A method for generating hollow array light sources

Abstract

This invention discloses a method for generating a hollow array light source, comprising: selecting a vortex phase with Gaussian intensity distribution and carrying topological charge in an initial light field; introducing a Hermitian-Gaussian correlation function, and constructing a cross-spectral density function of the Hermitian-Gaussian correlated vortex light source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermitian-Gaussian correlation function; introducing an ABCD optical system, constructing a transmission model based on the cross-spectral density function of the Hermitian-Gaussian correlated vortex and the ABCD optical system, adjusting various parameters in the transmission model to form multiple hollow array beams, and then forming a hollow array light source through multiple hollow array beams; this invention, through the joint modulation of the Hermitian-Gaussian correlation structure and the vortex topological charge, can achieve effective control of the array light intensity distribution, realize the preparation of hollow array beams, and form an array light source by adjusting the array beams. The method is simple to operate and easy to implement.

Description

Technical Field

[0001] This invention relates to the field of optical technology, and more particularly to a method for generating a hollow array light source. Background Technology

[0002] In recent years, with the rapid development of light field manipulation technology, researchers have been striving to achieve arbitrary control over the morphology of light fields. Light field manipulation involves controlling light fields individually or in combination in the spatial, temporal, or spatiotemporal domains to achieve customized control over their characteristics. Recent research has found that by manipulating the spatial coherence structure of the light field, various types of partially coherent light sources can be realized. The transmission characteristics of these sources are jointly influenced by the spatial coherence structure and the light field parameters, and they can exhibit properties such as hollowness, self-focusing, self-coupling, and self-healing. These advantages have found wide applications in fields such as particle capture, target recognition and detection, wireless optical communication, and optical navigation.

[0003] Currently, with the increasing demand for laser types in fields such as optical imaging, optical information processing, and laser target exploration and recognition, optical field manipulation technology has been introduced into novel optical field manipulation. Array beams and hollow beams have advantages that traditional Gaussian beams do not possess. The generation of array light sources generally employs laser beam combining methods, such as combining multiple fiber beams or superimposing reflected or refracted beams from multiple lenses. The generation of array beams involves various types of optical devices, making beam preparation relatively complex. Furthermore, to generate an array beam with hollow sub-beams, each sub-beam must be pre-prepared as a hollow beam, further complicating the light source generation system. Summary of the Invention

[0004] This invention provides a method for generating a hollow array light source, overcoming the technical problem that in the process of preparing an array light source with hollow sub-beams, it is necessary to prepare each sub-beam as a hollow beam in advance and then combine them to form a hollow array light source, which is complex and costly.

[0005] To achieve the above objectives, the technical solution of the present invention is as follows:

[0006] A method for generating a hollow array light source includes:

[0007] S1: Select the vortex phase in the initial light field that has a Gaussian intensity distribution and carries a topological charge;

[0008] S2: Introducing the Hermetic Gaussian correlation function, and constructing the cross spectral density function of the Hermetic Gaussian correlated vortex source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermetic Gaussian correlation function;

[0009] S3: Introduce the ABCD optical system, construct a transmission model based on the cross spectral density function of Hermetic Gaussian correlated vortex and the ABCD optical system, adjust the various parameters in the transmission model to form multiple hollow array beams, and then form a hollow array light source through multiple hollow array beams.

[0010] Furthermore, a vortex phase with a Gaussian intensity distribution and carrying topological charge is selected in the initial light field, as shown in Equation (1).

[0011]

[0012] In the formula, M is the topological charge number of the vortex phase, i is the imaginary unit, and w0 represents the waist radius of the Gaussian beam. The Gaussian intensity distribution is represented by E(r); the light field vector is represented by r = (x, y), which represents the position vector at z = 0 on the source plane.

[0013] Furthermore, a Hermetic Gaussian correlation function is introduced. Based on the vortex phase with Gaussian intensity distribution and carrying topological charge, and the Hermetic Gaussian correlation function, a cross-spectral density function of the Hermetic Gaussian correlated vortex source is constructed, including:

[0014] S21. Obtain the expression for the cross spectral density function of the partially coherent beam at the source plane z = 0, as shown in formula (2).

[0015] W(r1,r2)=E(r1)E*(r2)μ(r1,r2) (2)

[0016] In equation (1), W(r1,r2) is the cross spectral density function, r1=(x1,y1) and r2=(x2,y2) are the transverse position coordinates of any two points in the light field at z=0 in the source plane, E(r) is the electric field describing the completely coherent light, the symbol * denotes complex conjugate, and μ(r1,r2) is the spatial coherence function;

[0017] S22. Introduce the Hermetic correlation function and obtain the spatial coherence expression in the Hermetic correlation function, as shown in formula (3).

[0018]

[0019] In the formula, 2m and 2m are Hermitian polynomials H 2m and H 2n The order of ; G0 represents the normalization coefficient, δ 0x δ represents the coherence length in the horizontal direction of space. 0y The coherence length in the ordinate direction in space is represented by the equation (4).

[0020]

[0021] In the formula, l is a constant and n is the order of the Hermitian polynomial;

[0022] S23. Substituting formulas (1) and (3) into formula (2), we obtain the cross spectral density function of the Hermetic Gaussian correlated vortex source at z=0 in the source plane, as shown in formula (5).

[0023]

[0024] W1(r1,r2) represents the cross spectral density function of the Hermetic Gaussian correlated vortex source, which has Hermetic Gaussian correlated coherent structure and vortex phase.

[0025] Furthermore, an Hermetic Gaussian correlation function and an ABCD optical system are introduced. A transmission model is constructed based on the cross-spectral density function of the Hermetic Gaussian correlation vortex and the ABCD optical system, including:

[0026] S31. Obtain the cross spectral density function of the beam transmitted in the ABCD optical system in the spatial domain at the transmission distance z, as shown in formula (6).

[0027]

[0028] In equation (6), ρ1=(ρ 1x ,ρ 1y ) and ρ2=(ρ 2x ,ρ 2y Let z be the position coordinates at the transmission distance z, and A, B, C, and D be the matrix elements of the ABCD optical system. Where λ is the wave number, λ is the wavelength, and z is the transmission distance;

[0029] S32. Substitute formula (5) into formula (6) and perform integration to obtain the cross spectral density function at any position, as shown in formula (7).

[0030]

[0031] In the formula, h1, h2, l x ,l y Let h1, h2 ∈ (0, M) be constants. x ∈(0,m), l y ∈(0,n);

[0032] In the formula, W(ρ) x ,z) represents the partial x-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (8).

[0033]

[0034]

[0035] Where s x ,t x ,d x s is a constant x ∈(0,2m-2l x ), d x ∈(0,M-h1+s x -2t x );

[0036] W(ρ y ,z) represents the partial y-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (9).

[0037]

[0038] Where s y s is a constant y ∈(0,2n-2l y ), ρ x, ρ y This represents the x-axis and y-axis coordinates in a Cartesian coordinate system at a distance z from the source plane; a x ,a y ,a x ,c y These are intermediate variables in the calculation process, as shown in formulas (10)-(13).

[0039]

[0040] When the Hermigas-correlated vortex source propagates in free space, the ABCD matrix of the optical system is as shown in equation (14).

[0041]

[0042] When ρ1 = ρ2 in formula (6), the Collins formula for beam transmission in free space, i.e., the transmission model, is as shown in formula (15).

[0043]

[0044] In equation (15), I(ρ,z) represents the intensity; z represents the transmission distance;

[0045] Substituting the cross spectral density function of the Hermigass correlated vortex source, i.e., formula (5), into formula (15), the intensity of the transmission model at any transmission distance z is obtained by integration, as shown in formula (16).

[0046]

[0047] In the formula, I1(ρ,z) represents the intensity of the transmission model at any transmission distance z, I x I y As intermediate variables, as shown in formulas (17) and (18),

[0048]

[0049] a x2, a y2 These are intermediate variables in the calculation process, as shown in formulas (19)-(20).

[0050]

[0051] Furthermore, by adjusting various parameters in the transmission model, multiple hollow array beams are formed, which in turn form a hollow array light source, including:

[0052] By setting the orders 2m and 2n of the Hermitian function and the topological charge M in the transmission model, and gradually increasing the transmission distance z, different hollow array beams are obtained. The different hollow array beams are then superimposed to obtain a hollow array light source.

[0053] Beneficial effects: This invention provides a method for generating a hollow array light source. By jointly controlling the Hermetic Gaussian correlation structure and the vortex topological charge, the array light intensity distribution can be effectively controlled. The parameters of the Hermetic Gaussian correlation structure and the number of vortex topological charges can be arbitrarily selected for control, and the hollow array beam can be prepared. The array light source is formed by adjusting the array beam. The method is simple to operate and easy to implement. Attached Figure Description

[0054] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0055] Figure 1 A flowchart of a method for generating a hollow array light source provided by the present invention;

[0056] Figure 2 This is a ring-shaped distribution diagram of the Hermigass-correlated vortex light source in free space at z = 10m in an embodiment of the present invention;

[0057] Figure 3 This is a hollow array diagram of the Hermigass-correlated vortex light source in free space at z = 150m in an embodiment of the present invention;

[0058] Figure 4 This is an array light intensity distribution diagram of the Hermigass-correlated vortex light source in free space at z = 200m in an embodiment of the present invention;

[0059] Figure 5 The array light intensity distribution at z=200m of a Hermetic Gaussian correlated vortex light source with vortex topological charge M=1 in free space in an embodiment of the present invention;

[0060] Figure 6 The hollow array diagram of the Hermetic-Gaussian correlated vortex light source with vortex topological charge M=4 in free space at z=200m in this embodiment of the invention. Detailed Implementation

[0061] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] This embodiment provides a method for generating a hollow array light source, such as... Figure 1 Shown, including:

[0063] S1: Select the vortex phase in the initial light field that has a Gaussian intensity distribution and carries a topological charge;

[0064] S2: Introducing the Hermetic Gaussian correlation function, and constructing the cross spectral density function of the Hermetic Gaussian correlated vortex source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermetic Gaussian correlation function;

[0065] S3: Introduce the ABCD optical system, construct a transmission model based on the cross spectral density function of Hermetic Gaussian correlated vortex and the ABCD optical system, adjust the various parameters in the transmission model to form multiple hollow array beams, and then form a hollow array light source through multiple hollow array beams.

[0066] Specifically, firstly, a vortex phase with a Gaussian intensity distribution and carrying topological charge is selected in the initial light field. Combining the Gaussian intensity distribution and the vortex phase, a light field with both stability and orbital angular momentum can be generated, providing a foundation for obtaining a hollow array light source in the future.

[0067] Secondly, the Hermetic Gaussian correlation function is introduced. Based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermetic Gaussian correlation function, the cross spectral density function of the Hermetic Gaussian correlated vortex source is constructed. The obtained cross spectral density function is the analytical expression of the Hermetic Gaussian correlated vortex source. Based on this cross spectral density function, the basic characteristics of the light field can be solved, and the hollow array light source that meets the requirements can be generated better.

[0068] Finally, an ABCD optical system is introduced. A transmission model is constructed based on the cross spectral density function of Hermetic Gaussian correlated vortices and the ABCD optical system. By adjusting the parameters in the transmission model, multiple hollow array beams are formed, which in turn form a hollow array light source. The ABCD optical system is a general optical transmission model. By adjusting the parameters of the ABCD matrix, the transmission and transformation of the light field can be flexibly controlled. The distribution and characteristics of the light field can be adjusted according to requirements. By adjusting the parameters in the transmission model, multiple hollow beams can be generated and form a regular array distribution.

[0069] In a specific embodiment, a vortex phase with a Gaussian intensity distribution and carrying a topological charge is selected in the initial light field, as shown in formula (21).

[0070]

[0071] In the formula, M is the topological charge number of the vortex phase, i is the imaginary unit, and w0 represents the waist radius of the Gaussian beam. The Gaussian intensity distribution is represented by E(r); the light field vector is represented by r = (x, y), which represents the position vector at z = 0 on the source plane.

[0072] In this scheme, by combining Gaussian intensity distribution and vortex phase, a light field with both stability and orbital angular momentum can be generated, providing a foundation for subsequent acquisition of hollow array light sources.

[0073] In a specific embodiment, the scheme for constructing the cross-spectral density function of the Hermetic Gaussian correlated vortex source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermetic Gaussian correlation function is as follows:

[0074] S21. Obtain the expression for the cross spectral density function of the partially coherent beam at the source plane z = 0, as shown in formula (22).

[0075] W(r1,r2)=E(r1)E*(r2)μ(r1,r2) (22)

[0076] In the formula, W(r1,r2) is the cross spectral density function, r1=(x1,y1) and r2=(x2,y2) are the transverse position coordinates of any two points in the light field at z=0 in the source plane, E(r) is the electric field describing the completely coherent light, the symbol * denotes complex conjugate, and μ(r1,r2) is the spatial coherence function;

[0077] S22. Introduce the Hermetic correlation function and obtain the spatial coherence expression in the Hermetic correlation function, as shown in formula (23).

[0078]

[0079] In the formula, 2m and 2n are Hermitian polynomials H 2m and H 2n The order of ; G0 represents the normalization coefficient, δ 0x δ represents the coherence length in the horizontal direction of space. 0y The coherence length in the ordinate direction in space is represented by the equation (24).

[0080]

[0081] In the formula, l and X are constants, and n is the order of the Hermitian polynomial;

[0082] S23. Substituting formulas (21) and (23) into formula (22), we obtain the cross spectral density of the Hermetic Gaussian correlated vortex source at z=0 in the source plane, as shown in formula (25).

[0083]

[0084] W1(r1,r2) represents the cross spectral density function of the Hermetic Gaussian correlated vortex source. The Hermetic Gaussian correlated vortex source has a Hermetic Gaussian correlated coherent structure and vortex phase. If m = n = 0 in equation (25), the Hermetic Gaussian correlated vortex source will degenerate into a Gaussian Sher mode vortex source.

[0085] In this scheme, the obtained cross-spectral density function is the analytical expression of the Hermigass correlated vortex light source. Based on this cross-spectral density function, the basic characteristics of the light field can be solved, and a hollow array light source that meets the requirements can be generated in a better way.

[0086] In a specific embodiment, an ABCD optical system is introduced. A transmission model is constructed based on the cross spectral density function of Hermetic Gaussian correlated vortices and the ABCD optical system. By adjusting the various parameters in the transmission model, multiple hollow array beams are formed. The scheme of forming a hollow array light source through multiple hollow array beams is as follows:

[0087] S31. Obtain the cross spectral density of the beam transmitted in the ABCD optical system at the transmission distance z in the spatial domain, as shown in formula (26).

[0088]

[0089] In equation (26), ρ1=(ρ 1x ,ρ 1y ) and ρ2=(ρ 2x ,ρ 2y Let z be the position coordinates at the transmission distance z, and A, B, C, and D be the matrix elements of the ABCD optical system. Where λ is the wave number, λ is the wavelength, and z is the transmission distance;

[0090] S32. Substitute formula (25) into formula (26) and perform integration to obtain the cross spectral density at any position, as shown in formula (27).

[0091]

[0092] In the formula, h1, h2, l x ,l y Let h1, h2 ∈ (0, M) be constants. x ∈(0,m), l y ∈(0,n);

[0093] In the formula, W(ρ) x ,z) represents the partial x-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (28).

[0094]

[0095]

[0096] Where s x ,t x ,d x s is a constant x ∈(0,2m-2l x ), d x ∈(0,M-h1+s x -2t x );

[0097] W(ρ y ,z) represents the partial y-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (29).

[0098]

[0099] Where sy s is a constant y ∈(0,2n-2l y ), ρ x ,ρ y This represents the x-axis and y-axis coordinates in a Cartesian coordinate system at a distance z from the source plane; a x ,a y ,c x ,c y These are intermediate variables in the calculation process, as shown in formulas (30)-(33).

[0100]

[0101] When the Hermigas-correlated vortex light source propagates in free space, the ABCD matrix of the optical system is as shown in equation (34).

[0102]

[0103] When ρ1 = ρ2 in formula (26), the Collins formula for beam transmission in free space is as shown in formula (35).

[0104]

[0105] In equation (15), I(ρ,z) represents the intensity; z represents the transmission distance;

[0106] Substituting the cross spectral density function of the Hermigass-correlated vortex source, i.e., formula (25), into formula (35), the intensity of the transmission model at any transmission distance z is obtained by integration, as shown in formula (36).

[0107]

[0108] In the formula, I1(ρ,z) represents the intensity of the transmission model at any transmission distance z, I x I y As intermediate variables, as shown in formulas (37) and (38),

[0109]

[0110] a x2, a y2 These are intermediate variables in the calculation process, as shown in formulas (39)-(40).

[0111]

[0112]

[0113] S34. Set the orders 2m and 2n of the Hermitian function and the topological charge M in the transmission model. Based on empirical values, they are usually set to 1-4. At the same time, set the coherence length δ. 0x and δ 0y By gradually increasing the transmission distance z by waist w0, different hollow array beams are obtained. By superimposing the different hollow array beams, a hollow array light source is obtained.

[0114] The parameters of the Hermigass-correlated vortex source were set as follows: λ = 532 nm, w0 = 4 mm, δ 0x =δ 0y =2mm, M=2, m=n=2; λ is the wavelength;

[0115] By adjusting the value of z, the normalized light intensity distribution at different transmission distances z is obtained. Figures 2-4 As shown, by Figure 2-4 It is evident that the intensity distribution of the Hermetic-correlated vortex source can exhibit different intensity distribution patterns at different transmission distances z, evolving from a hollow beam to a hollow array beam or an array beam. Figure 2 , Figure 3 and Figure 4 The transmission distances z are 10m, 150m and 200m respectively, such as Figure 1 In a light source with z = 10m, the light source has a hollow ring distribution. As the transmission distance increases, the light source exhibits self-splitting behavior, such as in... Figure 2 When z = 150m, the light source will evolve into a hollow array light source. Figure 3 When z = 200m, the light source will evolve into an array beam;

[0116] Therefore, a transmission distance of z = 200 m was chosen, and the parameters of the Hermigass-correlated vortex source were set as follows: λ = 532 nm, w0 = 4 mm, δ 0x =δ 0y =2mm, m=n=2.

[0117] Normalized light intensity distribution of this light source at z = 200 m for different vortex topological charges Figures 5-6 As shown, Figure 5 M ＝ At time 1, the light source has an array distribution, while Figure 6 When M=4, the light source can have a hollow array light intensity distribution, that is, the light source is a hollow array light source.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the above embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for generating a hollow array light source, characterized in that, include: S1: Select the vortex phase in the initial light field that has a Gaussian intensity distribution and carries a topological charge; S2: Introducing the Hermetic Gaussian correlation function, and constructing the cross spectral density function of the Hermetic Gaussian correlated vortex source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermetic Gaussian correlation function; S3: Introduce the ABCD optical system, construct a transmission model based on the cross spectral density function of Hermetic Gaussian correlated vortex and the ABCD optical system, adjust the various parameters in the transmission model to form multiple hollow array beams, and then form a hollow array light source through multiple hollow array beams.

2. The method for generating a hollow array light source according to claim 1, characterized in that, The vortex phase with Gaussian intensity distribution and carrying topological charge is selected in the initial light field, as shown in Equation (1). In the formula, M is the topological charge number of the vortex phase, i is the imaginary unit, and w0 represents the waist radius of the Gaussian beam. The Gaussian intensity distribution is represented by E(r); the light field vector is represented by r = (x, y), which represents the position vector at z = 0 on the source plane.

3. The method for generating a hollow array light source according to claim 2, characterized in that, Introducing the Hermitian-Gaussian correlation function, a cross-spectral density function for the Hermitian-Gaussian correlated vortex source is constructed based on the vortex phase with Gaussian intensity distribution and carrying topological charge, including: S21. Obtain the expression for the cross spectral density function of the partially coherent beam at the source plane z = 0, as shown in formula (2). W(r1,r2)=E(r1)E * (r2)μ(r1,r2)(2) In the formula, W(r1,r2) is the cross spectral density function, r1=(x1,y1) and r2=(x2,y2) are the transverse position coordinates of any two points in the light field at z=0 in the source plane, E(r) is the electric field describing the completely coherent light, the symbol * denotes complex conjugate, and μ(r1,r2) is the spatial coherence function; S22. Introduce the Hermetic correlation function and obtain the spatial coherence expression in the Hermetic correlation function, as shown in formula (3). In the formula, 2m and 2n are Hermitian polynomials H 2m and H 2n The order of ; G0 represents the normalization coefficient, δ 0x δ represents the coherence length in the horizontal direction of space. 0y The coherence length in the ordinate direction in space is represented by the equation (4). In the formula, l is a constant and n is the order of the Hermitian polynomial; S23. Substituting formulas (1) and (3) into formula (2), we obtain the cross spectral density function formula (5) for the Hermetic Gaussian correlated vortex source at z=0 in the source plane. W1(r1,r2) represents the cross spectral density function of the Hermetic Gaussian correlated vortex source, which has Hermetic Gaussian correlated coherent structure and vortex phase.

4. The method for generating a hollow array light source according to claim 3, characterized in that, A Hermitian correlation function and an ABCD optical system are introduced. A transmission model is constructed based on the cross-spectral density function of the Hermitian correlation vortex and the ABCD optical system, including: S31. Obtain the cross spectral density function of the beam transmitted in the ABCD optical system in the spatial domain at the transmission distance z, as shown in formula (6). In equation (6), ρ1=(ρ 1x ,ρ 1y ) and ρ2=(ρ 2x ,ρ 2y Let z be the position coordinates at the transmission distance z, and A, B, C, and D be the matrix elements of the ABCD optical system. Where λ is the wave number, λ is the wavelength, and z is the transmission distance; S32. Substitute formula (5) into formula (6) and perform integration to obtain the cross spectral density function at any position, as shown in formula (7). In the formula, h1, h2, l x ,l y Let h1, h2 ∈ (0, M) be constants. x ∈(0,m), l y ∈(0,n); In the formula, W(ρ) x ,z) represents the partial x-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (8). Where s x ,t x ,d x s is a constant x ∈(0,2m-2l x ), d x ∈(0,M-h1+s x -2t x ); W(ρ y ,z) represents the partial y-component of the cross spectral density function at a distance z from the source plane, as shown in Equation (9). Where s y s is a constant y ∈(0,2n-2l y ), ρ x, ρ y This represents the x-axis and y-axis coordinates in a Cartesian coordinate system at a distance z from the source plane; a x ,a y ,c x ,c y These are intermediate variables in the calculation process, as shown in formulas (10)-(13). When the Hermigas-correlated vortex source propagates in free space, the ABCD matrix of the optical system is as shown in equation (14). When ρ1 = ρ2 in formula (6), the Collins formula for beam transmission in free space, i.e., the transmission model, is as shown in formula (15). In equation (15), I(ρ,z) represents the intensity; z represents the transmission distance; Substituting the cross spectral density function of the Hermigass correlated vortex source, i.e., formula (5), into formula (15), the intensity of the transmission model at any transmission distance z is obtained by integration, as shown in formula (16). In the formula, I1(ρ,z) represents the intensity of the transmission model at any transmission distance z, I x I y As intermediate variables, as shown in formulas (17) and (18), a x2, a y2 These are intermediate variables in the calculation process, as shown in formulas (19)-(20).

5. A method for generating a hollow array light source according to claim 4, characterized in that, Adjusting various parameters in the transmission model to form multiple hollow array beams, and then forming a hollow array light source through multiple hollow array beams, includes: setting the order of the Hermetic Gaussian function 2m and 2n and the value of the topological charge M in the transmission model, gradually increasing the transmission distance z to obtain different hollow array beams, and superimposing the different hollow array beams to obtain a hollow array light source.

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