplitude of the pixel point is modulated by changing the amplitude of the driving voltage of the micro loudspeaker;

in order to realize the encryption of the acoustic holographic image and the storage of large-capacity acoustic information, the topological charge sign of the evanescent acoustic vortex can be realized by switching the sign of the driving voltage phase of the micro-speaker under the condition of keeping the voltage amplitude unchanged.

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