A method of generating an array of flattened light beams
By constructing a multi-cosine multi-Gaussian correlated light field, utilizing the superposition of multi-Gaussian and hyperbolic functions, and combining partially coherent light and free-space propagation formulas, the problems of complex operation and inability to control the number of sub-beams in the generation of flat-top beam arrays in existing technologies are solved, thus realizing flexible generation of flat-top beam arrays.
Patent Information
- Application Number
- CN202510892587.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-30
- Publication Date
- 2026-02-17
- Estimated Expiration
- 2045-06-30
AI Technical Summary
Existing technologies for generating flat-top beam arrays are complex to operate, cannot adjust the number of flat-top sub-beams according to actual needs, and lack flexibility and adaptability.
By introducing the superposition of multi-Gaussian and hyperbolic functions to construct weighting and kernel functions, and combining partially coherent light and free space transmission formulas, a multi-cosine multi-Gaussian correlated light field is constructed. The transmission distance and parameters are adjusted to achieve flat-top beam arrays with different numbers of rows and columns.
It enables adjustable number of sub-beams in the flat-top beam array, providing an efficient and flexible generation method to adapt to different needs.
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Figure CN120559853B_ABST
Abstract
Description
TECHNICAL FIELD
[0001] The present application relates to the field of light field regulation, and in particular to a method for generating a flat-top beam array. BACKGROUND
[0002] With the development of laser technology, array beams are increasingly attracting attention in the fields of laser communication, laser radar, particle manipulation and laser processing. At present, the engineering implementation of array beams is mainly based on fiber array synthesis technology, that is, multiple laser beams are emitted in an array form, and array beams are realized by superimposing sub-beams, which can be Gaussian beams, hollow beams or flat-top beams. Among them, flat-top beams have the advantage of uniform light intensity distribution, which makes them have significant advantages in material processing, semiconductor wafer processing and other fields. At present, the array composed of flat-top sub-beams also adopts the beam combining method (Optics and Laser Technology, 124, 106003).
[0003] The correlation structure function of partially coherent light determines the transmission characteristics of the light beam in space. Partially coherent light can have self-repairing and self-splitting characteristics, and the light beam can evolve into a hollow beam or an array beam, which has important application value in the realization of new type of light beams. Traditional array beams need to combine multiple sub-beams to generate, or use the self-splitting characteristics of partially coherent light with special light correlation structure, but the usual self-splitting characteristics divide the light beam into a fixed number of array beams. If the sub-beam is a flat-top beam array, the method of combining flat-top sub-beams is used, which has a relatively complex experimental structure, and the generated flat-top beam array cannot adjust the number of flat-top sub-beams according to actual needs. SUMMARY
[0004] The present application provides a method for generating a flat-top beam array to overcome the technical problems of the prior art that the flat-top beam sequence is usually generated by using the beam combining method, which is complex to operate and cannot adjust the number of flat-top sub-beams according to actual needs, lacking flexibility and poor adaptability.
[0005] In order to achieve the above-mentioned purpose, the technical scheme of the present application is:
[0006] A method for generating a flat-top beam array, comprising:
[0007] S1: introducing a multi-Gaussian function and a hyperbolic function, superimposing the hyperbolic function, and constructing a weight function and a kernel function with a Gaussian distribution intensity based on the superimposed hyperbolic function and the multi-Gaussian function, the weight function and the kernel function being used to construct a multi-cosine multi-Gaussian correlation light field;
[0008] S2: Introducing a partially coherent light configuration formula, combining a weight function and a kernel function to construct a cross-spectral density function of a multiple-cosine multi-Gaussian correlated light field containing multiple-cosine functions at the source plane;
[0009] S3: Introducing a free-space transmission formula, constructing an intensity expression of the multiple-cosine multi-Gaussian correlated light field at any transmission distance, i.e., an expression of the multiple-cosine multi-Gaussian correlated light field, according to the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field;
[0010] S4: Adjusting the transmission distance and the parameters of the multiple-cosine multi-Gaussian correlated light field to obtain a flat-top beam array with different numbers of rows and columns, and realizing an array form with adjustable flat-top sub-beams.
[0011] Further, a multi-Gaussian function and a hyperbolic function are introduced, the hyperbolic function is superimposed, a weight function and a kernel function with Gaussian distribution intensity are constructed based on the superimposed hyperbolic function and the multi-Gaussian function, including:
[0012] The weight function and the kernel function with Gaussian distribution intensity are constructed, as shown in formulas (1) and (2),
[0013]
[0014] Wherein, p(v) is the weight function, H(v) is the kernel function, is the hyperbolic function; v=(v x ,v y ) is the frequency in the Fourier space; n and m are positive real numbers; C0 is a normalization coefficient; F is the order of the multi-Gaussian function; f is an intermediate variable for summation; δ is the coherence length; i is an imaginary unit; w0 is the beam waist width of the Gaussian intensity term N x is the number of superpositions of the hyperbolic function along the x-axis direction, indicating 2N x +1 column beams along the x-axis direction; M y is the number of superpositions of the hyperbolic function along the y-axis direction, indicating 2M y +1 row beams along the y-axis direction; β x and β y are adjustable real numbers.
[0015] Further, a partially coherent light configuration formula is introduced, and a cross-spectral density function of a multiple-cosine multi-Gaussian correlated light field containing multiple-cosine functions at the source plane is constructed by combining a weight function and a kernel function, including:
[0016] S21, introducing a cross-spectral density configuration formula of partially coherent light, as shown in formula (3),
[0017] W(r1,r2)=∫p(v)H * (r1,v)H(r2,v)d2 v (3)
[0018] where W(r1, r2) is the cross-spectral density of partially coherent light at the source plane; p(v) is the weight function; H(r, v) is the kernel function at the source plane; r1=(x1, y1) and r2=(x2, y2) are the position vectors at the source plane;
[0019] S22, substituting the weight function and the kernel function into formula (3), constructing the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field at the source plane, as shown in formula (4),
[0020]
[0021] Further, the free space transmission formula is introduced, and the light intensity expression of the multiple-cosine multi-Gaussian correlated light field at any transmission distance is constructed according to the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field, including:
[0022] S31, introducing the free space transmission formula, the light intensity expression of the light field transmitted in the free space at any position z is shown in formula (5),
[0023]
[0024] where ρ=(ρ x ,ρ y ) is the position vector at any position z, k is the wave number, k=2π / λ, and λ is the wavelength;
[0025] S32, substituting formula (4) into formula (5), obtaining the light intensity expression of the multiple-cosine multi-Gaussian correlated light field at any transmission distance, as shown in formula (6),
[0026]
[0027] where W x+ , W x- , W y+ and W y- are the intermediate components of the light intensity, as shown in formulas (7)-(10),
[0028]
[0029]
[0030] where a, b, c x+ , c x- , c y+ and c y- are intermediate variables in the calculation process, as shown in formulas (11)-(16),
[0031]
[0032] Further, the parameters of the multiple-cosine multiple-Gaussian correlation light field are adjusted, different row and column numbers of flat-top beam arrays are obtained, and an array form of the flat-top sub-beam is realized, including:
[0033] Setting the parameters N x , M y , beta x , beta y , F of the multiple-cosine multiple-Gaussian correlation light field
[0034] Adjusting the values of the parameters N x and M y of the multiple-cosine multiple-Gaussian correlation light field, different row and column numbers of flat-top beam arrays are obtained, and the number of sub-beams of the flat-top beam array is controlled.
[0035] Beneficial effects: the application provides a method for generating a flat-top beam array, constructs a multiple-cosine multiple-Gaussian correlation spatial structure function, adjusts the parameters of the multiple-cosine multiple-Gaussian correlation light field, realizes controllable transmission of the multiple-cosine multiple-Gaussian correlation light field, obtains different row and column numbers of flat-top beam arrays, and effectively controls the number of sub-beams of the flat-top beam array. BRIEF DESCRIPTION OF DRAWINGS
[0036] In order to more clearly illustrate the technical solutions of the embodiments of the application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are some embodiments of the application, and other drawings can also be obtained by those skilled in the art without creative labor.
[0037] Figure 1 A flowchart of a method for generating a flat-top beam array provided by the application;
[0038] Figure 2 A light intensity distribution diagram of a flat-top beam array provided by the application at different transmission distances;
[0039] Figure 3 A light intensity distribution diagram of a multiple-cosine multiple-Gaussian correlation light field with different F at a transmission distance z=100m;
[0040] Figure 4 A light intensity distribution diagram of a multiple-cosine multiple-Gaussian correlation light field with an embodiment N x =3 at a transmission distance z=100m;
[0041] Figure 5 A light intensity distribution diagram of a multiple-cosine multiple-Gaussian correlation light field with an embodiment M yThe light intensity distribution diagram of the multiple-cosine multi-Gaussian correlation light field with = 3 at a transmission distance z = 100 m. DETAILED DESCRIPTION
[0042] To make the objects, technical solutions and advantages of the embodiments of the present application clearer, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.
[0043] The embodiment provides a method for generating a flat-top beam array, as shown in the formula. Figure 1 The method comprises the following steps of:
[0044] S1: introducing a multi-Gaussian function and a hyperbolic function, superimposing the hyperbolic function, constructing a weight function and a kernel function with Gaussian distribution intensity based on the superimposed hyperbolic function and the multi-Gaussian function, and the weight function and the kernel function are used to construct a multiple-cosine multi-Gaussian correlation light field;
[0045] S2: introducing a partial coherent light construction formula, combining the weight function and the kernel function to obtain a cross-spectral density function of the multiple-cosine multi-Gaussian correlation light field containing a multiple-cosine function at a source plane;
[0046] S3: introducing a free space transmission formula, constructing an intensity expression of the multiple-cosine multi-Gaussian correlation light field at an arbitrary transmission distance according to the cross-spectral density function of the multiple-cosine multi-Gaussian correlation light field, that is, an expression of the multiple-cosine multi-Gaussian correlation light field;
[0047] S4: adjusting the transmission distance and the parameters of the multiple-cosine multi-Gaussian correlation light field to obtain a flat-top beam array with different numbers of rows and columns, and realizing an array form with adjustable flat-top sub-beams.
[0048] Specifically, first, a multi-Gaussian function and a hyperbolic function are introduced, the hyperbolic function is superimposed, a weight function and a kernel function with Gaussian distribution intensity are constructed based on the superimposed hyperbolic function and the multi-Gaussian function, the weight function and the kernel function are used to construct a multiple-cosine multi-Gaussian correlation light field, a scheme of superimposing multiple hyperbolic functions is proposed, a weight function containing multiple hyperbolic functions and multi-Gaussian terms is constructed, and the cross-spectral density function of the multiple-cosine multi-Gaussian correlation light field is constructed subsequently, which provides a basis for adjusting and controlling the number of sub-beams in the flat-top beam array by adjusting the multiple-cosine multi-Gaussian correlation light field, and overcomes the problems of fixed number of sub-beams and complex experiments in the prior art, thereby providing an efficient and flexible solution for generating a flat-top beam array.
[0049] Secondly, the configuration formula of partially coherent light is introduced, and the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field containing multiple cosine functions at the source plane is constructed by combining the weight function and the kernel function, which has high flexibility and controllability, is suitable for actual non-ideal light sources, and provides a basis for obtaining the light intensity expression at any transmission distance z.
[0050] Thirdly, the free-space transmission formula is introduced, and the light intensity expression of the multiple-cosine multi-Gaussian correlated light field at any transmission distance is constructed according to the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field, that is, the expression of the multiple-cosine multi-Gaussian correlated light field. The free-space transmission formula can be used to describe the evolution of the light field from the source plane to any transmission distance z. Combined with the cross-spectral density function of the multiple-cosine multi-Gaussian correlated light field, the light intensity distribution after transmission can be derived, the light field transmission can be accurately predicted, and the flat-top beam array after transmission can be dynamically controlled to obtain the required light field.
[0051] Finally, by adjusting the transmission distance and the parameters of the multiple-cosine multi-Gaussian correlated light field, flat-top beam arrays with different numbers of rows and columns are obtained, and the array form of the flat-top sub-beam is adjusted.
[0052] In specific embodiments, a multi-Gaussian function and a hyperbolic function are introduced, the hyperbolic function is superimposed, a weight function and a kernel function with Gaussian distribution intensity are constructed based on the superimposed hyperbolic function and the multi-Gaussian function, and the weight function and the kernel function are used to construct a scheme of the multiple-cosine multi-Gaussian correlated light field.
[0053] The weight function and the kernel function with Gaussian distribution intensity are constructed, as shown in formulas (17) and (18),
[0054]
[0055] where p(v) is the weight function, H(v) is the kernel function, is the hyperbolic function; v=(v x ,v y ) is the frequency in the Fourier space; n and m are positive real numbers; C0 is a normalization coefficient; F is the order of the multi-Gaussian function; f is an intermediate variable for summation; δ is the coherence length; i is the imaginary unit; w0 is the beam waist width of the Gaussian intensity term N x is the number of superposition of the hyperbolic function along the x-axis direction, indicating that there are 2N x +1 columns of beams along the x-axis direction; M y is the number of superposition of the hyperbolic function along the y-axis direction, indicating that there are 2M y +1 rows of beams along the y-axis direction; β x and β y are adjustable real numbers.
[0056] The multi-Gaussian function is a superposition of multiple Gaussian functions, the multi-Gaussian function can flexibly describe the intensity distribution of multiple sub-beams in the light field, and the hyperbolic function can realize the smooth transition and boundary control of the light field distribution, therefore, in the scheme, multiple hyperbolic functions are superimposed to construct a weight function containing multiple hyperbolic functions and multi-Gaussian terms, which provides a basis for subsequent construction of the cross-spectral density function of the multi-cosine multi-Gaussian correlated light field, and realizes the adjustable and controllable number of sub-beams in the flat-top beam array by adjusting the multi-cosine multi-Gaussian correlated light field, which overcomes the problems of fixed number of sub-beams and complex experiments in the prior art, and provides an efficient and flexible solution for generating a flat-top beam array.
[0057] In specific embodiments, the cross-spectral density construction formula of the partially coherent light is introduced, and the cross-spectral density function of the multi-cosine multi-Gaussian correlated light field containing the multi-cosine function at the source plane is constructed by combining the weight function and the kernel function, and the scheme is as follows:
[0058] S21, the cross-spectral density construction formula of the partially coherent light is introduced, as shown in formula (19),
[0059] W(r1,r2)=∫p(v)H * (r1,v)H(r2,v)d 2 v (19)
[0060] Wherein, W(r1,r2) is the cross-spectral density of the partially coherent light at the source plane; p(v) is the weight function; H(r,v) is the kernel function at the source plane; r1=(x1,y1) and r2=(x2,y2) are the position vectors at the source plane;
[0061] S22, the weight function and the kernel function are substituted into formula (19), and the cross-spectral density function of the multi-cosine multi-Gaussian correlated light field at the source plane is constructed, as shown in formula (20),
[0062]
[0063] In the scheme, the partial coherence theory is introduced, the weight function and the kernel function are substituted into the cross-spectral density function of the partially coherent light, and the cross-spectral density function of the multi-cosine multi-Gaussian correlated light field at the source plane is obtained, which has high flexibility and controllability, and is suitable for actual non-ideal light source, and provides a basis for obtaining the light intensity expression at any transmission distance z.
[0064] In specific embodiments, the free space transmission formula is introduced, and the light intensity expression of the multi-cosine multi-Gaussian correlated light field at any transmission distance is constructed according to the cross-spectral density function of the multi-cosine multi-Gaussian correlated light field, that is, the expression of the multi-cosine multi-Gaussian correlated light field is as follows:
[0065] S31, introduce the free space transmission formula, the light intensity expression of the light field transmitted in free space at any position z is shown in formula (21),
[0066]
[0067] In the formula, ρ=(ρ x ,ρ y ) is the position vector at any position z, k is the wave number, k=2π / λ, and λ is the wavelength;
[0068] S32, substitute formula (20) into formula (21) to obtain the light intensity expression of the multiple-cosine multiple-Gaussian correlated light field at any transmission distance, as shown in formula (22),
[0069]
[0070] In the formula, W x+ , W x- , W y+ and W y- are intermediate components of light intensity, as shown in formulas (23)-(26),
[0071]
[0072] Wherein, a, b, c x+ , c x- , c y+ and c y- are intermediate variables in the calculation process, as shown in formulas (27)-(32),
[0073]
[0074]
[0075] In the scheme, the free space transmission formula can be used to describe the evolution of the light field from the source plane to any transmission distance z, combined with the cross-spectral density function of the multiple-cosine multiple-Gaussian correlated light field, the light intensity distribution after transmission can be derived, the light field transmission can be accurately predicted, and the flat-top beam array after transmission can be dynamically controlled to obtain the required light field.
[0076] In specific embodiments, the transmission distance and the parameters of the multiple-cosine multiple-Gaussian correlated light field are adjusted to obtain flat-top beam arrays with different numbers of rows and columns, and the scheme of adjusting the array form of the flat-top sub-beam is realized.
[0077] The parameters N x , M y , β x , β y , F of the multiple-cosine multiple-Gaussian correlated light field are set, and the value of the transmission distance z is adjusted to obtain a flat-top beam array.
[0078] Readjust the parameters N of the multi-cosine multi-Gaussian correlated light field x and M y The value is used to obtain flat-top beam arrays with different numbers of rows and columns, thereby controlling the number of sub-beams in the flat-top beam array.
[0079] Example 1:
[0080] The parameters are selected as λ = 532 nm, w0 = 3 mm, δ = 1 mm, N x =M y =2,β x =β y =3, F=10;
[0081] By adjusting the value of z, the light intensity distribution of the flat-top beam array at different transmission distances is obtained, as shown below. Figure 2 As shown, Figure 2 The transmission distances in (a)-(d) are z = 1m, z = 10m, z = 30m, and z = 100m, respectively. As the transmission distance increases, the light intensity distribution of the light field will exhibit a self-splitting phenomenon, changing from a Gaussian distribution ( Figure 2 (a) gradually evolved into an array consisting of 5×5 Gaussian subbeams. Figure 2 (c) As the transmission distance further increases, it can evolve into an array with 5×5 sub-beams as flat-top beams. Figure 2 (d) Therefore, by setting the transmission distance, the light source can obtain a flat-top beam array;
[0082] Example 2:
[0083] The parameters are selected as λ = 532 nm, w0 = 3 mm, δ = 1 mm, N x =M y =2,β x =β y =3;
[0084] By adjusting the value of F, we obtain the light intensity distribution diagrams of cosine-Gaussian correlated light fields with different values at a transmission distance of z = 100 m, as shown below. Figure 3 As shown, Figure 3 (a) and Figure 3 (b) shows F = 1 and F = 5 respectively; when F = 1, the cosine-gaussian correlated optical field will split into an array of 5×5 Gaussian sub-beams at a transmission distance of z = 100m. Figure 3 (a)); When F = 5, the cosine-gaussian correlated optical field will have a 5×5 array of flat-topped sub-beams at a transmission distance z = 100m. Figure 3 (b)), and the flatness of the sub-beam is lower than that of the cosine-gaussian correlated light field when F is larger.Figure 2 (d) Therefore, by setting F, the flatness of the multi-coil Gaussian multi-correlated optical field can be controlled to meet the requirements for different flatnesses;
[0085] Example 3:
[0086] The parameters are selected as λ = 532 nm, w0 = 3 mm, δ = 1 mm, β x =β y =3, F=10;
[0087] Set N x The value of N, when N x When z = 3, the intensity distribution of the cosine-gaussian correlated light field at a transmission distance of z = 100 m is obtained, as shown below. Figure 4 As shown, Figure 4 M in (a)-(b) y M respectively y =0, M y =1; when M y When = 0, the multi-cosine multi-Gaussian correlated light field will evolve into a 2N along the x-axis. x +1 flat-top beam ( Figure 4 (a)), with M y As the number of beams increases, it can be seen from the diagram that the number of rows of the flat-top beam also increases, becoming 2M. y +1 line;
[0088] The parameters are selected as λ = 532 nm, w0 = 3 mm, δ = 1 mm, β x =β y =3, F=10;
[0089] Setting M y The value of M y When z = 3, the intensity distribution of the cosine-gaussian correlated light field at a transmission distance of z = 100 m is obtained, as shown below. Figure 5 As shown, Figure 5 N in (a)-(b) x N x =0, N x =1; when N x When = 0, the multi-cosine multi-Gaussian correlated light field will evolve into a 2M-axis along the y-axis. y +1 flat-top beam ( Figure 5 (a)), with N x As the number of beams increases, it can be seen from the diagram that the number of columns of the flat-top beams also increases, becoming 2N. x +1 column, therefore, by setting N x and M y The number of rows and columns of the flat-top array can be adjusted.
[0090] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, and are not intended to limit the present application; although the present application has been described in detail with reference to the above embodiments, those skilled in the art should understand that the technical solutions recorded in the above embodiments can be modified, or some or all of the technical features can be replaced by equivalents; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present application.
Claims
1. A method for generating a flat-top beam array, characterized in that, include: S1: Introduce a multi-Gaussian function and a hyperbolic function, superimpose the hyperbolic function, and construct a weighting function and a kernel function with Gaussian intensity based on the superimposed hyperbolic and multi-Gaussian functions. The weighting function and kernel function are used to construct a multi-cosine multi-Gaussian correlated light field; the specific steps include: Construct the weight function and the kernel function with Gaussian distribution intensity, as shown in formulas (1) and (2). (1) (2) in, For the weight function, For kernel function, It is a hyperbolic function; The frequency of the Fourier space; and It is a positive real number; These are the normalization coefficients; The order of the multi-Gaussian function; For the intermediate variable in the summation; The length of coherence; It is the imaginary unit; It is a Gaussian intensity term The waist width; For hyperbolic functions along x The number of superpositions along the axial direction indicates the number of times along the axis. x axial direction has Column beam; For hyperbolic functions along y The number of superpositions along the axial direction indicates the number of times along the axis. y axial direction has Straight beam; and It is an adjustable real number; S2: Introduce a partially coherent light construction formula, and combine a weighting function and a kernel function to construct the cross spectral density function of the cosine multi-Gaussian correlated light field containing a cosine function at the source plane; S3: Introduce the free space transmission formula, and construct the light intensity expression of the cosine-gaussian correlated light field at any transmission distance based on the cross spectral density function of the cosine-gaussian correlated light field, that is, the expression of the cosine-gaussian correlated light field. S4: Adjust the transmission distance and the parameters of the cosine-gaussian correlated optical field to obtain flat-top beam arrays with different numbers of rows and columns, thereby achieving an adjustable array configuration for the flat-top sub-beams.
2. The method for generating a flat-top beam array according to claim 1, characterized in that, By introducing a partially coherent light construction formula and combining a weighting function and a kernel function, we obtain the cross-spectral density function of the cosine-Gaussian correlated light field containing cosine functions at the source plane, including: S21. Introduce the formula for constructing the cross-spectral density of partially coherent light, as shown in formula (3). (3) in, The cross-spectral density of partially coherent light at the source plane; For weighting functions; The kernel function at the source plane; and The position vector at the source plane; S22. Substitute the weighting function and kernel function into formula (3) to construct the cross-spectral density function of the multicosine multigaussian correlated light field at the source plane, as shown in formula (4). (4)。 3. The method for generating a flat-top beam array according to claim 2, characterized in that, Introducing the free-space transport formula, and constructing the intensity expression of the cosine-gaussian correlated light field at any transport distance based on the cross-spectral density function of the cosine-gaussian correlated light field, including: S31. Introducing the free-space propagation formula, the expression for the light intensity of the light field propagating in free space at any position z is shown in formula (5). (5) In the formula, Let z be the position vector at any position z. For wave number, , Wavelength; S32. Substituting formula (4) into formula (5), we obtain the expression for the light intensity of the multi-cosine multi-Gaussian correlated light field at any transmission distance, as shown in formula (6). (6) In the formula, , , and The intermediate component of light intensity is shown in formulas (7)-(10). (7) (8) (9) (10) in, , , , , and These are intermediate variables in the calculation process, as shown in formulas (11)-(16). (11) (12) (13) (14) (15) (16)。 4. The method for generating a flat-top beam array according to claim 3, characterized in that, By adjusting the transmission distance and the parameters of the multi-cosine multi-Gaussian correlated optical field, flat-top beam arrays with different numbers of rows and columns are obtained, achieving adjustable array configurations of the flat-top subbeams, including: Setting parameters for the multi-cosine multi-Gaussian correlated light field , , , , Adjust the transmission distance z to obtain a flat-top beam array; Readjust the parameters of the multicosine- and multigaussian correlated light field and The value is used to obtain flat-top beam arrays with different numbers of rows and columns, thereby controlling the number of sub-beams in the flat-top beam array.
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