Method for regulating cosine multi-gaussian associated structured light field

Abstract

The application discloses a method for regulating and controlling cosine multi-Gaussian associated structured light field, comprising the following steps: introducing hyperbolic cosine function and multi-Gaussian function, constructing weight function and kernel function based on the hyperbolic cosine function and the multi-Gaussian function; introducing a partial coherent light construction formula, combining the weight function and the kernel function to construct the cross-spectral density function of the cosine multi-Gaussian associated structured light field at a source plane; introducing a free space transmission formula, constructing the light intensity expression of the cosine multi-Gaussian associated structured light field at an arbitrary transmission distance according to the cross-spectral density function, i.e. the expression of the cosine multi-Gaussian associated structured light field; adjusting the transmission distance and the parameters of the cosine multi-Gaussian associated structured light field to obtain the light intensity distribution regulation of the cosine multi-Gaussian associated structured light field, and then obtaining the array form of the sub-beam as a flat-top beam according to the light intensity distribution regulation; the application can realize the controllable transmission of the cosine multi-Gaussian associated structured light field and effectively regulate and control the array form of the sub-beam as a flat-top beam.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of light field regulation, and particularly relates to a method for regulating a cosine multi-Gaussian associated structured light field. BACKGROUND

[0002] With laser technology playing an increasingly important role in the fields of industry, national defense and communication, various new laser beams are constantly proposed, such as hollow beams, abnormal hollow beams, Hermite-Gaussian beams, Laguerre-Gaussian beams, Lorentz beams, Lorentz-Gaussian beams and flat-top beams. Among them, the flat-top beam has a flat distribution of light intensity cross section in a large range, and has a wide application in laser manufacturing industry, such as laser drilling. At present, beam shaping or multi-Gaussian Schell model source is generally used to generate flat-top beams, but when a flat-top beam array is needed, a common method is to combine multiple flat-top beams to form a beam, which is relatively complex.

[0003] The light intensity distribution of partially coherent light with special associated structure is regulated by the associated structure, and has different light intensity distribution patterns at different transmission distances. For example, the Hermite-Gaussian associated beam has a self-splitting property, and the Laguerre-Gaussian associated beam evolves into a hollow beam. The cosine-Gaussian associated beam also has a self-splitting property, and can evolve into an array of four sub-beams with Gaussian distribution. However, if the sub-beams are flat-top beams to form a flat-top beam array, the common method is still to combine beams. Therefore, it is still difficult to realize multiple sub-beams as flat-top beams by regulating the coherence structure. SUMMARY

[0004] The present application provides a method for regulating a cosine multi-Gaussian associated structured light field to overcome the technical problem that when a flat-top beam array is needed, multiple flat-top beams are generally combined to form a beam, which is relatively complex in technology and cannot directly generate a beam array with sub-beams as flat-top beams.

[0005] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0006] A method for regulating a cosine multi-Gaussian associated structured light field, comprising:

[0007] S1: introducing a hyperbolic cosine function and a multi-Gaussian function, constructing a weight function and a kernel function based on the hyperbolic cosine function and the multi-Gaussian function, and the weight function and the kernel function are used to construct a cosine multi-Gaussian associated structured light field;

[0008] S2: introducing a partially coherent light construction formula, combining the weight function and the kernel function to construct a cross-spectral density function of the cosine multi-Gaussian associated structured light field at a source plane;

[0009] S3: introducing a free-space transmission formula, constructing an intensity expression of the cosine multi-Gaussian correlated structured light field at an arbitrary transmission distance according to the cross-spectral density function, i.e., an expression of the cosine multi-Gaussian correlated structured light field;

[0010] S4: adjusting the transmission distance and the parameters of the cosine multi-Gaussian correlated structured light field to obtain intensity distribution regulation of the cosine multi-Gaussian correlated structured light field, and then obtaining an array form of the sub-beam as a flattop beam according to the intensity distribution regulation.

[0011] Further, hyperbolic cosine functions and multi-Gaussian functions are introduced, and a weight function and a kernel function are constructed based on the hyperbolic cosine functions and the multi-Gaussian functions, including:

[0012] The weight function and the kernel function 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 a hyperbolic cosine function; v=(v x ,v y ) is a frequency in the Fourier space; n and m are positive real numbers; C0 is a normalization coefficient; F is an order of the multi-Gaussian function; f is an intermediate variable for summation; δ is a coherence length; i is an imaginary unit; and w0 is a waist width of the Gaussian intensity.

[0015] Further, a partial coherence light construction formula is introduced, and a cross-spectral density function of the cosine multi-Gaussian correlated structured light field at a source plane is constructed in combination with the weight function and the kernel function, including:

[0016] S21: introducing a cross-spectral density construction formula of the partial coherence light, as shown in formula (3),

[0017] W(r1,r2)=∫p(v)H * (r1,v)H(r2,v)d 2 v (3)

[0018] wherein W(r1,r2) is the cross-spectral density of the partial coherence 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 position vectors at the source plane;

[0019] S22: substituting the weight function and the kernel function into formula (3) to construct the cross-spectral density function of the cosine multi-Gaussian correlated structured light field at the source plane, as shown in formula (4),

[0020]

[0021]

[0022] Further, the free space transmission formula is introduced, and the light intensity expression of the cosine multi-Gaussian correlated structured light field at any transmission distance is constructed according to the cross-spectral density function, that is, the expression of the cosine multi-Gaussian correlated structured light field, including:

[0023] S31, the free space transmission formula is introduced, and the light intensity expression of the light field transmitted in the free space at any position z is as shown in formula (5),

[0024]

[0025] 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;

[0026] S32, formula (4) is substituted into formula (5), and the light intensity expression of the cosine multi-Gaussian correlated structured light field at any transmission distance is obtained, as shown in formula (6),

[0027]

[0028] In the formula, W x+ , W x- , W y+ and W y- are the middle components of the light intensity, as shown in formulas (7)-(10),

[0029]

[0030] Wherein, 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]

[0033] Further, the transmission distance and the parameters of the cosine multi-Gaussian correlated structured light field are adjusted to obtain the light intensity distribution regulation of the cosine multi-Gaussian correlated structured light field, and then the array form of the sub-beam as a flat-top light beam is obtained according to the light intensity distribution regulation, including:

[0034] The number of the order F of the multi-Gaussian function in the weight function, the number of the positive real numbers n and m in the cosine multi-Gaussian correlated structured light field, and the number of the transmission distance z are gradually adjusted to obtain a plurality of flat-top light beam arrays.

[0035] Beneficial effects: This invention provides a method for controlling a cosine multi-Gaussian correlated structured light field. By constructing a weighting function and a kernel function, a cross-spectral density function of the cosine multi-Gaussian correlated structured light field with self-splitting characteristics is constructed. By adjusting the parameters of the cosine multi-Gaussian correlation, the controllable transmission of the cosine multi-Gaussian correlated structured light field is achieved. The self-splitting characteristics of the cosine multi-Gaussian correlated structured light field enable effective control of the array morphology of the sub-beams as flat-top beams. Attached Figure Description

[0036] 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.

[0037] Figure 1 A flowchart of a method for controlling a cosine multi-Gaussian correlated structure optical field provided by the present invention;

[0038] Figure 2 This is a light intensity distribution diagram of the cosine multi-Gaussian correlation structure light field at different transmission distances in the embodiment of the present invention;

[0039] Figure 3 In this embodiment of the invention, the light intensity distribution of a cosine multi-Gaussian correlation structure light field with different orders F at a transmission distance z = 200m is shown.

[0040] Figure 4 The light intensity distribution diagram of the cosine multi-Gaussian correlation structure light field with different positive real numbers n at a transmission distance z = 200m in the embodiment of the present invention;

[0041] Figure 5 The light intensity distribution diagram of the cosine multi-Gaussian correlation structure light field with different positive real numbers m at a transmission distance z = 200m in the embodiment of the present invention. Detailed Implementation

[0042] 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.

[0043] This embodiment provides a method for controlling the cosine multi-Gaussian correlated structured light field, such as Figure 1 As shown, it includes:

[0044] S1: introducing a hyperbolic cosine function and a multi-Gaussian function, constructing a weight function and a kernel function based on the hyperbolic cosine function and the multi-Gaussian function, the weight function and the kernel function being used to construct a cosine multi-Gaussian correlated structured light field;

[0045] S2: introducing a partial coherent light construction formula, combining the weight function and the kernel function to construct a cross-spectral density function of the cosine multi-Gaussian correlated structured light field at a source plane;

[0046] S3: introducing a free space transmission formula, constructing an intensity expression of the cosine multi-Gaussian correlated structured light field at an arbitrary transmission distance, i.e., an expression of the cosine multi-Gaussian correlated structured light field, according to the cross-spectral density function;

[0047] S4: adjusting a transmission distance and parameters of the cosine multi-Gaussian correlated structured light field to obtain intensity distribution regulation of the cosine multi-Gaussian correlated structured light field, and then obtaining an array form of the sub-beams as a flat-top beam according to the intensity distribution regulation.

[0048] Specifically, first, a hyperbolic cosine function and a multi-Gaussian function are introduced, and a weight function and a kernel function are constructed based on the hyperbolic cosine function and the multi-Gaussian function, the weight function and the kernel function being used to construct a cosine multi-Gaussian correlated structured light field. By constructing special weight functions and kernel functions, the initial spatial correlation characteristics of the light field can be flexibly constructed, forming a cosine multi-Gaussian correlated structured light field with self-splitting characteristics, which provides a basis for obtaining the cross-spectral density of the cosine multi-Gaussian correlated structured light field and the expression of the cosine multi-Gaussian correlated structured light field;

[0049] Secondly, a partial coherent light construction formula is introduced, and a cross-spectral density function of the cosine multi-Gaussian correlated structured light field at a source plane is constructed by combining the weight function and the kernel function. By introducing the partial coherent theory, the constructed weight function and the kernel function are substituted into the partial coherent light construction cross-spectral density function to obtain the cross-spectral density function of the cosine multi-Gaussian correlated structured light field at the source plane. The statistical characteristics of the light field can be accurately described, which is suitable for actual non-ideal light sources and provides a basis for obtaining the intensity expression at an arbitrary transmission distance z.

[0050] Thirdly, a free space transmission formula is introduced, and an intensity expression of the cosine multi-Gaussian correlated structured light field at an arbitrary transmission distance, i.e., an expression of the cosine multi-Gaussian correlated structured light field, is constructed according to the cross-spectral density function. By adjusting the beam parameters and the transmission distance, the regulation result of the intensity distribution form of the light field can be obtained, and the required light field is obtained.

[0051] Finally, the parameters of the cosine multi-Gaussian correlated structured light field are adjusted, the intensity distribution regulation of the cosine multi-Gaussian correlated structured light field is obtained, and then the array form of the sub-beam as a flat-top beam is obtained according to the intensity distribution regulation, and by adjusting the weight function, the kernel function and the parameters of the partially coherent light, the initial correlation structure of the light field can be accurately controlled, the intensity distribution, coherence and other characteristics can be flexibly customized, and the required flat-top beam array is obtained.

[0052] In specific embodiments, the hyperbolic cosine function and the multi-Gaussian function are introduced, the weight function and the kernel function are constructed based on the hyperbolic cosine function and the multi-Gaussian function, and the scheme for constructing the cosine multi-Gaussian correlated structured light field using the weight function and the kernel function is as follows:

[0053] The weight function and the kernel function are constructed, as shown in formulas (17) and (18),

[0054]

[0055] wherein p(v) is the weight function, H(v) is the kernel function, is the hyperbolic cosine 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; and w0 is the waist width of the Gaussian intensity.

[0056] The hyperbolic function has symmetry, monotonicity, growth and smoothness, and can describe the smooth transition of the light field. In the present scheme, the hyperbolic cosine function is used to construct a special weight function and a kernel function, which can flexibly construct the initial spatial correlation characteristics of the light field, provide a basis for obtaining the cross-spectral density of the cosine multi-Gaussian correlated structured light field and the expression of the cosine multi-Gaussian correlated structured light field, and form a cosine multi-Gaussian correlated structured light field with self-splitting characteristics, without the need for beam combining.

[0057] In specific embodiments, the cross-spectral density function scheme of the cosine multi-Gaussian correlated structured light field at the source plane is constructed by introducing a partially coherent light construction formula and combining the weight function and the kernel function.

[0058] S21, the partially coherent light construction formula 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, substituting the weight function and the kernel function into formula (19), the cross-spectral density function of the cosine multi-Gaussian correlated structured 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 constructed weight function and kernel function are substituted into the partial coherence light to construct the cross-spectral density function, the cross-spectral density function of the cosine multi-Gaussian correlated structured light field at the source plane is obtained, the statistical characteristics of the light field can be accurately described, which 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, the light intensity expression of the cosine multi-Gaussian correlated structured light field at any transmission distance is constructed according to the cross-spectral density function, that is, the expression of the cosine multi-Gaussian correlated structured light field is:

[0065] S31, introducing the free space transmission formula, the light intensity expression of the light field transmitted in free space at any position z is as 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, substituting formula (20) into formula (21), the light intensity expression of the cosine multi-Gaussian correlated structured light field at any transmission distance is obtained, as shown in formula (22),

[0069]

[0070] In the formula, W x+ , W x- , W y+ and W y- are the middle components of the light intensity, as shown in formulas (23)-(26),

[0071]

[0072] Wherein a, b, c x+ , cx- c y+ and c y- These are intermediate variables in the calculation process, as shown in formulas (27)-(32).

[0073]

[0074] In this scheme, the light intensity expression of the cosine multi-Gaussian correlated structured light field at any position can be obtained. By adjusting the beam parameters and transmission distance, the control result of the light intensity distribution pattern of the light field can be obtained, and the desired light field can be obtained.

[0075] In a specific embodiment, the scheme of adjusting the transmission distance and the parameters of the cosine multi-Gaussian correlated structured light field to obtain the intensity distribution modulation of the cosine multi-Gaussian correlated structured light field, and then obtaining the array shape of the sub-beams as flat-top beams based on the intensity distribution modulation, is as follows:

[0076] By setting the order F of the multi-Gaussian function in the weighting function and the values ​​of n and m in the cosine multi-Gaussian correlated structured light field, and gradually adjusting the value of the transmission distance z, multiple flat-top beam arrays are obtained.

[0077] Specifically, by adjusting the order F of the multi-Gaussian function, different flat-top characteristics of the sub-beams can be obtained at the transmission distance z. By adjusting the values ​​of the cosine function parameters n and m, flat-top beam arrays such as 2×2, 2×1, and 1×2 can be obtained as the transmission distance z increases.

[0078] By adjusting the weighting function, kernel function, and parameters of some coherent light, the initial correlation structure of the light field can be precisely controlled, enabling flexible customization of characteristics such as light intensity distribution and coherence, thus obtaining the desired flat-top beam array.

[0079] Example 1:

[0080] The parameters were selected as λ = 632.8 nm, w0 = 3 mm, δ = 2 mm, n = 2, m = 2, F = 5;

[0081] By adjusting the value of z, we obtain the intensity distribution of the cosine multi-Gaussian correlated structured light field at different transmission distances, as shown below. Figure 2 As shown, Figure 2 The transmission distances in (a)-(d) are z = 5m, z = 20m, z = 50m, and z = 200m, 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 with four sub-beams as flat-top beams. Figure 2 (d)); Therefore, by controlling different transmission distances, the light field can obtain different light intensity distribution patterns.

[0082] Example 2:

[0083] Parameters are selected as λ = 632.8 nm, w0= 3 mm, δ = 2 mm, n = 2, m = 2;

[0084] Adjust the value of F to obtain the light intensity distribution diagram of the cosine multi-Gaussian correlation structured light field with different F at the transmission distance z = 200 m, as shown in Figure 3 Figure 3 F in (a)-(b) is F = 1, F = 20 respectively, when F = 1, the light field is a cosine Gaussian correlation light field, which will split into an array of four sub-beams as Gaussian beams at the transmission distance z = 200 m ( Figure 3 (a));when F = 20, the cosine multi-Gaussian correlation light field will split into an array of four sub-beams as flat-top beams at the transmission distance z = 200 m ( Figure 3 (b)), and the flat-top property of the sub-beams is better than that of the cosine multi-Gaussian correlation light field with smaller F ( Figure 2 (d));therefore, by controlling F, the sub-beams of the light field can obtain different flat-top properties;

[0085] Example 3:

[0086] Parameters are selected as λ = 632.8 nm, w0= 3 mm, δ = 2 mm, m = 0, F = 5;

[0087] Adjust the value of n to obtain the light intensity distribution diagram of the cosine multi-Gaussian correlation structured light field with different n at the transmission distance z = 200 m, as shown in Figure 4 Figure 4 n in (a)-(b) is n = 2, n = 5 respectively; when m = 0, the light field will evolve into two flat-top sub-beams along the x-axis direction, and the distance between the two sub-beams of the light field with larger n also increases ( Figure 4 (b));

[0088] Parameters are selected as λ = 632.8 nm, w0= 3 mm, δ = 2 mm, n = 0, F = 5;

[0089] Adjust the value of m to obtain the light intensity distribution diagram of the cosine multi-Gaussian correlation structured light field with different m at the transmission distance z = 200 m, as shown in Figure 5 Figure 5 m in (a)-(b) is m = 2, m = 5 respectively. When n = 0, the light field will evolve into two flat-top sub-beams along the y-axis direction, and the distance between the two sub-beams of the light field with larger m also increases ( Figure 5 (b));therefore, by controlling n and m, the light field can obtain different distribution patterns and spatial intervals of the sub-beams.

[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 controlling the optical field of a cosine multi-Gaussian correlated structure, characterized in that, include: S1: Introducing hyperbolic cosine and multi-Gaussian functions, and constructing weighting and kernel functions based on these functions. The weighting and kernel functions are used to construct a cosine-multi-Gaussian correlated structured light field. Specific steps include: Construct the weight function and kernel function as shown in formulas (1) and (2). （1） （2） in, For the weight function, For kernel function, It is a hyperbolic cosine 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 the waist width of the Gaussian strength; 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 structured light field at the source plane; S3: Introduce the free space transmission formula and construct the light intensity expression of the cosine multi-Gaussian correlated structure light field at any transmission distance based on the cross spectral density function, that is, the expression of the cosine multi-Gaussian correlated structure light field. S4: Adjust the transmission distance and the parameters of the cosine multi-Gaussian correlated structured light field to obtain the intensity distribution control of the cosine multi-Gaussian correlated structured light field, and then obtain the array shape of the sub-beams as flat-top beams based on the intensity distribution control.

2. The method for controlling the cosine multi-Gaussian correlated structured optical field according to claim 1, characterized in that, A partially coherent light construction formula is introduced, and a cross-spectral density function of the cosine multi-Gaussian correlated structured light field at the source plane is constructed by combining a weighting function and a kernel function, 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 cosine multi-Gaussian correlated structured light field at the source plane, as shown in formula (4). （4）。 3. The method for controlling the cosine multi-Gaussian correlated structured optical field according to claim 2, characterized in that, Introducing the free-space transport formula, an expression for the light intensity of the cosine multi-Gaussian correlated structured light field at any transport distance is constructed based on the cross-spectral density function. This expression, namely the expression for the cosine multi-Gaussian correlated structured light field, includes: 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 light intensity expression of the cosine multi-Gaussian correlation structure 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 controlling the cosine multi-Gaussian correlated structured optical field according to claim 3, characterized in that, By adjusting the transmission distance and the parameters of the cosine multi-Gaussian correlated structured light field, the intensity distribution of the cosine multi-Gaussian correlated structured light field is controlled. Then, based on the intensity distribution control, the array configuration of the sub-beams as flat-top beams is obtained, including: Set the order of the multi-Gaussian function in the weighting function In the numerical, cosine-multi-Gaussian correlation structured light field and By gradually adjusting the value of the transmission distance z, multiple flat-top beam arrays can be obtained.

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