Method for generating hollow array light source

Abstract

The invention discloses a method for generating a hollow array light source. The method comprises the following steps: selecting a vortex phase which has Gaussian intensity distribution and carries topological charges in an initial light field; introducing a Hermite-Gaussian correlation function, and constructing a cross spectral density function of the Hermite-Gaussian correlation vortex light source based on a vortex phase having Gaussian intensity distribution and carrying a topological charge and the Hermite-Gaussian correlation function; an ABCD optical system is introduced, a transmission model is constructed based on a cross spectral density function of Hermitian associated vortex and the ABCD optical system, parameters in the transmission model are adjusted, a plurality of hollow array light beams are formed, and then a hollow array light source is formed through the plurality of hollow array light beams; through combined regulation and control of the Hermitian correlation structure and the vortex topological charge, effective control of array light intensity distribution can be realized, preparation of the hollow array light beam is realized, the array light source is formed by adjusting the array light beam, and the method is simple to operate and easy to realize.

Description

Technical Field

[0001] The present invention relates to the field of optical technologies, and in particular, to a method for generating a hollow array light source. Background Art

[0002] In recent years, with the rapid development of optical field modulation technologies, researchers have been expecting to achieve arbitrary modulation of the form of the optical field. Optical field modulation is to modulate alone or jointly in the spatial domain, time domain or spatio-temporal domain to achieve customized modulation of the characteristics of the optical field. Recently, it has been found that by modulating the spatial coherence structure of the optical field, various types of partially coherent light sources can be realized. The transmission characteristics of such light sources are jointly affected by the spatial coherence structure and optical field parameters, such as being able to have a hollow shape, self-focusing, self-coupling, self-healing, etc. These advantages have been widely applied in the fields of particle trapping, target recognition and detection, wireless optical communication, optical navigation, etc.

[0003] Currently, with the growing demand for laser types in the fields of optical imaging, optical information processing, laser target exploration and recognition, etc., optical field modulation technologies have been introduced into new optical field modulation. Array beams and hollow beams have advantages that traditional Gaussian beams do not have. The generation methods of array light sources generally adopt the method of laser beam combination. For example, multiple fiber syntheses are used, or the reflected or refracted beams of multiple lenses are superimposed to obtain the array beam. In the process of generating the array beam, various types of optical devices are involved, and the beam preparation is relatively complex. And to generate an array beam with sub-beams being hollow beams, it is also necessary to pre-prepare each sub-beam into a hollow beam, and the light source generation system will be more complex. Summary of the Invention

[0004] The present invention provides a method for generating a hollow array light source to overcome the technical problems that in the process of preparing an array light source with sub-beams being hollow beams, it is necessary to pre-prepare each sub-beam into a hollow beam and then combine them to form a hollow array light source, with complex preparation and high cost.

[0005] To achieve the above object, the technical solution of the present invention is:

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

[0007] S1: Select, in the initial optical field, a vortex phase having a Gaussian intensity distribution and carrying a topological charge;

[0008] S2: Introduce a Hermite-Gaussian correlation function, and construct a cross-spectral density function of a Hermite-Gaussian correlated vortex light source based on the vortex phase having a Gaussian intensity distribution and carrying a topological charge and the Hermite-Gaussian correlation function;

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

[0010] Further, select the vortex phase with Gaussian intensity distribution and carrying topological charge in the initial optical field, as shown in formula (1):

[0011]

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

[0013] Further, introduce the Hermite-Gaussian correlation function, and construct the cross-spectral density function of the Hermite-Gaussian correlated vortex light source based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermite-Gaussian correlation function, including:

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

[0015] W(r 1 , r 2 ) = E(r 1 )E*(r 2 )μ(r 1 , r 2 ) (2)

[0016] In formula (1), W(r 1 , r 2 ) is the cross-spectral density function, r 1 = (x 1 , y 1 ) and r 2 = (x 2 , y 2 ) are the transverse position coordinates of any two points in the optical field at the source plane z = 0, E(r) is the electric field describing the completely coherent light, the symbol * represents the complex conjugate, and μ(r 1 , r 2 ) is the spatial coherence function;

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

[0018]

[0019] where 2m and 2m are the orders of the Hermite polynomials H 2m and H 2n ; G 0 represents the normalization coefficient, δ 0x represents the coherence length in the horizontal coordinate direction in space, and δ 0y represents the coherence length in the vertical coordinate direction in space; the expression of the Hermite polynomial H is as shown in formula (4),

[0020]

[0021] where l is a constant and n is the order of the Hermite polynomial;

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

[0023]

[0024] W 1 (r 1 , r 2 ) represents the cross-spectral density function of the Hermite-Gaussian correlated vortex light source, and the Hermite-Gaussian correlated vortex light source has a Hermite-Gaussian correlated coherence structure and a vortex phase.

[0025] Furthermore, introduce the Hermite-Gaussian correlation function, introduce the ABCD optical system, and construct a propagation model based on the cross-spectral density function of the Hermite-Gaussian correlated vortex and the ABCD optical system, including:

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

[0027]

[0028] In formula (6), ρ 1 =(ρ 1x , ρ 1y ) and ρ 2 =(ρ 2x , ρ 2y ) are the position coordinates at the propagation distance z, and A, B, C, and D are the matrix elements of the ABCD optical system; is the wave number, λ is the wavelength, and z is the propagation distance;

[0029] S32. Substitute formula (5) into formula (6), and after integral operation, obtain the cross-spectral density function at any position, as shown in formula (7),

[0030]

[0031] Wherein, h 1 , h 2 , l x , l y are constants, h 1 , h 2 ∈(0, M), l x ∈(0, m), l y ∈(0, n);

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

[0033]

[0034]

[0035] Wherein, s x , t x , d x are constants, s x ∈(0, 2m - 2l x ), d x ∈(0, M - h 1 + s x - 2t x );

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

[0037]

[0038] Wherein, s y is a constant, s y ∈(0, 2n - 2l y ), ρ x, ρ y represents the coordinates of the x-axis and y-axis in the rectangular coordinate system at z from the source plane; a x , a y , a x , c y are intermediate variables in the calculation process, as shown in Equations (10)-(13),

[0039]

[0040] When the Hermite-Gaussian correlated vortex light source propagates in free space, the ABCD matrix of the optical system is as shown in Equation (14),

[0041]

[0042] When ρ in formula (6) 1 = ρ 2 , the Collins formula for the beam transmission in free space, that is, the transmission model is as shown in formula (15),

[0043]

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

[0045] Substitute the cross-spectral density function of the Hermite-Gaussian correlated vortex light source, that is, formula (5), into formula (15), and obtain the intensity of the transmission model at an arbitrary transmission distance z through integral calculation, as shown in formula (16),

[0046]

[0047] In the formula, I 1 (ρ, z) represents the intensity of the transmission model at an arbitrary transmission distance z, and I x I y is an intermediate variable, as shown in formulas (17) and (18),

[0048]

[0049] a x2, a y2 is an intermediate variable in the calculation process, as shown in formulas (19)-(20),

[0050]

[0051] Furthermore, adjust each parameter in the transmission model to form multiple hollow array beams, and then form a hollow array light source through the multiple hollow array beams, including:

[0052] Set the values of the orders 2m and 2n of the Hermite-Gaussian function and the topological charge number M in the transmission model, gradually increase the transmission distance z, obtain different hollow array beams, and superimpose the different hollow array beams to obtain a hollow array light source.

[0053] Beneficial effects: The present invention provides a method for generating a hollow array light source. Through the joint regulation of the Hermite-Gaussian correlation structure and the vortex topological charge, effective control of the array light intensity distribution can be achieved. The parameters of the Hermite-Gaussian correlation structure and the vortex topological charge number can be arbitrarily selected for regulation, and the preparation of hollow array beams can be realized. By adjusting the array beams to form an array light source, the method is simple to operate and easy to implement. Description of the Drawings

[0054] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

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

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

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

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

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

[0060] Figure 6 A hollow array diagram of a Hermite-Gaussian correlated vortex light source with a vortex topological charge number M=4 in free space at z=200m in an embodiment of the present invention. DETAILED DESCRIPTION

[0061] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work 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 As shown, including:

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

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

[0065] S3: Introduce the ABCD optical system, build a transmission model based on the cross-spectral density function of the Hermite-Gaussian correlation vortex and the ABCD optical system, adjust various parameters in the transmission model, 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 Gaussian intensity distribution and topological charge is selected in the initial light field. Combining the Gaussian intensity distribution and the vortex phase can generate a light field with both stability and orbital angular momentum, which provides a basis for the subsequent acquisition of a hollow array light source.

[0067] Secondly, the Hermite-Gaussian correlation function is introduced. Based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermite-Gaussian correlation function, the cross-spectral density function of the Hermite-Gaussian correlation vortex light source is constructed. The obtained cross-spectral density function is the analytical expression of the Hermite-Gaussian correlation 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 better generated.

[0068] Finally, the ABCD optical system is introduced, and a transmission model is constructed based on the cross-spectral density function of the Hermite-Gaussian correlation vortex and the ABCD optical system. The various parameters in the transmission model are adjusted to form multiple hollow array beams, and then a hollow array light source is formed through multiple hollow array beams. The ABCD optical system is a universal optical transmission model. By adjusting the parameters of the ABCD matrix, the transmission and transformation of the light field can be flexibly controlled, and the distribution and characteristics of the light field can be adjusted according to needs. By adjusting the parameters in the transmission model, multiple hollow beams can be generated and a regular array distribution can be formed.

[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] Where M is the topological charge of the vortex phase, i is the imaginary unit, and w 0 represents the waist radius of the Gaussian beam, represents Gaussian intensity distribution; E(r) represents the light field vector, and r=(x, y) represents the position vector at z=0 in 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 basis for the subsequent acquisition of hollow array light sources.

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

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

[0075] W(r 1 ,r 2 )=E(r 1 )E*(r 2 )μ(r 1 ,r 2 ) (twenty two)

[0076] In the formula, W(r 1 ,r 2 ) is the cross spectral density function, r 1 =(x 1 ,y 1 ) and r 2 =(x 2 ,y 2 ) are the lateral 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 fully coherent light, the symbol * represents the complex conjugate, μ(r 1 ,r 2 ) is the spatial coherence function;

[0077] S22, introduce the Hermite-Gaussian correlation function, and obtain the spatial coherence expression in the Hermite-Gaussian correlation function, as shown in formula (23),

[0078]

[0079] Where 2m and 2n are Hermitian polynomials H 2m and H 2n The order of G 0 represents the normalization coefficient, δ 0x represents the coherence length in the horizontal direction of space, δ 0y represents the coherence length in the ordinate direction in space; the expression of the Hermitian polynomial H is shown in formula (24),

[0080]

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

[0082] S23. Substituting formula (21) and formula (23) into formula (22), the cross spectral density of the Hermite-Gaussian correlation vortex light source at the source plane z=0 is obtained, as shown in formula (25),

[0083]

[0084] W 1 (r 1 ,r 2 ) represents the cross spectral density function of the Hermite-Gaussian correlation vortex light source. The Hermite-Gaussian correlation vortex light source has a Hermite-Gaussian correlation coherent structure and vortex phase. If m=n=0 in equation (25), the Hermite-Gaussian correlation vortex light source will degenerate into a Gaussian Scherrer mode vortex light source.

[0085] In this scheme, the obtained cross-spectral density function is the analytical expression of the Hermite-Gaussian 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 better generated.

[0086] In a specific embodiment, an ABCD optical system is introduced, a transmission model is constructed based on the cross spectral density function of the Hermite-Gaussian correlation vortex and the ABCD optical system, and various parameters in the transmission model are adjusted to form a plurality of hollow array beams. Then, a hollow array light source is formed by the plurality of hollow array beams:

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

[0088]

[0089] In formula (26), ρ 1 =(ρ 1x ,ρ 1y ) and ρ 2 =(ρ 2x ,ρ 2y ) is the position coordinate at the transmission distance z, A, B, C and D are the matrix elements of the ABCD optical system; is the wave number, λ is the wavelength, and z is the transmission distance;

[0090] S32, substitute formula (25) into formula (26), and obtain the cross-spectral density at any position through integration operation, as shown in formula (27),

[0091]

[0092] In the formula, h 1 ,h 2 ,l x ,ly is a constant, h 1 ,h 2 ∈(0,M),l 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 formula (28),

[0094]

[0095]

[0096] In the formula, s x ,t x ,d x is a constant, s x ∈(0,2m-2l x ), d x ∈(0,Mh 1 +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 formula (29),

[0098]

[0099] In the formula, s y is a constant, s y ∈(0,2n-2l y ), ρ x ,ρ y represents the x-axis and y-axis coordinates in the rectangular coordinate system at a distance z from the source plane; a x ,a y ,c x ,c y is the intermediate variable in the calculation process, as shown in formulas (30)-(33),

[0100]

[0101] When the Hermite-Gaussian correlation vortex light source is transmitted in free space, the ABCD matrix of the optical system is as shown in formula (34):

[0102]

[0103] When ρ in formula (26) 1 =ρ2 When , the Collins formula for beam propagation in free space is as shown in formula (35):

[0104]

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

[0106] Substituting the cross spectral density function of the Hermite-Gaussian correlation vortex light source, that is, formula (25), into formula (35), the intensity of the transmission model at any transmission distance z is obtained through integral calculation, as shown in formula (36):

[0107]

[0108] In the formula, I 1 (ρ,z) represents the strength of the transmission model at any transmission distance z, I x I y is an intermediate variable, as shown in formulas (37) and (38),

[0109]

[0110] a x2, a y2 is the intermediate variable in the calculation process, as shown in formulas (39)-(40),

[0111]

[0112]

[0113] S34, set the order 2m and 2n of the Hermite-Gaussian function in the transmission model and the value of the topological charge M, which are usually set to 1-4 based on empirical values, and set the coherence length δ 0x and δ 0y , waist 0 , gradually increase the transmission distance z, obtain different hollow array beams, and superimpose the different hollow array beams to obtain a hollow array light source;

[0114] The parameters of the Hermite-Gaussian vortex light source are set to: λ = 532nm, w 0 =4mm,δ 0x =δ 0y =2mm, M=2, m=n=2; λ is the wavelength;

[0115] Adjust the value of z to obtain the normalized light intensity distribution at different transmission distances z Figures 2 - 4 As shown by Figures 2 - 4It can be seen that the light intensity distribution of the Hermite-Gaussian vortex light source can have different light intensity distribution forms at different transmission distances z, and can evolve from a hollow beam to a hollow array beam or an array beam, where Figure 2 , Figure 3 and Figure 4 The transmission distances z are 10m, 150m and 200m respectively. Figure 1 In z = 10m, the light source has a hollow annular distribution. As the transmission distance increases, the light source produces a self-splitting phenomenon, such as 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, the transmission distance z = 200m is selected, and the parameters of the Hermite-Gaussian correlation vortex light source are set to: λ = 532nm, w 0 =4mm,δ 0x =δ 0y =2mm, m=n=2.

[0117] Normalized light intensity distribution of the light source with different vortex topological charges at z = 200m Figures 5 - 6 As shown, Figure 5 Medium ＝ 1, the light source has an array distribution, and Figure 6 When M=4, the light source may 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 aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned 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 with Gaussian intensity distribution and topological charge in the initial light field; S2: Introducing the Hermite-Gaussian correlation function, based on the vortex phase with Gaussian intensity distribution and carrying topological charge and the Hermite-Gaussian correlation function, constructing the cross-spectral density function of the Hermite-Gaussian correlated vortex light source; S3: Introduce the ABCD optical system, build a transmission model based on the cross-spectral density function of the Hermite-Gaussian correlation vortex and the ABCD optical system, adjust various parameters in the transmission model, form multiple hollow array beams, and then form a hollow array light source through multiple hollow array beams.

2. A method for generating a hollow array light source according to claim 1, characterized in that: Select the vortex phase with Gaussian intensity distribution and topological charge in the initial light field, as shown in formula (1), Where M is the topological charge of the vortex phase, i is an imaginary unit, w0 represents the waist radius of the Gaussian beam, represents Gaussian intensity distribution; E(r) represents the light field vector, and r=(x, y) represents the position vector at z=0 in the source plane.

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

4. A method for generating a hollow array light source according to claim 3, characterized in that: The Hermite-Gaussian correlation function and the ABCD optical system are introduced, and a transmission model is constructed based on the cross-spectral density function of the Hermite-Gaussian correlation vortex and the ABCD optical system, including: S31, obtaining the cross spectral density function of the light beam transmitted in the ABCD optical system in the spatial domain at the transmission distance z, as shown in formula (6), In formula (6), ρ1=(ρ 1x ,ρ 1y ) and ρ2=(ρ 2x ,ρ 2y ) is the position coordinate at the transmission distance z, A, B, C and D are the matrix elements of the ABCD optical system; is the wave number, λ is the wavelength, and z is the transmission distance; S32, substitute formula (5) into formula (6), and obtain the cross spectral density function at any position through integration operation, as shown in formula (7), In the formula, h1,h2,l x ,l y are constants, h1,h2∈(0,M), l 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 formula (8), In the formula, s x ,t x ,d x is a constant, s 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 the distance z from the source plane, as shown in formula (9), In the formula, s y is a constant, s y ∈(0,2n-2l y ), ρ x, ρ y represents the x-axis and y-axis coordinates in the rectangular coordinate system at a distance z from the source plane; a x ,a y ,c x ,c y is the intermediate variable in the calculation process, as shown in formulas (10)-(13), When the Hermite-Gaussian correlation vortex light source is transmitted in free space, the ABCD matrix of the optical system is as shown in formula (14): When ρ1=ρ2 in formula (6), the Collins formula for beam propagation in free space, i.e., the transmission model, is as shown in formula (15): In formula (15), I(ρ,z) represents the intensity; z represents the transmission distance; Substituting the cross spectral density function of the Hermite-Gaussian correlation vortex light source, that is, formula (5), into formula (15), the intensity of the transmission model at any transmission distance z is obtained through integral calculation, as shown in formula (16): Where I1(ρ,z) represents the strength of the transmission model at any transmission distance z, I x I y is an intermediate variable, as shown in formulas (17) and (18), a x2, a y2 is the intermediate variable in the calculation process, as shown in formulas (19)-(20), 5. A method for producing a hollow array light source according to claim 4, characterized in that: Adjust 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, including: setting the values ​​of the orders 2m and 2n of the Hermite-Gaussian function and the topological charge number M in the transmission model, gradually increasing the transmission distance z, obtaining different hollow array beams, and superimposing different hollow array beams to obtain a hollow array light source.

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