Design method of optical vortex array mask plate with controllable sub-vortex shape

Abstract

The invention discloses a design method of an optical vortex array mask plate with a controllable sub-vortex shape, and the method comprises the steps: modulating the phase of a conventional optical vortex array through combining a discrete shaping technology and a Fourier phase shift theorem; therefore, the polygonal optical vortex array with 100% space utilization rate and self-similarity characteristics is generated under the tight arrangement theory and the fractal rule. The complex transmittance function of the polygonal optical vortex array mask plate is constructed according to the method, the complex transmittance function is loaded into a spatial light modulator through a computer in an experiment, the mask plate of the polygonal optical vortex array is generated, and the mask plate can be used for generating an optical vortex array with controllable sub-vortex shapes. According to the optical vortex array with the controllable sub-vortex shape, the space utilization rate is 100% under the tight arrangement theory, the optical vortex array has self-similarity under the fractal rule, the functionality of the optical vortex array is remarkably improved, and therefore the optical vortex array has very important application prospects in the optical field.

Description

Technical Field

[0001] This invention relates to the field of optics, and more specifically to a design method for an optical vortex array mask with controllable sub-vortex shape. Background Technology

[0002] In recent years, vortex beams carrying orbital angular momentum have been widely used in cutting-edge fields such as optical communication, optical tweezers, optical encryption, and measurement. With further research and increasingly complex application requirements, optical vortex arrays with rich spatial modes have attracted much attention. An optical vortex array consists of multiple vortex beams, primarily using orbital angular momentum as the carrier of information and energy, with each sub-vortex operating independently. Compared to a single vortex beam, optical vortex arrays add the degree of freedom of spatial arrangement, providing richer information dimensions and greater controllability, making them promising for applications in high-capacity optical communication, multi-particle manipulation, and parallel micro / nano fabrication.

[0003] Classical optical vortex arrays are typically generated using Dammann gratings, but due to diffraction rules, the resulting arrays are limited to square shapes, making it difficult to effectively utilize the spatial positions of sub-vortices. To address this issue, researchers have proposed optical vortex arrays with rich spatial patterns, such as fractal optical vortex arrays, optical vortex arrays generated based on arbitrary curve techniques, optical vortex arrays with compact arrangement characteristics, and elliptical optical vortex arrays with controllable sub-vortex directions [Optics Letters, 41(14), 3161(2016); Optics Express, 26(8), 9798(2018); Optics Express, 26(18), 22965(2018); Applied Physics Letters, 116(1), 011101(2020)]. To date, the degree of freedom regarding the spatial position of sub-vortices in optical vortex arrays has been fully developed and utilized, greatly promoting the development and application of optical vortex arrays. However, the shapes of sub-vortices in traditional optical vortex arrays are mostly limited to circular / elliptical shapes. The degree of freedom of sub-vortex shape in optical vortex arrays is ignored, which limits the functionality of traditional optical vortex arrays. For example, optical vortex arrays under the compact packing theory can hardly meet 100% space utilization, and sub-vortices under fractal rules do not have self-similarity with the optical vortex array, thus greatly limiting the application scenarios and scope of application of optical vortex arrays.

[0004] In summary, there is currently a lack of an optical vortex array laser mode with controllable sub-vortex shape that can be applied to the field of optics. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the above-mentioned technical problems and provide a design method for an optical vortex array mask with controllable sub-vortex shape, and to generate an optical vortex array with controllable sub-vortex shape using the mask.

[0006] This invention utilizes the principle of computational holography to obtain an amplitude-modulated phase mask template for an optical vortex array with controllable sub-vortex shape through computer encoding. This can generate an optical vortex array with controllable sub-vortex shape, and therefore has important application value in the field of optics.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] First, based on discrete shaping technology and Fourier phase shift theorem, the electric field expression for an optical vortex array with controllable sub-vortex shape is:

[0009]

[0010] Where F() is the Fourier transform function, (x,y) are the coordinates before the Fourier transform, (η,ξ) are the coordinates after the Fourier transform, m is the number of sub-vortices in the optical vortex array, i is the imaginary unit, (S m,1 ,S m,2 H and H are the x and y coordinates in the sub-vortex position matrix S, respectively. l (x,y) is a regular polygonal discrete shaping beam, specifically expressed as:

[0011]

[0012] Where l is the parameter of the regular polygon, n is the number of discrete points in the discrete shaping beam, (Q n,1 Q n,2 H0(x,y) represents the horizontal and vertical coordinates in the discrete point difference matrix Q, and H0(x,y) is the complex amplitude of the pre-generated circular beam. The purpose is to combine the difference matrix to achieve discrete shaping of the target image.

[0013] The phase expression of the blazed grating is P0 = 2πx / d, where x is the horizontal vector in the rectangular coordinate system and d is the phase period of the blazed grating. Its function is to generate the electric field expression of the optical vortex array with controllable sub-vortex shape in the experiment.

[0014] A mask for an optical vortex array with controllable subvortex shape, using discrete shaping techniques and Fourier phase shift theorem, generates the amplitude, phase, and a blazed grating of the beam. The specific expression for its complex transmittance function is as follows:

[0015] t=A(η,ξ)exp{i[angle(G(η,ξ))+P0]}

[0016] Where A(η,ξ) is the amplitude term of the optical vortex array with controllable sub-vortex shape, and angle() is the angular direction function. The mask described based on this complex transmittance function is the mask of the optical vortex array with controllable sub-vortex shape described in this invention.

[0017] Technical effects of the present invention:

[0018] The mask designed in this invention can generate an optical vortex array with controllable sub-vortex shapes. By adjusting the difference matrix, sub-vortices with different shapes can be obtained, and then by adjusting the position matrix, an optical vortex array with controllable sub-vortex shapes can be achieved. Compared with traditional optical vortex arrays, the optical vortex array with controllable sub-vortex shapes satisfies 100% space utilization under compact packing theory and exhibits self-similarity under fractal rules, significantly improving the functionality of the optical vortex array and thus having very important application prospects in the field of optics. Attached Figure Description

[0019] Figure 1 It is a mask for an optical vortex array with 100% space utilization under the compact arrangement theory.

[0020] Figure 2 yes Figure 1 The mask template shown generates a tightly packed polygonal optical vortex array.

[0021] Figure 3 It is a mask template for optical vortex arrays with self-similar properties under fractal rules.

[0022] Figure 4 yes Figure 3 The fractal polygon optical vortex array generated by the mask template is shown. Detailed Implementation

[0023] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0024] The design method for the optical vortex array mask with controllable sub-vortex shape described in this invention, firstly, based on discrete shaping technology and Fourier phase shift theorem, reveals that the electric field expression for the optical vortex array with controllable sub-vortex shape is:

[0025]

[0026] Where F() is the Fourier transform function, (x,y) are the coordinates before the Fourier transform, (η,ξ) are the coordinates after the Fourier transform, m is the number of sub-vortices in the optical vortex array, i is the imaginary unit, (S m,1 ,S m,2 H and H are the x and y coordinates in the sub-vortex position matrix S, respectively.l (x,y) is a regular polygonal discrete shaping beam, specifically expressed as:

[0027]

[0028] Where l is the parameter of the regular polygon, n is the number of discrete points in the discrete shaping beam, (Q n,1 Q n,2 H0(x,y) represents the horizontal and vertical coordinates in the discrete point difference matrix Q, and H0(x,y) is the complex amplitude of the pre-generated circular beam. The purpose is to combine the difference matrix to achieve discrete shaping of the target image.

[0029] The phase expression of the blazed grating is P0 = 2πx / d, where x is the horizontal vector in the rectangular coordinate system and d is the phase period of the blazed grating. Its function is to generate the electric field expression of the optical vortex array with controllable sub-vortex shape in the experiment.

[0030] A mask for an optical vortex array with controllable subvortex shape, using discrete shaping techniques and Fourier phase shift theorem, generates the amplitude, phase, and a blazed grating of the beam. The specific expression for its complex transmittance function is as follows:

[0031]

[0032] Where A(η,ξ) is the amplitude term of the optical vortex array with controllable sub-vortex shape, and angle() is the angular direction function. The mask described based on this complex transmittance function is the mask of the optical vortex array with controllable sub-vortex shape described in this invention.

[0033] In the experiment, the sub-vortex shapes were selected as l=3, 4, and 6. Using compact packing theory, polygonal optical vortex arrays with 100% space utilization were generated, such as... Figure 2 As shown, polygonal optical vortex arrays with self-similar properties were generated based on fractal rules, such as... Figure 4 As shown. Figure 1 and Figure 3 These are mask templates for polygonal optical vortex arrays under compact packing theory and fractal rules, respectively. The sub-vortex shapes are selected as l = 3, 4, and 6.

[0034] Example

[0035] The following example uses a 1024×1024 photomask to illustrate an optical vortex array with controllable sub-vortex shapes for a 532nm laser. The sub-vortex shapes of the optical vortex array are selected as l=3, 4, and 6. Based on the complex transmittance function of the photomask in the specific implementation, the photomask with controllable sub-vortex shapes is finally obtained. Figure 1 This refers to the polygonal optical vortex array mask template with controllable subvortex shape under the compact arrangement theory in the embodiment. Figure 3 This refers to the polygonal optical vortex array mask with controllable sub-vortex shape under fractal rules in the embodiment. This mask for a controllable sub-vortex optical vortex array can be implemented using a spatial light modulator. Taking the Core-I-101 spatial light modulator from Nanjing CoreVision Electronics Co., Ltd. as an example, its pixel size is 6μm, fill factor is 93.65%, and resolution is 1920×1080 pixels. A 532nm continuous-wave solid-state laser with adjustable power from 0-1W was used in the experiment.

[0036] like Figure 2 and Figure 4 As shown, this is the optical vortex array with controllable sub-vortex shape generated in the embodiment. It can be seen from the figure that an optical vortex array with controllable sub-vortex shape was obtained, and the sub-vortex shapes in the experiment are clearly distinguishable. The optical vortex array with 100% space utilization and self-similarity characteristics is clearly distinguishable.

[0037] In summary, this invention proposes a specific design and implementation scheme for a mask template of an optical vortex array with controllable sub-vortex shape. Taking sub-vortex shapes of l=3, 4, and 6 as examples, the optical vortex array generates two cases: compact arrangement and fractal arrangement. For laser with a working wavelength of 532nm, a technical implementation route for a mask template of an optical vortex array with controllable sub-vortex shape is proposed.

[0038] The mask template for generating an optical vortex array with controllable sub-vortex shape described above is merely an example of one specific embodiment of the present invention and should not be construed as limiting the scope of protection of the present invention. It should be noted that those skilled in the art can make various modifications and improvements to the specific implementation details proposed in this patent without departing from the basic idea of ​​the present invention, and these modifications and improvements all fall within the scope of protection of the present invention.

Claims

1. A method for designing a sub-vortex shape controllable optical vortex array mask, characterized in that: The phase of the optical vortex array is modulated by combining a discrete plastic shaping technique and a Fourier phase shift theorem to generate a polygonal optical vortex array with 100% spatial utilization and self-similarity characteristics under a close packing theory and a fractal rule, and an electric field expression of the polygonal optical vortex array is: where F() is the Fourier transform function, (x, y) is the spatial coordinate before Fourier transform, (η, ξ) is the coordinate after Fourier transform, m is the sub-vortex number in the optical vortex array, M is the maximum value of the sub-vortex number in the optical vortex array, i is the imaginary unit, (S m,1 ,S m,2 ) are the horizontal and vertical coordinates in the sub-vortex position matrix S respectively, l is the regular polygon parameter, H l (x, y) is the regular polygon discrete shaped beam, and the specific expression is as follows: wherein n is the number of discrete points in the discrete shaped beam, N is the maximum number of discrete points in the discrete shaped beam, (Q n,1 , n,2 ) are the horizontal and vertical coordinates of the discrete point difference matrix Q, respectively, and H0(x, y) is the complex amplitude of the pre-generated circular beam. The complex transmittance function of the mask plate t of the sub-vortex shape controllable optical vortex array is obtained by combining the amplitude, the phase and a blazed grating of the sub-vortex shape controllable optical vortex array, and an expression of the complex transmittance function is: t=A(η,ξ)exp{i[angle(G(η,ξ))+P0]} Wherein, A(η,ξ) is an amplitude term of the sub-vortex shape controllable optical vortex array, angle() is an angle function, and P0 is a phase of the blazed grating; the mask plate described based on the complex transmittance function is the mask plate of the sub-vortex shape controllable optical vortex array.

2. The method of designing a sub-vortex shape controllable optical vortex array mask according to claim 1, wherein: The phase P0 of the blazed grating is 2πx / d, wherein x is a horizontal direction vector of a rectangular coordinate system, and d is a phase period of the blazed grating.

3. The method of claim 1, wherein the sub-vortex shape-controllable optical vortex array mask design is characterized by: The pixel size of the mask plate is 1024×1024.

4. The method for generating a polygonal optical vortex array with 100% space utilization and self-similarity characteristics under the close packing theory and the fractal rule, characterized in that: The sub-vortex shape controllable optical vortex array mask plate is generated by using the design method according to any one of claims 1-2, and the method comprises: a laser emits a parallel light beam to a spatial light modulator loaded with the polygonal optical vortex array mask plate, and the light beam transmitted by the spatial light modulator passes through a double-convex lens filtering system to obtain the polygonal optical vortex array with 100% spatial utilization and self-similarity characteristics under a close packing theory and a fractal rule.

5. The method of claim 4, wherein: The laser is a continuous wave solid laser.

6. The method of claim 5, wherein: The wavelength of the laser is 532 nm.

7. The method of claim 4, wherein: The spatial light modulator is a reflective spatial light modulator.

8. The method of claim 7, wherein: The size of the spatial light modulator is 1920×1080 pixels, and the pixel size is 6μm.

9. The method of claim 4, wherein: The lens filtering system comprises two lenses with a focal length of 150 mm.

10. A laser light source for use in the field of optics, characterized in that: The sub-vortex shape controllable optical vortex array is generated by using the polygonal optical vortex array generation method according to any one of claims 4-8.

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