Nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition, electronic device

Abstract

The application discloses a nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition, and relates to the field of underwater acoustic parameter array and orbital angular momentum acoustic field simulation calculation, and comprises the following steps: initializing array parameters, fundamental wave parameters and medium parameters; calculating orbital angular momentum modal spectral coefficients, and defining pure modal acoustic field space base functions; weighting and superimposing the orbital angular momentum modal spectral coefficients and the corresponding pure modal acoustic field space base functions to obtain a fundamental wave total field; calculating a difference frequency virtual source expansion formula; adopting an orbital angular momentum decomposition method based on a Bessel integral identity and an analytical elimination of azimuth angle integral to carry out difference frequency volume integral dimension reduction calculation; and completing spectral decomposition and superposition of the difference frequency acoustic field. The application has high calculation efficiency, is highly universal for various arrays, provides solid theoretical support for accurate design and regulation of complex underwater vortex sound beam arrays, and is suitable for underwater acoustic communication, underwater target detection, acoustic tweezers and acoustic field regulation and other nonlinear acoustic application scenarios related to vortex sound beams.

Description

Technical Field

[0001] This invention belongs to the field of underwater acoustic parametric array and orbital angular momentum acoustic field simulation calculation technology, specifically involving a nonlinear acoustic vortex calculation method and electronic equipment based on orbital angular momentum decomposition. Background Technology

[0002] The underwater acoustic parametric array utilizes two high-frequency fundamental waves (frequency The nonlinear intermodulation effect in the medium generates a low-frequency difference wave (frequency) This enables the generation of low-frequency, highly directional sound beams using small-aperture fan-shaped discrete transducers. When the array is designed to generate vortex sound beams carrying orbital angular momentum, the sound waves exhibit a helical phase wavefront. (in As a topological charge, its spatial topology has unique application value in underwater target detection and acoustic communication (Shi C, Dubois M, Wang Y, et al. High-speed acoustic communication by multiplexing orbital angular momentum [J]. Proceedings of the National Academy of Sciences, 2017, 114(28): 7250-7253.). Currently, the calculation of the acoustic field of the orbital angular momentum parametric array based on the circular array of fan-ring discrete transducers faces two major technical challenges:

[0003] First, it is difficult to take into account the actual physical size in the calculation of nonlinear difference frequency volume integral. The actual fan-ring discrete transducer has a non-negligible radial width and cannot be simply equivalent to an infinite narrow ring or point source. The nonlinear mutual coupling problem between the actual size and the distributed array elements must be considered (Shi H, Yang D, Shi J, et al. Nonlinear interaction characteristics between acoustical transmitters in multiple parametric arrays [J]. The Journal of the Acoustical Society of America, 2025, 158(3): 2111-2129). In addition, when solving the difference frequency sound field based on the Westervelt equation, it is essentially a three-dimensional full-space volume integral containing the three-dimensional spatial distribution of the source and the Green's function. Since the integral kernel contains a complex product of multiple Bessel functions, there is no known fully analytical closed-form solution for this three-dimensional full-space volume integral. Existing narrow ring approximation methods introduce uncontrollable geometric approximation errors when dealing with fan-ring arrays with significant radial widths; while directly performing full-space three-dimensional numerical integration is extremely computationally intensive. Therefore, the core challenge in achieving rapid sound field calculation is how to accurately eliminate the azimuth integral dimension through analytical means while preserving the radial and axial physical dimensional accuracy of the fan-ring discrete transducer, that is, to reduce the three-dimensional volume integral of the entire space to a two-dimensional numerical integral (Chirag A. Gokani, Michael R. Haberman, Mark F. Hamilton. Paraxial and ray approximations of acoustic vortex beams [J].The Journal of the Acoustical Society of America, 2024, 155(4): 2707-2723.).

[0004] Second, there is a lack of general and interpretable analytical methods for irregular arrays. In practical applications, fan-ring discrete transducers may be arranged irregularly, and the orbital angular momentum spectrum will change from a sparse discrete spectrum to a dense continuous spectrum. In this case, the analytical formulas derived for specific regular arrays are no longer applicable.

[0005] In summary, existing methods either re-derive the acoustic field expression for each type of array, which is computationally cumbersome and lacks universality; or they use virtual source integration, which is computationally intensive and difficult to provide a physical interpretation of the orbital angular momentum spectrum structure. Summary of the Invention

[0006] The purpose of this invention is to provide a nonlinear acoustic vortex calculation method and electronic device based on orbital angular momentum decomposition, which aims to achieve rapid calculation of the fundamental and difference frequency sound fields of arbitrarily arranged fan-ring discrete transducers.

[0007] This invention targets arrays composed of multiple fan-ring discrete transducers (e.g., circular discrete arrays obtained by splicing quarter-rings). It unfolds the angular excitation distribution of the fan-ring discrete transducer array into a linear superposition of orbital angular momentum modes, thereby decoupling the array geometric information (number of fan-ring discrete transducers, arrangement angle, radial width) from the sound field propagation information. It quantitatively describes the generation mechanism of parasitic harmonics by leveraging the orthogonality of discrete Fourier transform, and finally obtains the distribution of the difference frequency sound field by analytically reducing the dimension of the nonlinear difference frequency triple volume integral.

[0008] The technical solution adopted by this invention to solve the technical problem is as follows:

[0009] This invention provides a nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition, comprising the following steps:

[0010] Step 1: Initialize array parameters, fundamental wave parameters, and dielectric parameters;

[0011] Step 2: Calculate the orbital angular momentum modal spectrum coefficients and define the spatial basis functions of the pure modal acoustic field;

[0012] Step 3: Weight the orbital angular momentum modal spectrum coefficients with the corresponding pure modal acoustic field spatial basis functions to obtain the orbital angular momentum expansion of the fundamental wave total field.

[0013] Step 4: According to the Westervelt equation, substitute the orbital angular momentum expansion of the fundamental wave into the formula for calculating the virtual source density to obtain the difference frequency virtual source expansion decomposed by mode pair.

[0014] Step 5: Perform difference-frequency volume integral dimensionality reduction calculations using the orbital angular momentum decomposition method based on Bessel integral identities and analytical elimination of azimuth integrals.

[0015] Step 6: Complete the spectral decomposition and superposition of the difference frequency sound field.

[0016] Furthermore, in step two, the angular excitation distribution of each ring-shaped discrete transducer is discretized and projected onto the orbital angular momentum base to obtain the first... The spectral coefficients of the orbital angular momentum modes are determined; under far-field conditions, the acoustic field spatial basis functions of each order of orbital angular momentum pure modes of the toroidal source are defined using Bessel functions; and the set of stimulated orbital angular momentum modes is established.

[0017] Furthermore, the first The mathematical expression for the modal spectral coefficients of the orbital angular momentum is:

[0018] (1);

[0019] in, Let θ be the azimuth angle of the center of the fan-shaped discrete transducer, c be the speed of sound, and θ be the azimuth angle of the observation point in cylindrical coordinates. Let be the initial surface amplitude of the j-th fundamental wave, i.e., the pump wave; m be the sector ring discrete transducer number; and i be the imaginary unit. To design topological loads, Fundamental frequency The design topology load is .

[0020] Furthermore, the excited orbital angular momentum mode set is defined as follows: n = 0 corresponds to the design mode. Corresponding to parasitic harmonics; To design topological loads, Fundamental frequency The design topology load is N represents the number of sector-ring discrete transducers.

[0021] Furthermore, in step three, the mathematical expression for the fundamental total field, i.e., the orbital angular momentum expansion of the fundamental wave, is:

[0022] (3);

[0023] Where r is the radial distance of the observation point in cylindrical coordinates, θ is the azimuth angle of the observation point in cylindrical coordinates, and z is the axial distance of the observation point in cylindrical coordinates. For the complex wavenumber containing absorption, Let i be a Bessel function of the first kind of order l, where i is the imaginary unit. Let be the average radius of the fan-shaped discrete transducer. The distance from the observation point to the origin; for; This is the set of stimulated orbital angular momentum modes.

[0024] Furthermore, in step four, the formula for calculating the virtual source density is: ;

[0025] The expansion of the difference-frequency virtual source is:

[0026] (4);

[0027] The difference frequency sound field is:

[0028] (5);

[0029] Where L represents the difference-frequency integration volume region, and r, θ, z are the radial distance, azimuth angle, and axial distance of the observation point in cylindrical coordinates, respectively. These represent the radial distance, azimuth angle, and axial distance of the integration point (source point / virtual source point) in cylindrical coordinates. Let be the complex wave number of the difference-frequency sound field containing acoustic absorption. These are the inner and outer diameters of the annular transducer, respectively. For nonlinear parameters, For difference frequency, For density, For the speed of sound, , The frequencies are respectively The complex sound pressure level and frequency of the sound wave are The conjugate of the complex sound pressure of the sound wave, This is the distance from the observation point to the origin.

[0030] Furthermore, in step five, the difference frequency virtual source expansion (4) is substituted into the difference frequency sound field calculation formula (5), and the integral term related to the source azimuth angle θ′ is extracted:

[0031] (6);

[0032] in, , The first Spectral coefficients of the first orbital angular momentum mode and the second The conjugate of the spectral coefficients of the orbital angular momentum modes; for each pair of modes Nonlinear intermodulation generates difference-frequency topological loads ; Physically, it describes the difference frequency virtual source generated by the nonlinear intermodulation of two specific orbital angular momentum fundamental waves. After successfully resolving and stripping the azimuth dimension, only the pure two-dimensional spatial distribution envelope varying along the radial and axial directions is retained.

[0033] Using the orthogonality of complex exponents and the identity of Bessel integrals, the source azimuth angle θ′ integral term within square brackets in formula (6) is solved analytically in closed form. Substituting the analytical solution back into formula (6) reduces the three-dimensional volume integral of the entire space to a two-dimensional numerical integral that retains only the radial and axial distances of the integration points (source points / virtual source points) in cylindrical coordinates:

[0034] (8);

[0035] in, For the first First-order Bessel function of the first kind; This is the effective center distance excluding azimuth intersection terms; The real part of the difference frequency wavenumber; The difference frequency wavenumber includes absorption.

[0036] Furthermore, in step six, the spatial geometry and attenuation integral functions generated by intermodulation are extracted, and a direct mapping from the fundamental wave parameters and orbital angular momentum mode spectrum coefficients to the complex amplitude of the difference frequency mode is established. Ultimately, the difference frequency sound field can be expressed as the coherent superposition of the spiral wavefront components of the topological charge of each order of difference frequency.

[0037] Furthermore, define a single pair of modes. The spatial geometry and decay integral function generated by intermodulation are:

[0038] (9);

[0039] The difference frequency sound field Spatial complex amplitude of orbital angular momentum modes This is explicitly expressed as a direct mapping between the fundamental parameters and the orbital angular momentum mode spectrum coefficients:

[0040] (10);

[0041] Complete basis based on orbital angular momentum space The final generated difference frequency sound field The complete expression is the difference-frequency topological charge of each order. Coherent superposition of spiral wavefront components:

[0042] (11);

[0043] Where r, θ, and z are the radial distance, azimuth angle, and axial distance of the observation point in cylindrical coordinates, respectively. These represent the radial distance, azimuth angle, and axial distance of the integration point (source point / virtual source point) in cylindrical coordinates. The real part of the difference frequency wavenumber is... , The first Spectral coefficients of the first orbital angular momentum mode and the second The conjugate of the spectral coefficients of the first orbital angular momentum mode. For nonlinear parameters, For difference frequency, For density, The speed of sound.

[0044] The present invention provides an electronic device comprising:

[0045] Memory, used to store computer programs and local data uploaded by users;

[0046] A processor is used to execute a computer program stored in the memory to implement the steps of the nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition.

[0047] A communication interface is used for communication between electronic devices and other devices.

[0048] The communication bus is used to enable communication between the processor, communication interface, and memory.

[0049] The beneficial effects of this invention are:

[0050] This invention completely decouples the array geometry information, such as the number, arrangement angle, and radial width of the fan-ring discrete transducers, from the sound field propagation process dominated by Bessel functions through spatial spectral decomposition. When it is necessary to modify the design topological load or adjust the array arrangement, it is only necessary to recalculate the spectral coefficients of the orbital angular momentum modes and perform weighted superposition, without having to repeatedly calculate the complex virtual source integral for each physical array element. Compared with the full numerical three-dimensional integration method, the computational efficiency of this invention is improved by several orders of magnitude, and it has extremely strong array versatility. The generation mechanism of each order orbital angular momentum mode in the difference frequency sound field is explicitly expressed as a mapping between the fundamental wave parameter and the spectral coefficients of the orbital angular momentum mode, clearly revealing the physical essence of the nonlinear orbital angular momentum sound field, and providing solid theoretical support for the precise design and control of complex underwater vortex acoustic beam arrays. This invention is applicable to nonlinear acoustic applications involving vortex acoustic beams, such as underwater acoustic communication, underwater target detection, acoustic tweezers, and sound field control. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of a ring-shaped emission array used for nonlinear acoustic vortex excitation.

[0052] Figure 2 This is a schematic diagram comparing the simulation results of sound pressure level using the virtual source integration method and the orbit decomposition method.

[0053] Figure 3 This is a schematic diagram comparing the phase simulation results of the virtual source integration method and the orbit decomposition method. Detailed Implementation

[0054] The present invention will be further described in detail below with reference to the accompanying drawings.

[0055] In a first aspect, the present invention provides a nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition.

[0056] The present invention provides a nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition, the specific implementation process of which is as follows:

[0057] Step 1: Initialize array parameters, fundamental wave parameters, and dielectric parameters;

[0058] A complete ring is formed by splicing together N identical sector-shaped discrete transducers. The m-th sector-shaped discrete transducer covers the azimuth angle. radial range , These represent the inner and outer diameters of the sector-ring discrete transducer, respectively. All sector-ring discrete transducers are located in the z'=0 plane and radiate normally along +z. Fundamental frequency. The design topology load is Medium parameters include sound velocity. ,density Nonlinear parameters Harmony diffusion rate .frequency The corresponding complex wavenumber containing absorption is Where i is the imaginary unit, absorption coefficient Difference frequency , , These are the frequencies of the first fundamental wave and the second fundamental wave, respectively.

[0059] Step 2: Extract and calculate the orbital angular momentum modal spectrum coefficients, and define the pure modal space basis functions;

[0060] (1) Discretely project the angular excitation distribution of each ring discrete transducer onto the orbital angular momentum base to obtain the first... Orbital angular momentum mode spectrum coefficients.

[0061] Specifically, let the angular excitation distribution of the m-th sector ring discrete transducer be as follows: (θ is the azimuth angle of the observation point in cylindrical coordinates) (Given the initial surface amplitude of the j-th fundamental wave (pump wave), this angular excitation is distributed towards the orbital angular momentum base.) (i is the imaginary unit, Discrete projection is performed on the center azimuth angle of the fan-shaped discrete transducer to obtain the first... Modal spectral coefficients of orbital angular momentum:

[0062] (1);

[0063] in, θ is the center azimuth angle of the fan-shaped discrete transducer, and c is the speed of sound.

[0064] (2) Under far-field conditions, the pure modal acoustic field basis functions of the orbital angular momentum of the ring source are defined by the Bessel function.

[0065] (3) Establish the set of stimulated orbital angular momentum modes to quantitatively characterize the generation mechanism of parasitic harmonics.

[0066] Specifically, the set of stimulated orbital angular momentum modes is defined as follows: n = 0 corresponds to the design mode. For parasitic harmonics, Z is a set of integers. The periodic excitation function is expanded into a complex exponential Fourier series:

[0067] (2);

[0068] in, The azimuth angle of the integration point (source point / virtual source point) in cylindrical coordinates.

[0069] Step 3: Decoupling expression of the fundamental total field;

[0070] The calculated first The fundamental total field is obtained by weighting and superimposing the spectral coefficients of the orbital angular momentum modes with the corresponding basis functions of the pure modal acoustic field, thus achieving complete decoupling between array geometric information and acoustic field propagation information. The specific formula for calculating the fundamental total field, i.e., the orbital angular momentum expansion of the fundamental wave, is as follows:

[0071] (3);

[0072] Where r, θ, and z are the radial distance, azimuth angle, and axial distance of the observation point in cylindrical coordinates, respectively. For sound wave number, For the l-th order Bessel function of the first kind, Let be the average radius of the fan-shaped discrete transducer. This represents the distance from the observation point to the origin. The decoupled representation of the fundamental total field separates the array geometry information from the sound field propagation information. Completely decoupled from Bessel functions.

[0073] Step 4: Construct the difference frequency virtual source expansion;

[0074] According to the Westervelt equation, the orbital angular momentum expansion of the fundamental wave (Equation (3)) is substituted into the formula for calculating the virtual source density to obtain the difference frequency virtual source expansion decomposed by mode pair.

[0075] Specifically, according to the Westervelt equation, the difference frequency The virtual source density is ( , The frequencies are respectively. The complex sound pressure level and frequency of the sound wave are Substituting the conjugate of the complex sound pressure of the sound wave into the orbital angular momentum expansion of the fundamental wave, we obtain the difference-frequency imaginary source expansion decomposed according to the mode pairs:

[0076] (4);

[0077] The difference frequency sound field is:

[0078] (5);

[0079] Where L represents the difference-frequency integral volume region. These represent the radial distance, azimuth angle, and axial distance of the integration point (source point / virtual source point) in cylindrical coordinates. denoted as the complex wavenumber of the difference-frequency sound field containing absorption.

[0080] Each pair of modes Nonlinear intermodulation generates difference-frequency topological loads It follows the conservation of orbital angular momentum. The difference-frequency sound field consists of a difference-frequency imaginary source and an absorbing Helmholtz Green's function. The three-dimensional volume fraction.

[0081] Step 5: Perform difference-frequency volume integral dimensionality reduction calculation using the orbital angular momentum decomposition method based on the analytical elimination of azimuth integrals using the Bessel integral identity.

[0082] The integral terms related to the azimuth angle are extracted from the difference frequency imaginary source expansion. The azimuth angle is solved analytically in closed form using the complex exponential orthogonality and the Bessel integral identity. The three-dimensional volume integral of the whole space is accurately reduced to a two-dimensional numerical integral that retains only the radial and axial directions.

[0083] Specifically, the difference frequency virtual source expansion (4) is substituted into the difference frequency sound field calculation formula (5), and the integral term related to the source azimuth angle θ′ is extracted. The mathematical expression of this process is as follows:

[0084] (6);

[0085] in, , The first Spectral coefficients of the first orbital angular momentum mode and the second The conjugate of the spectral coefficients of the orbital angular momentum modes. Physically, it describes the difference-frequency virtual source generated by the nonlinear intermodulation of two specific orbital angular momentum fundamental waves. After successfully resolving and stripping the azimuth dimension, it retains only the pure two-dimensional spatial distribution envelope that varies along the radial and axial directions.

[0086] By utilizing the orthogonality of complex exponents and the identity of Bessel integrals, the source azimuth angle θ′ integral term within square brackets in formula (6) is solved analytically in closed form, thereby achieving dimensionality reduction of the difference-frequency imaginary source integral. Specifically, let the difference-frequency topological load... The specific calculation process for analytical closed-form solution is as follows:

[0087] (7);

[0088] in, This is the effective center distance excluding azimuth intersection terms; The difference frequency wavenumber is the real part; Let be the wavenumber of the difference frequency sound field. Substituting this analytical solution back into formula (6), the three-dimensional volume integral of the entire space is successfully reduced to a two-dimensional numerical integral that retains only the radial and axial distances of the integration points (source points / virtual source points) in cylindrical coordinates:

[0089] (8);

[0090] in, For the first The first-order Bessel function of the order.

[0091] Step 6: Spectral decomposition and superposition of the difference frequency sound field;

[0092] By extracting the spatial geometry and attenuation integral functions generated by intermodulation, a direct mapping from the fundamental wave parameters and orbital angular momentum mode spectrum coefficients to the complex amplitude of the difference frequency mode is established. Ultimately, the difference frequency sound field can be expressed as the coherent superposition of the spiral wavefront components of the topological charge of each order of difference frequency.

[0093] Specifically, to clarify the generation mechanism of each orbital angular momentum mode in the difference frequency sound field, the above integral term (the part within square brackets in formula (8)) is extracted, and a single pair of modes is defined. The spatial geometry and decay integral function generated by intermodulation are:

[0094] (9);

[0095] The difference frequency sound field Spatial complex amplitude of orbital angular momentum modes This is explicitly expressed as a direct mapping between the fundamental parameters and the orbital angular momentum mode spectrum coefficients:

[0096] (10);

[0097] Complete basis based on orbital angular momentum space The final generated difference frequency sound field The complete expression is the difference-frequency topological charge of each order. Coherent superposition of spiral wavefront components:

[0098] (11).

[0099] In a second aspect, the present invention provides an electronic device for implementing the steps of the nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition provided in the first aspect.

[0100] This invention provides an electronic device, mainly comprising: a processor, a communication interface, a memory, and a communication bus; wherein the processor, communication interface, and memory communicate with each other via the communication bus. The functions of each module are as follows:

[0101] Memory is used to store computer programs and local data uploaded by users.

[0102] A processor is used to execute a computer program stored in memory to implement the steps of a nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition provided in the first aspect.

[0103] A communication interface is used for communication between an electronic device of the present invention and other devices.

[0104] The communication bus is used to enable communication between the processor, communication interface, and memory.

[0105] The technical solutions of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0106] Taking underwater acoustic applications as an example, this embodiment conducts difference-frequency acoustic vortex simulation verification under free-field conditions. The inner diameter of the ring-shaped transmitting array is set to 3.5 cm, and the outer diameter to 4.5 cm. The array structure is as follows: Figure 1 As shown. The two emitted dual fundamental waves (pump waves) have frequencies of 60kHz and 50kHz, respectively, with an initial surface sound pressure amplitude of 0.1 MPa. The topological charge numbers of the orbital angular momentum carried by the two fundamental waves are selected as 1, 0, and -1 for cross-combination simulation. Under the above conditions, the target difference frequency generated by the nonlinear intermodulation is 10kHz, the axial observation distance is set to 10m, and the lateral observation surface size is 4m×4m. The orbital angular momentum decomposition method based on Bessel identities to eliminate azimuth integrals is used for difference frequency volume integral dimension reduction calculation. Under the premise of preserving the directivity of the parametric array and the accuracy of the sound pressure level amplitude, the difference frequency sound field sound pressure level and spiral phase spatial distribution generated by various modal intermodulations, as well as the difference diagrams between the virtual source integration method and the orbital decomposition method, are shown in the figure. Figure 2 and Figure 3 As shown.

[0107] Figure 2 This is a schematic diagram comparing the simulation results of sound pressure level using the virtual source integration method and the orbit decomposition method. Figure 2 It can be seen that, Figure 2The difference-frequency sound field level distributions of the traditional virtual source integral and the orbit decomposition method of this invention were compared. The results show that for each order of vortex beam with a central sound pressure minimum (dark nucleus)... ), and the degraded conventional solid beam ( The sound field morphology and energy distribution output by the two methods are completely consistent, and the difference plot shows that the error is extremely small. The dimensionality reduction algorithm of this invention not only significantly reduces the amount of three-dimensional integral calculation, but also perfectly preserves the high-fidelity accuracy of the original physical model, accurately restoring the spatial distribution law of sound energy under nonlinear topological load intermodulation.

[0108] Figure 3 This is a schematic diagram comparing the phase simulation results of the virtual source integration method and the orbit decomposition method. Figure 3 It can be seen that, Figure 3 The spatial distribution of the spiral phase of the difference-frequency sound field calculated by the two methods was compared. As shown in the figure, with different topological charges, the sound field precisely exhibits alternating first-order, second-order spiral wavefronts or flat wavefronts. The phase difference plot on the right shows that the phase deviation within the entire observation section is almost zero (presenting a solid-color background). Conclusion: The dimensionality reduction calculation method of this invention is not only highly accurate in terms of sound pressure amplitude, but also extremely precise in reconstructing the complex spatial spiral phase topology of the difference-frequency vortex sound beam, further confirming the algorithm's extremely high reliability at the phase level.

[0109] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition, characterized in that, Includes the following steps: Step 1: Initialize array parameters, fundamental wave parameters, and dielectric parameters; Step 2: Calculate the orbital angular momentum modal spectrum coefficients and define the spatial basis functions of the pure modal acoustic field; Step 3: Weight the orbital angular momentum modal spectrum coefficients with the corresponding pure modal acoustic field spatial basis functions to obtain the orbital angular momentum expansion of the fundamental wave total field. Step 4: According to the Westervelt equation, substitute the orbital angular momentum expansion of the fundamental wave into the formula for calculating the virtual source density to obtain the difference frequency virtual source expansion decomposed by mode pair. Step 5: Perform difference-frequency volume integral dimensionality reduction calculations using the orbital angular momentum decomposition method based on Bessel integral identities and analytical elimination of azimuth integrals. Step 6: Complete the spectral decomposition and superposition of the difference frequency sound field.

2. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 1, characterized in that, In step two, the angular excitation distribution of each ring-shaped discrete transducer is discretized and projected onto the orbital angular momentum base to obtain the first... Orbital angular momentum mode spectrum coefficients; Under far-field conditions, the acoustic field spatial basis functions of each order orbital angular momentum pure mode of the toroidal source are defined by Bessel functions; and the set of stimulated orbital angular momentum modes is established.

3. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 2, characterized in that, The first The mathematical expression for the modal spectral coefficients of the orbital angular momentum is: (1)； in, Let θ be the azimuth angle of the center of the fan-shaped discrete transducer, c be the speed of sound, and θ be the azimuth angle of the observation point in cylindrical coordinates. Let m be the initial surface amplitude of the j-th fundamental wave, i.e., the pump wave, where m is the sector ring discrete transducer number and i is the imaginary unit. To design topological loads, Fundamental frequency The design topology load is .

4. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 3, characterized in that, Define the excited orbital angular momentum mode set as n = 0 corresponds to the design mode. Corresponding to parasitic harmonics; To design topological loads, Fundamental frequency The design topology load is ; N represents the number of sector-ring discrete transducers.

5. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 1, characterized in that, In step three, the mathematical expression for the fundamental wave total field, i.e., the orbital angular momentum expansion of the fundamental wave, is: (3)； Where r is the radial distance of the observation point in cylindrical coordinates, θ is the azimuth angle of the observation point in cylindrical coordinates, and z is the axial distance of the observation point in cylindrical coordinates. For the complex wavenumber containing absorption, Let i be a Bessel function of the first kind of order l, where i is the imaginary unit. Let be the average radius of the fan-shaped discrete transducer. The distance from the observation point to the origin; for; This is the set of stimulated orbital angular momentum modes.

6. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 1, characterized in that, In step four, the formula for calculating the virtual source density is: ; The expansion of the difference-frequency virtual source is: (4)； The difference frequency sound field is: (5)； Where L represents the difference-frequency integration volume region, and r, θ, z are the radial distance, azimuth angle, and axial distance of the observation point in cylindrical coordinates, respectively. These represent the radial distance, azimuth angle, and axial distance of the integration point (source point / virtual source point) in cylindrical coordinates. Let be the complex wave number of the difference-frequency sound field containing acoustic absorption. These are the inner and outer diameters of the annular transducer, respectively. For nonlinear parameters, For difference frequency, For density, For the speed of sound, , The frequencies are respectively The complex sound pressure level and frequency of the sound wave are The conjugate of the complex sound pressure of the sound wave, This is the distance from the observation point to the origin.

7. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 6, characterized in that, In step five, the difference frequency virtual source expansion (4) is substituted into the difference frequency sound field calculation formula (5), and the integral term related to the source azimuth angle θ′ is extracted: (6)； in, , The first Spectral coefficients of the first orbital angular momentum mode and the second The conjugate of the spectral coefficients of the orbital angular momentum modes; for each pair of modes Nonlinear intermodulation generates difference-frequency topological loads ; Physically, it describes the difference frequency virtual source generated by the nonlinear intermodulation of two specific orbital angular momentum fundamental waves. After successfully resolving and stripping the azimuth dimension, only the pure two-dimensional spatial distribution envelope varying along the radial and axial directions is retained. Using the orthogonality of complex exponents and the identity of Bessel integrals, the source azimuth angle θ′ integral term within square brackets in formula (6) is solved analytically in closed form. Substituting the analytical solution back into formula (6) reduces the three-dimensional volume integral of the entire space to a two-dimensional numerical integral that retains only the radial and axial distances of the integration points (source points / virtual source points) in cylindrical coordinates: (8)； in, For the first First-order Bessel function of the first kind; This is the effective center distance excluding azimuth intersection terms; The real part of the difference frequency wavenumber; The difference frequency wavenumber includes absorption.

8. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 1, characterized in that, In step six, the spatial geometry and attenuation integral functions generated by intermodulation are extracted, and a direct mapping from the fundamental wave parameters and orbital angular momentum mode spectrum coefficients to the complex amplitude of the difference frequency mode is established. Finally, the difference frequency sound field can be expressed as the coherent superposition of the spiral wavefront components of the topological charge of each order of difference frequency.

9. The nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition according to claim 8, characterized in that, Define a single pair of modes The spatial geometry and decay integral function generated by intermodulation are: (9)； The difference frequency sound field Spatial complex amplitude of orbital angular momentum modes This is explicitly expressed as a direct mapping between the fundamental parameters and the orbital angular momentum mode spectrum coefficients: (10)； Complete basis based on orbital angular momentum space The final generated difference frequency sound field The complete expression is the difference-frequency topological charge of each order. Coherent superposition of spiral wavefront components: (11)； Where r, θ, and z are the radial distance, azimuth angle, and axial distance of the observation point in cylindrical coordinates, respectively. These represent the radial distance, azimuth angle, and axial distance of the integration point (source point / virtual source point) in cylindrical coordinates. The real part of the difference frequency wavenumber is... , The first Spectral coefficients of the first orbital angular momentum mode and the second The conjugate of the spectral coefficients of the first orbital angular momentum mode. For nonlinear parameters, For difference frequency, For density, The speed of sound.

10. An electronic device, characterized in that, include: Memory, used to store computer programs and local data uploaded by users; A processor for executing a computer program stored in a memory to implement the steps of the nonlinear acoustic vortex calculation method based on orbital angular momentum decomposition as described in any one of claims 1-9; A communication interface is used for communication between electronic devices and other devices. The communication bus is used to enable communication between the processor, communication interface, and memory.

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