Method for generating hollow light array with rectangular distribution

Abstract

The invention discloses a method for generating a hollow light array with rectangular distribution. The method comprises the following steps: constructing a kernel function based on a spiral phase and a Gaussian function; superposing hyperbolic cosine functions to construct a weighting function so as to obtain a multi-cosine correlation vortex light field; introducing a partially coherent light construction formula, and constructing a cross spectral density function of the multi-cosine correlation vortex light field at the initial plane in combination with the kernel function and the weighting function; a free space transmission formula is introduced, a light intensity expression of the multi-cosine correlation vortex light field at any transmission distance is constructed in combination with a cross spectral density function, parameters of the transmission distance and the multi-cosine correlation vortex light field are adjusted, and light intensity distribution regulation and control of the multi-cosine correlation vortex light field are obtained. According to parameter regulation and control, the array form that the sub-beams are hollow beams is obtained, and a rectangular distribution hollow light array is obtained; according to the invention, the controllable transmission of the multi-cosine Gaussian correlation vortex beam can be realized, and the effective regulation and control of the array distribution with the sub-beams being hollow beams can be realized.

Description

Technical Field

[0001] This invention relates to the field of light field manipulation technology, and in particular to a method for generating a hollow light array with a rectangular distribution. Background Technology

[0002] With the development of laser technology, hollow beams with a hollow intensity distribution pattern of zero central intensity have wide applications in cooling and trapping microscopic particles, laser processing, and biomedical imaging.

[0003] Hollow beams, due to their unique physical characteristics such as small dark spot size, no heating effect, barrel-shaped intensity distribution, and "self-focal distance" during transmission, possess enormous potential and broad application prospects in fields such as laser ranging, optical information communication, and scanning imaging. In hollow beam-based imaging, array non-scanning imaging, compared to unit scanning imaging, can simultaneously acquire information from multiple pixels, thus improving imaging efficiency. Unit scanning imaging stitches together multiple images to obtain the entire image, while array non-scanning imaging can acquire the entire image in a single pass, reducing the amount of data processed and accelerating data processing speed.

[0004] However, in the actual fabrication of hollow beam arrays, existing technologies largely rely on complex optical beam combining systems, resulting in cumbersome overall optical path structures and high stability requirements. In recent years, optical field manipulation techniques have achieved flexible control over transmission characteristics by designing the spatial coherence structure of the beam, such as the "self-splitting" or "self-focusing" behavior of the beam. Nevertheless, the array beams generated by current coherent manipulation-based self-splitting methods typically still have Gaussian distributions in their sub-beams. These sub-beams suffer from technical limitations such as non-hollowing, low system integration, and insufficient manipulation flexibility, making it difficult to directly generate beam arrays with hollow characteristics. This technical limitation restricts the further application of hollow beam arrays in optical imaging, especially in applications requiring high contrast, low thermal damage, and precise dark-field imaging. It prevents the application of hollow beams in more optical imaging applications, hindering the development of optical imaging. Summary of the Invention

[0005] This invention provides a method for generating a hollow optical array with a rectangular distribution to overcome the above-mentioned technical problems.

[0006] To achieve the above objectives, the technical solution of the present invention is as follows: A method for generating a hollow optical array with a rectangular distribution includes: S1: Introduce spiral phase and Gaussian function, and construct kernel function based on spiral phase and Gaussian function; S2: Introduce hyperbolic cosine functions and superimpose them to construct weighting functions to obtain the multicosine-correlated vortex light field; S3: Introduce a partially coherent light construction formula, and combine kernel function and weighting function to construct the cross spectral density function of the cosine-correlated vortex light field at the initial plane; S4: Introduce the free space transmission formula and combine it with the cross spectral density function to construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance, that is, the expression of the cosine-correlated vortex light field. S5: Adjust the transmission distance and the parameters of the cosine-correlated vortex light field to obtain the intensity distribution control of the cosine-correlated vortex light field, and then obtain the array shape of the sub-beams as hollow beams according to the parameter control, that is, obtain the rectangular distribution hollow light array.

[0007] Furthermore, a spiral phase and a Gaussian function are introduced, and a kernel function is constructed based on the spiral phase and the Gaussian function, including: The kernel function is constructed based on the spiral phase and the Gaussian function, as shown in formula (1). (1) in, For kernel function, Let be the position vector at the initial plane. For the topological charge of the spiral phase, It is the imaginary unit. It is the waist width. The frequency of the Fourier space; It is a Gaussian function.

[0008] Furthermore, hyperbolic cosine functions are introduced and superimposed to construct weighting functions to obtain the multi-cosine correlated vortex light field, including: The weighting function is constructed by superimposing hyperbolic cosine functions, as shown in formula (2).

[0009] (2) in, For the weight function, Coherence length The normalization coefficient is... and The coefficients representing the number of columns describing the hyperbolic function along the x and y axes. and It is a positive real number. and It is a positive real number. It is a hyperbolic cosine function.

[0010] Furthermore, a partially coherent light construction formula is introduced, and the cross-spectral density function of the multisine correlated vortex light field at the initial plane is constructed by combining the kernel function and the weighting function, including: A partially coherent light construction formula is introduced, 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; The cross-spectral density function of the cosine-correlated vortex light field at the initial plane is constructed by combining the kernel function and the weighting function, as shown in Equation (4).

[0011] (4).

[0012] Furthermore, a free-space transport formula is introduced, and an expression for the light intensity of the cosine-correlated vortex light field at any transport distance is constructed based on the cross-spectral density function, including: S41. Introducing the free-space transmission formula, we obtain the expression for the light intensity of the cosine-correlated vortex light field at any transmission distance z, as shown in formula (5). (5) in, Let z be the position vector at any position. For wave number, , Wavelength; S42. Construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance by combining the cross spectral density function, as shown in formula (6). (6) in, , , 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).

[0013] Furthermore, by adjusting the transmission distance and the parameters of the cosine-correlated vortex optical field, the intensity distribution of the cosine-correlated vortex optical field can be controlled, including: Setting parameters for the cosine-correlated vortex light field , , , , and The value of z is adjusted from small to large to obtain an array composed of hollow sub-beams; Readjust the parameters of the cosine-correlated vortex light field from small to large. and The value of is used to obtain hollow beam arrays with different numbers of rows and columns, thereby realizing the control of the number of rows and columns of the hollow beam array.

[0014] Beneficial effects: This invention provides a method for generating a hollow optical array with a rectangular distribution, constructing a cosine Gaussian correlated vortex beam. By adjusting the parameters of the cosine Gaussian correlated vortex beam, controllable transmission of the beam is achieved, and effective control of the array distribution of hollow sub-beams is realized. This allows the hollow beam array to be applied to more optical imaging applications, promoting the development of optical imaging. Attached Figure Description

[0015] 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.

[0016] Figure 1 A flowchart of a method for generating a hollow optical array with a rectangular distribution, provided by the present invention; Figure 2Light intensity distribution diagram of hollow beam array at different transmission distances provided for the implementation of this invention; Figure 3 To have different Cosine-correlated vortex optical field in transmission distance Light intensity distribution map at the location; Figure 4 For cosine-correlated vortex light field ( , Light intensity distribution diagram at different transmission distances; Figure 5 For having Cosine-correlated vortex optical field in transmission distance Light intensity distribution at that location. Detailed Implementation

[0017] 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.

[0018] This embodiment provides a method for generating a hollow optical array with a rectangular distribution, such as... Figure 1 As shown, it includes: S1: Introduce spiral phase and Gaussian function, and construct kernel function based on spiral phase and Gaussian function; S2: Introduce hyperbolic cosine functions and superimpose them to construct weighting functions to obtain the multicosine-correlated vortex light field; S3: Introduce a partially coherent light construction formula, and combine kernel function and weighting function to construct the cross spectral density function of the cosine-correlated vortex light field at the initial plane; S4: Introduce the free space transmission formula and combine it with the cross spectral density function to construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance, that is, the expression of the cosine-correlated vortex light field. S5: Adjust the transmission distance and the parameters of the cosine-correlated vortex light field to obtain the intensity distribution control of the cosine-correlated vortex light field, and then obtain the array shape of the sub-beams as hollow beams according to the parameter control, that is, obtain the rectangular distribution hollow light array.

[0019] Specifically, a spiral phase and a Gaussian function are first introduced, and a kernel function is constructed based on the spiral phase and Gaussian function. A hyperbolic cosine function is then introduced, and a weighting function is constructed by superimposing the hyperbolic cosine function to obtain a multi-cosine correlated vortex light field. The spiral phase generates a phase singularity at the beam center, resulting in zero central light intensity, thus forming a dark kernel. This is crucial for generating a hollow beam. The construction of the weighting function and kernel function through the spiral phase provides the foundation for subsequently obtaining a hollow beam array. Secondly, a partially coherent light construction formula is introduced, and the cross spectral density function of the cosine-correlated vortex light field at the initial plane is constructed by combining the kernel function and the weighting function. The complete statistical characteristics of the initial light source are strictly defined, which provides a basis for obtaining the light intensity expression in the future. Furthermore, the free-space transmission formula is introduced, and the intensity expression of the cosine-correlated vortex light field at any transmission distance is constructed by combining the cross spectral density function. That is, the expression of the cosine-correlated vortex light field. By analyzing the intensity expression at different transmission distances, it is possible to determine at which position the light field will form the clearest and most stable rectangular hollow light array, providing key parameters for experimental setup and potential applications. Finally, by adjusting the transmission distance and the parameters of the cosine-correlated vortex optical field, the intensity distribution of the cosine-correlated vortex optical field is controlled. Then, based on the parameter control, the array shape of the sub-beams as hollow beams is obtained, that is, a rectangular distributed hollow optical array is obtained, realizing the flexible control of the optical array.

[0020] In a specific embodiment, a spiral phase and a Gaussian function are introduced. The scheme for constructing the kernel function based on the spiral phase and the Gaussian function is as follows: Introducing a spiral phase and a Gaussian function, a kernel function is constructed based on the spiral phase and the Gaussian function, as shown in formula (17). (17) in, For kernel function, Let be the position vector at the initial plane. For the topological charge of the spiral phase, It is the imaginary unit. It is the waist width. The frequency of the Fourier space; It is a Gaussian function.

[0021] The spiral phase generates a phase singularity at the beam center, resulting in zero central light intensity and thus forming a dark nucleus. This is crucial for generating a hollow beam. In this scheme, the kernel function is constructed using the spiral phase and a Gaussian function, ensuring that the final generated light field possesses the core properties of vortex light, limiting the effective range of each vortex unit, and preventing unlimited energy diffusion. This provides the foundation for subsequently separating multiple independent sub-beams (i.e., array elements) in space.

[0022] In a specific embodiment, the scheme of introducing a hyperbolic cosine function and superimposing the hyperbolic cosine function to construct a weighting function to obtain the multicosine correlated vortex optical field is as follows: Introducing the hyperbolic cosine function and superimposing it to construct the weighting function, as shown in formula (18),

[0023] (18) in, For the weight function, Coherence length The normalization coefficient is... and The coefficients representing the number of columns describing the hyperbolic function along the x and y axes. and It is a positive real number. and It is a positive real number. It is a hyperbolic cosine function.

[0024] In this scheme, the introduction of hyperbolic cosine function modulates the initial continuous optical field distribution, and the energy is preferentially concentrated at the positions corresponding to these peaks, laying the structural foundation for the final array distribution. The parameters in the hyperbolic cosine function can control the interval and number of its peaks. By adjusting these parameters, the number of rows / columns and the spacing of the sub-beams in the final optical array can be determined in advance, realizing the preliminary design of the array structure.

[0025] In a specific embodiment, the scheme of introducing a partially coherent light construction formula and combining a kernel function and a weighting function to construct the cross spectral density function of the multi-cosine correlated vortex light field at the initial plane is as follows: A partially coherent light construction formula is introduced, as shown in formula (19). (19) 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; The cross-spectral density function of the cosine-correlated vortex light field at the initial plane is constructed by combining the kernel function and the weighting function, as shown in Equation (20).

[0026] (20).

[0027] In this scheme, the complete statistical characteristics of the initial light source are strictly defined by the partially coherent light construction formula, which provides a basis for obtaining the light intensity expression in the future.

[0028] In a specific embodiment, the scheme for constructing the light intensity expression of the cosine-correlated vortex light field at any transmission distance by introducing the free-space transmission formula and combining it with the cross spectral density function is as follows: S41. Introducing the free-space transmission formula, we obtain the expression for the light intensity of the cosine-correlated vortex light field at any transmission distance z, as shown in formula (21). (twenty one) in, Let z be the position vector at any position. For wave number, , Wavelength; S42. Construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance by combining the cross spectral density function, as shown in formula (22). (twenty two) in, , , and The intermediate component of light intensity is shown in formulas (23)-(26). (twenty three) (twenty four) (25) (26) in, , , , , and These are intermediate variables in the calculation process, as shown in formulas (27)-(32). (27) (28) (29) (30) (31) (32).

[0029] In this scheme, by analyzing the light intensity expression under different transmission distances, we can determine at which position the light field will form the clearest and most stable rectangular hollow light array, providing key parameters for experimental setup and potential applications.

[0030] In a specific embodiment, by adjusting the transmission distance and the parameters of the cosine-correlated vortex optical field, the intensity distribution of the cosine-correlated vortex optical field is controlled. Then, based on the parameter control, the array configuration of the sub-beams as hollow beams is obtained, that is, the scheme of rectangular distributed hollow optical array is obtained: Setting parameters for the cosine-correlated vortex light field , , , , and The value of z is adjusted from small to large to obtain an array composed of hollow sub-beams; Readjust the parameters of the cosine-correlated vortex light field from small to large. and The value of is used to obtain hollow beam arrays with different numbers of rows and columns, thereby realizing the control of the number of rows and columns of the hollow beam array.

[0031] Example 1: The parameters are selected as follows , , , , , . Figure 2 The transmission distances in (a)-(d) are respectively: , , , As the transmission distance increases, the light intensity distribution of the light field will undergo a self-splitting phenomenon, changing from a hollow distribution ( Figure 3 (a) evolved into an array consisting of 3×3 hollow sub-beams. Figure 3 (c) As the transmission distance further increases, the dark center of the sub-beam in the obtained 5×5 hollow beam array tends to gradually decrease. Figure 3 (d) Therefore, by setting the transmission distance, the light source can obtain a flat-top beam array.

[0032] Example 2: The parameters are selected as follows , , , , . Figure 3(a)-(b) They are respectively , .when At that time, the cosine-correlated vortex optical field, during the transmission distance The beam will split into an array of 3×3 sub-beams, but the hollow characteristic of the sub-beams is not obvious. Figure 3 (a)). when At that time, the multi-cosine multi-correlated vortex optical field, during the transmission distance The location will have an array with 3×3 hollow sub-beams. Figure 3 (b) Therefore, by setting the topological charge number of the light field... The hollowness of the sub-beams of the optical field can be adjusted.

[0033] Example 3: The parameters are selected as follows , , , , . Figure 4 The transmission distances in (a)-(b) are respectively: , .when As the transmission distance increases, the light field will evolve from a hollow distribution to a shape along the x-axis. An array of hollow sub-beams ( Figure 4 (b)).

[0034] Example 4: The parameters are selected as follows , , , , . Figure 5 (a)-(b) They are respectively and .when At that time, the light field will evolve into a direction along the y-axis. A hollow beam of light ( Figure 5 (a) The number of columns in the y-direction is Column. When At that time, the light field will evolve into a 3×3 array of hollow sub-beams ( Figure 5 (b)). Therefore, by setting and The number of rows and columns of the hollow beam array can be adjusted.

[0035] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions 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 optical array with a rectangular distribution, characterized in that, include: S1: Introduce spiral phase and Gaussian function, and construct kernel function based on spiral phase and Gaussian function; S2: Introduce hyperbolic cosine functions and superimpose them to construct weighting functions to obtain the multicosine-correlated vortex light field; S3: Introduce a partially coherent light construction formula, and combine kernel function and weighting function to construct the cross spectral density function of the cosine-correlated vortex light field at the initial plane; S4: Introduce the free space transmission formula and combine it with the cross spectral density function to construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance, that is, the expression of the cosine-correlated vortex light field. S5: Adjust the transmission distance and the parameters of the cosine-correlated vortex light field to obtain the intensity distribution control of the cosine-correlated vortex light field, and then obtain the array shape of the sub-beam as a hollow beam according to the parameter control, that is, obtain the rectangular distribution hollow light array.

2. The method for generating a hollow optical array with a rectangular distribution according to claim 1, characterized in that, Introducing spiral phase and Gaussian function, a kernel function is constructed based on spiral phase and Gaussian function, including: The kernel function is constructed based on the spiral phase and the Gaussian function, as shown in formula (1). （1） in, For kernel function, Let be the position vector at the initial plane. For the topological charge of the spiral phase, It is the imaginary unit. It is the waist width. The frequency of the Fourier space; It is a Gaussian function.

3. The method for generating a hollow optical array with a rectangular distribution according to claim 2, characterized in that, Introducing hyperbolic cosine functions and superimposing them to construct weighting functions yields a multi-cosine correlated vortex optical field, including: The weighting function is constructed by superimposing hyperbolic cosine functions, as shown in formula (2). （2） in, For the weight function, Coherence length The normalization coefficient is... and The coefficients representing the number of columns describing the hyperbolic function along the x and y axes. and It is a positive real number. and It is a positive real number. It is a hyperbolic cosine function.

4. The method for generating a hollow optical array with a rectangular distribution according to claim 3, characterized in that, A partially coherent light construction formula is introduced, and a cross-spectral density function of the multi-cosine correlated vortex light field at the initial plane is constructed by combining kernel functions and weighting functions, including: A partially coherent light construction formula is introduced, 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; The cross-spectral density function of the cosine-correlated vortex light field at the initial plane is constructed by combining the kernel function and the weighting function, as shown in Equation (4). （4）。 5. The method for generating a hollow optical array with a rectangular distribution according to claim 4, characterized in that, Introducing the free-space transport formula, an expression for the light intensity of the multi-cosine correlated vortex light field at any transport distance is constructed based on the cross-spectral density function, including: S41. Introducing the free-space transmission formula, we obtain the expression for the light intensity of the cosine-correlated vortex light field at any transmission distance z, as shown in formula (5). （5） in, Let z be the position vector at any position. For wave number, , Wavelength; S42. Construct the light intensity expression of the cosine-correlated vortex light field at any transmission distance by combining the cross spectral density function, as shown in formula (6). （6） in, , , 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）。 6. The method for generating a hollow optical array with a rectangular distribution according to claim 1, characterized in that, Adjusting the transmission distance and the parameters of the cosine-correlated vortex optical field allows for the control of the light intensity distribution of the cosine-correlated vortex optical field, including: Setting parameters for the cosine-correlated vortex light field , , , , and The value of z is adjusted from small to large to obtain an array composed of hollow sub-beams; Readjust the parameters of the cosine-correlated vortex light field from small to large. and The value of is used to obtain hollow beam arrays with different numbers of rows and columns, thereby realizing the control of the number of rows and columns of the hollow beam array.

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