Analysis method for acoustic mode distribution in acousto-optic tunable filter

Abstract

The invention relates to an acousto-optic tunable filter (AOTF). The acousto-optic tunable filter (AOTF) is an electric control tunable spectrum light splitting element, and the diffraction performance of an AOTF device is influenced by the sound field distribution in the AOTF. Sound field distribution in an existing AOTF device mainly considers that a sound field only comprises a single sound mode which is propagated in a specific direction and has a single wavelength. Therefore, the invention provides the analysis method for the acoustic mode distribution in the AOTF device, and the amplitude of each acoustic mode in the AOTF device is solved and obtained by establishing a non-homogeneous linear equation set through the elastic mechanical boundary condition of the AOTF device and the anisotropic solid constitutive equation. Compared with an existing AOTF device internal sound field modeling method, the AOTF device internal sound mode distribution analysis method provided by the invention has the advantages that a three-dimensional steady-state sound field in the AOTF device can be dispersed into superposition of different sound modes; the method can effectively calculate and analyze the influence of multiple reflections and mode conversion of sound waves on each solid surface of the AOTF device on sound field distribution, and is suitable for any crystal material.

Description

Technical Field

[0001] This invention relates to the field of acousto-optic tunable filtering technology, specifically to a method for analyzing the internal acoustic mode distribution of an acousto-optic tunable filter (AOTF). Background Technology

[0002] An acousto-optic transducer (AOTF) is a spectroscopic device based on the principle of acousto-optic diffraction. It boasts advantages such as high spectral resolution, arbitrarily tunable wavelength, fast tuning speed, and no moving parts, making it widely used in spectral detection, polarization imaging, notch filtering, beam deflection, and spatial filtering. An AOTF device mainly consists of an acousto-optic crystal and a piezoelectric transducer. Its primary working principle involves applying a radio frequency signal to the piezoelectric transducer, thereby generating an acoustic field within the acousto-optic crystal through the inverse piezoelectric effect. This acoustic field alters the refractive index distribution within the acousto-optic crystal, forming a volume grating, which in turn causes diffraction of the incident light.

[0003] Currently, it is generally believed that the acoustic field in AOTF devices only contains acoustic modes with a single wavelength propagating along a specific direction. The interaction between the incident light and this single acoustic mode will produce Bragg diffraction or Raman-Nath diffraction. However, in actual AOTF devices, the acoustic field exists in a three-dimensional bounded closed space composed of acousto-optic crystals of finite size. The sound waves generated by the piezoelectric transducer will undergo multiple reflections and mode transitions on various solid surfaces of the acousto-optic crystal, ultimately resulting in the steady-state acoustic field in the acousto-optic crystal simultaneously containing acoustic modes with different wavelengths propagating along different directions.

[0004] Since the incident light and these different acoustic modes interact to produce nonlinear diffraction effects such as cross-modulation, analyzing and calculating the acoustic mode distribution inside the AOTF device is an important part of AOTF device design. Summary of the Invention

[0005] The purpose of this invention is to provide an analytical method for solving the acoustic mode distribution inside an AOTF device based on the elastic mechanical boundary conditions and the constitutive equation of anisotropic solids. This method can be used to analyze and calculate the acoustic mode distribution inside an AOTF device along the axis, thereby obtaining the sound field distribution inside the AOTF device.

[0006] To address the aforementioned technical problems, the present invention provides an analytical method for solving the acoustic mode distribution inside an AOTF device based on the elastic mechanical boundary conditions of the AOTF device and the constitutive equation of anisotropic solids. This method first determines all possible acoustic mode types inside the AOTF device based on the constitutive equation of the anisotropic solid. Then, it samples the solid surface of the AOTF device to obtain the elastic mechanical boundary conditions at each sampling point. Finally, it establishes and solves a non-homogeneous linear equation system based on the obtained elastic mechanical boundary conditions to obtain the amplitude of each acoustic mode, thereby achieving the acquisition of the acoustic field distribution inside the AOTF device.

[0007] The analytical method proposed in this invention mainly includes the following steps:

[0008] (1) Determine all possible acoustic modes that exist inside the AOTF device;

[0009] (2) Obtain the elastic mechanical boundary conditions at each sampling point on the surface of the AOTF device;

[0010] (3) Establish a non-homogeneous linear equation system based on the obtained elasticity boundary conditions;

[0011] (4) Solve the non-homogeneous linear equations to obtain the amplitude of each acoustic mode;

[0012] Compared with existing methods for the distribution of sound field inside AOTF devices, the advantages of this invention are: (1) This method discretizes the three-dimensional steady-state sound field inside the AOTF device into a superposition of different sound modes, and can accurately represent the three-dimensional steady-state sound field inside the AOTF device through analytical solutions; (2) This method can calculate and analyze the influence of the size parameters of the AOTF device on the distribution of sound modes inside the AOTF device; (3) The designed analysis method is not limited to a certain specific crystal material, and is applicable to any crystal material. Attached Figure Description

[0013] The invention will be further described below with reference to the accompanying drawings:

[0014] Figure 1 Flowchart of acoustic mode distribution analysis method;

[0015] Figure 2 Schematic diagram of AOTF device;

[0016] Figure 3 This is a schematic diagram of the sampling point spacing; Detailed Implementation

[0017] The following describes in further detail, with reference to the accompanying drawings, a method for analyzing the internal acoustic mode distribution of an AOTF device proposed in this invention.

[0018] like Figure 1 As shown, the analysis method proposed in this invention mainly includes three key steps: determining the type of acoustic mode, sampling and obtaining the elastic boundary conditions, and establishing and solving a system of non-homogeneous linear equations. The main objective is to obtain the amplitude of each acoustic mode within the AOTF device.

[0019] Firstly, regarding the determination of the types of acoustic modes present within the AOTF device, the acoustic modes present within the AOTF device must satisfy the constitutive equations of anisotropic solids:

[0020] (1)

[0021] Where i, k, l and h take values ​​of 1, 2, and 3; These represent the magnitudes of the particle displacement projected onto the x, y, and z coordinate axes, respectively. These represent the projections of the wave vector k of the acoustic mode onto the x, y, and z coordinate axes, respectively. , and (where k is the angle between the wave vector of the acoustic mode and the positive directions of the x, y, z coordinate axes, respectively); w is the angular frequency of the acoustic mode. These are the stiffness matrix coefficients of anisotropic solids; It is the Kronecker function.

[0022] This formula is about For a system of ternary homogeneous linear equations, the necessary and sufficient condition for the equation to have a solution is that the determinant of the corresponding matrix is ​​0. This can be expressed as follows:

[0023] (2)

[0024] in, (The values ​​of n and m are in the range of 1, 2, 3) :

[0025] (3)

[0026] By simplifying equation (2), we can obtain a univariate sixth-degree equation for the acoustic mode wave vector k:

[0027] (4)

[0028] This equation indicates that along any wave vector direction... , There are 6 acoustic modes with different wave vectors k in anisotropic solids.

[0029] Substituting each wave vector k obtained through equation (4) back into equation (1), we have:

[0030] (5)

[0031] achievable

[0032] (6)

[0033] This formula is about The system of three homogeneous linear equations in three variables can be solved to obtain... The general solution is .

[0034] Then, assuming that there are N acoustic modes in the anisotropic solid, the expression for the acoustic mode distribution inside the AOTF device is:

[0035] (7)

[0036] Where n=1,...,N represents the N directions of the acoustic mode; m=1,...,6 represents the 6 acoustic modes with different wave vectors contained along a specific direction; This represents the angle between the wave vector of each acoustic mode along a specific direction and the positive directions of the x, y, z coordinate axes; Six wave vectors representing the acoustic pattern along a specific direction; The six sound modes along a specific direction correspond to equation (6). The general solution; The six sound modes along a specific direction correspond to equation (6). The particular solution (magnitude) obtained based on the boundary conditions of elasticity.

[0037] Furthermore, the elastic boundary conditions at each sampling point on the surface of the AOTF device were obtained through sampling. The AOTF device surface mainly contains two types of elastic boundary conditions:

[0038] (1) Boundary conditions for continuous displacement of particles

[0039] A continuous boundary condition for particle displacement means that the magnitude and direction of the particle displacements of two adjacent particles at the interface of two solid media are equal. The AOTF device piezoelectric transducer coverage area adopts a continuous boundary condition for particle displacement, such as... Figure 2 As shown. The continuous boundary condition of the particle displacement in the piezoelectric transducer coverage area of ​​the actual AOTF device is determined by the cut of the piezoelectric crystal and can be considered as a constant, i.e.

[0040] (8)

[0041] in, The magnitude of the particle displacement component along the x, y, z coordinate axes represents the particle displacement of the particle in the area covered by the piezoelectric transducer of the AOTF device.

[0042] (2) Stress free boundary conditions

[0043] The stress-free boundary condition means that the stress magnitude at the particle point at the interface between vacuum and solid medium is 0. The AOTF device surface, excluding the area covered by the piezoelectric transducer, adopts the stress-free boundary condition, such as... Figure 2 As shown. The relationship between stress, strain, and displacement at a particle at the interface between vacuum and solid medium is as follows:

[0044] (9)

[0045] Where i, j, l and m take values ​​of 1, 2, 3; These represent the x, y, and z variables corresponding to the coordinate axes, respectively. It is a strain component; It is a stress component.

[0046] If the particle lies on the surface of the AOTF device parallel to the x-axis, then the stress free boundary condition is:

[0047] (10)

[0048] If the particle lies on the surface of the AOTF device parallel to the y-axis, then the stress free boundary condition is:

[0049] (11)

[0050] If the particle lies on the surface of the AOTF device parallel to the z-axis, then the stress free boundary condition is:

[0051] (12)

[0052] At the same time, in order to meet the calculation accuracy, such as Figure 3 As shown, the spacing between adjacent sampling points needs to be less than one-quarter of the wavelength of the smallest acoustic mode corresponding to all acoustic modes present in the AOTF device:

[0053] (13)

[0054] in, Represents the spacing between sampling points; This represents the minimum acoustic mode wavelength corresponding to all acoustic modes present in the AOTF device.

[0055] Since the amplitudes of a total of 6N sound modes can be obtained through equation (7), The solution needs to be obtained. From each sampling point on the surface of the AOTF device, three continuous boundary conditions of mass displacement or three free boundary conditions of stress can be obtained. Therefore, a total of 2N sampling points need to be obtained on the surface of the AOTF device through sampling.

[0056] Finally, by combining the elastic boundary conditions and the expression for the acoustic mode (7) obtained simultaneously, a non-homogeneous linear equation system is established, and the amplitude of each acoustic mode is obtained by solving the non-homogeneous linear equation system. For the sampling points in the piezoelectric transducer coverage area of ​​the AOTF device, three equations can be obtained from each sampling point based on the continuous boundary conditions of the mass displacement and in combination with equation (7):

[0057] (14)

[0058] For sampling points on the surface of the AOTF device, excluding the area covered by the piezoelectric transducer, three equations can be obtained from each sampling point based on the stress free boundary conditions and in combination with equations (7) and (9):

[0059] (15)

[0060] Combining equations (14) and (15), a non-homogeneous linear system of 6N equations obtained from the 2N sampling points on the surface of the AOTF device through elastic boundary conditions is established. Solving this non-homogeneous linear system of equations yields the amplitude corresponding to each acoustic mode. This allows us to obtain the acoustic mode distribution within the AOTF device.

[0061] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for analyzing the internal acoustic mode distribution of an AOTF device, characterized in that, By establishing a non-homogeneous linear equation system based on the elastic boundary conditions of the AOTF device and the constitutive equation of anisotropic solids, the amplitude of each acoustic mode existing in the AOTF device can be obtained, thereby obtaining the acoustic field distribution within the AOTF device. The influence of multiple reflections and mode conversions of sound waves on various solid surfaces of the acousto-optic crystal on the acoustic mode distribution of the three-dimensional steady-state acoustic field inside the AOTF device can be quantitatively analyzed.

2. The method for analyzing the internal acoustic mode distribution of an AOTF device as described in claim 1, characterized in that, The specific steps of this method are as follows: (1) Determine all possible acoustic modes that exist inside the AOTF device; (2) Obtain the elastic mechanical boundary conditions at each sampling point on the surface of the AOTF device; (3) Establish a non-homogeneous linear equation system based on the obtained elasticity boundary conditions; (4) Solve the non-homogeneous linear equations to obtain the amplitude of each acoustic mode.

3. The method for analyzing the internal acoustic mode distribution of an AOTF device as described in claim 2, characterized in that, In step (1): the acoustic modes existing within the AOTF device need to satisfy the constitutive equation of anisotropic solids, and the wave vector k of the acoustic mode is the wave vector direction. , The function.

4. The method for analyzing the internal acoustic mode distribution of an AOTF device as described in claim 2, characterized in that, In step (2), the surface of the AOTF device mainly includes two types of elastic mechanical boundary conditions: the continuous boundary condition of mass displacement used in the piezoelectric transducer coverage area of ​​the AOTF device and the stress free boundary condition used in the area on the surface of the AOTF device excluding the piezoelectric transducer coverage area.

5. The method for analyzing the internal acoustic mode distribution of an AOTF device as described in claim 2, characterized in that, In step (2), in order to meet the calculation accuracy, the spacing between adjacent sampling points on the surface of the AOTF device needs to be less than one-quarter of the minimum acoustic mode wavelength corresponding to all acoustic modes existing in the AOTF device.

6. The method for analyzing the internal acoustic mode distribution of an AOTF device as described in claim 2, characterized in that, In step (3): for the sampling points in the piezoelectric transducer coverage area of ​​the AOTF device, three equations can be obtained from each sampling point based on the continuous boundary condition of particle displacement. For the sampling points in the area outside the piezoelectric transducer coverage area on the surface of the AOTF device, three equations can be obtained from each sampling point based on the stress free boundary condition. Therefore, if there are a total of 6N acoustic modes whose amplitudes need to be solved, a total of 2N sampling points need to be obtained on the surface of the AOTF device to obtain a total of 6N equations.

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