Generation system and method based on vector light beam of any structure

Abstract

The invention discloses a generation system and method based on a vector light beam of any structure, and the system comprises a laser, a collimating and beam expanding element, a polarizing film, a first half-wave plate, a beam splitting cube, a polarization beam splitting cube, a reflector, a second half-wave plate, a quarter-wave plate, a Fourier lens, a spatial light modulator, a computer, and a camera. Two parallel light beams which are generated by a continuous wave solid laser and a half-wave plate and have an orthogonal polarization state are respectively irradiated on spatial light modulators which are loaded with different topological charge values and are used for customizing light beam holograms with any shapes and structures, are modulated by the spatial light modulators, and are coaxially superposed with a Fourier lens through a quarter-wave plate; and the customized vector light beam with any shape and uniform intensity can be generated. According to the invention, the direct mapping of a real object can be realized, the light beam quality is improved, and the polarization state is flexibly regulated and controlled.

Description

Technical Field

[0001] This invention relates to the field of optical technology, and in particular to a system and method for generating arbitrary structure vector beams. Background Technology

[0002] In recent years, the generation and manipulation of vector beams have gradually become a major research hotspot in the field of optical field manipulation. With independently adjustable intensity, phase, and polarization states, they have become active research topics in cutting-edge fields such as particle trapping [Nat. Commun. 4, 2891 (2013)] and laser micro / nano fabrication [Opt. Laser Technol. 163, 109338 (2023)]. To meet increasingly complex application demands, researchers need to construct special vector beams to satisfy the requirements of complex applications.

[0003] To construct vector beams, researchers investigated the modulation of typical toroidal vector beams, including vector Laguerre-Gaussian beams [Appl. Phys. Lett. 122, 161106 (2023)], vector Bessel beams [Adv. Photonics Nexus 3, 36010 (2024)], and vector perfect vortex beams [Photonics Res. 13, 468 (2025)]. Furthermore, researchers explored vector beams with irregular geometries, including spiral cones [Opt. Lett. 48, 4897 (2023)], four-leaf clover shapes [Appl. Phys. Lett. 114, 41101 (2019)], and cardioids [Opt. Lett. 42, 3884 (2017)], and developed versatile polarization distributions. However, existing methods for shaping arbitrary vector beams rely excessively on explicit mathematical representations. When generating beams with complex shapes, the intensity distribution is often non-uniform. Furthermore, the lack of compatibility between polarization state manipulation and shape design limits the application of vector beams in practical scenarios.

[0004] In summary, in the field of vector beam shaping, it is of great significance to develop a vector beam generation method that can flexibly map the shape of real objects without explicit mathematical expressions, while optimizing intensity distribution and polarization control. Summary of the Invention

[0005] To address the aforementioned technical problems, the present invention aims to provide an arbitrary structure vector beam generation system and method based on the epicycle model and Poincaré sphere technique, enabling direct mapping of real objects, improving beam quality, and flexibly controlling the polarization state.

[0006] The technical solution adopted in this invention is: A system for generating vector beams based on arbitrary structure, the system comprising a laser, a collimating and expanding element, a polarizer, a first half-wave plate, a beam splitter cube, a polarizing beam splitter cube, a mirror, a second half-wave plate, a spatial light modulator, a quarter-wave plate, a Fourier lens, and a camera; The beam emitted by laser 1 passes sequentially through a collimating and expanding element, a polarizer, a first half-wave plate, a beam splitter cube, and a polarization beam splitter cube. The beam is split into a horizontally polarized beam and a vertically polarized beam by the polarization beam splitter cube. The horizontally polarized beam directly illuminates the spatial light modulator, while the vertically polarized beam passes sequentially through a mirror and a second half-wave plate before illuminating the spatial light modulator. The two modulated beams are then recombined by the polarization beam splitter cube and reflected by the beam splitter cube. The reflected beam is converted from linearly polarized to circularly polarized by a quarter-wave plate. Finally, the two scalar beams carrying orthogonal basis vectors are combined into a vector beam by a Fourier lens and generated on the focal plane by a camera. As a preferred embodiment, a computer is also provided. After the light beam passes through the polarization beam splitting cube, it is split into two beams and illuminates the screen. The screen is a phase hologram loaded by the computer connected to the spatial light modulator. After being modulated by the spatial light modulator, the two beams of light are recombined through the polarization beam splitting cube. As a preferred embodiment, the method of generating a custom arbitrary-shaped vector beam using the system described above involves using two parallel beams with orthogonal polarization generated by a continuous-wave solid-state laser and a half-wave plate to illuminate a spatial light modulator of a custom arbitrary-shaped structural beam hologram loaded with different topological charges. The beam is modulated by the spatial light modulator and then coaxially superimposed by a quarter-wave plate and a Fourier lens to generate a custom arbitrary-shaped vector beam with uniform intensity. As a preferred method, the steps for obtaining a customized hologram of a beam with an arbitrary shape are as follows: Based on this model and the principle of computational holography, the phase hologram generated by computer calculation is as follows: First, the electric field expression for a scalar beam with an arbitrary shape can be customized: Where a(x,y) is the amplitude. The phase distribution along the preset trajectory [x(t), y(t)] is given by x(t) and y(t), which are analytical expressions of the customized trajectory. Secondly, based on computational holography, a hologram is generated in the front focal plane of the lens, and its complex amplitude can be expressed as: In the formula: E(x) d ,y dH(x) represents the target field, which can be directly obtained from E(x,y) by simply replacing the coordinate variables with the target plane coordinate system; j ,y j () indicates the incident field; x j and y j x represents the coordinates of the j-th pixel on the spatial light modulator; d and y d λ represents the spatial coordinates of the d-th focal point in the target; λ is the laser wavelength; f is the focal length of the focusing lens. Finally, based on the above, the modulation function of the complex amplitude phase function is obtained to create a hologram of a beam with a custom arbitrary shape. T = angle[H(x) j ,y j )] Here, angle() is the phase function. As a preferred option, the above method, utilizing the current-round model and Fourier series, can be expressed as: Where N is the number of rounds, Re() represents the real part of the complex number, Im() represents the imaginary part of the complex number, and c k The radius and initial rotation angle of each current cycle are determined, and can be written as: Where, f(g) = x g +iy g , g represents the g-th key point, (x,y) are the coordinates of each key point on the curve, and ω=2πk / N is the rotational speed of this round. As a preferred option, from a mathematical perspective, in the above methods, H(x) j ,y j ) indicates that it has a weighting factor E(x) d ,y d The summation of individual plane waves; therefore, to increase the beam generation speed, summation is usually used instead of integration. D represents the total number of foci. To achieve a uniform intensity distribution, a random phase Ψ is introduced at each focal point. d =q*Rand(0,1), where 0≤q≤2π represents the modulation depth, and Rand(0,1) is a uniform random number in the range [0,1].

[0007] Technical effects of the present invention: The arbitrary structure vector beam generation system and method designed in this invention can generate a customized arbitrary shape vector beam with uniform intensity. The shape and polarization state of the vector beam are controllable, and a vector beam with uniform intensity and amplitude distributed along any preset trajectory can be generated according to actual needs. Compared with previous beam shaping techniques, this greatly improves the controllability of the vector beam. Therefore, it has very important application prospects in the fields of particle manipulation and micromaterial shaping. Attached Figure Description

[0008] Figure 1 This is a schematic diagram of the arbitrary structure vector beam generation system in this invention;

[0009] Figure 2 The phase holograms obtained in this invention are obtained by using an arbitrary vector beam generation method when the preset shape is a hat shape with a topological charge value of 1 and n is -1, and when the preset shape is a glove with a topological charge value of 2 and n is -1.

[0010] Figure 3 It is to utilize Figure 2 The beams generated by phase holograms with the same shape but different topological charge values ​​are shown, and vector beams with custom shapes are produced by coaxial superposition of the proposed system. Figure descriptions: 1. Laser; 2. Collimating and expanding element; 3. Polarizer; 4. First half-wave plate; 5. Beam splitter cube; 6. Polarizing beam splitter cube; 7. Mirror; 8. Second half-wave plate; 9. Spatial light modulator; 10. Quarter-wave plate; 11. Fourier lens; 12. Camera. Detailed Implementation

[0011] This invention utilizes epicycle modeling, Poincaré sphere technology, and computational holography principles to generate arbitrary structure vector beams through an arbitrary structure vector beam generation system based on epicycle modeling and Poincaré sphere technology. This greatly improves the controllability of vector beams and has very important application prospects in the fields of particle manipulation and micromaterial shaping.

[0012] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0013] Figure 1 This invention is a system for generating arbitrary structure vector beams. The system mainly consists of a laser 1, a collimating and expanding element 2, a polarizer 3, a first half-wave plate 4, a beam splitter cube 5, a polarizing beam splitter cube 6, a mirror 7, a second half-wave plate 8, a spatial light modulator 9, a quarter-wave plate 10, a Fourier lens 11, a computer, and a camera 12. A laser is used as the light source, and a beam expander 2 is used as the collimating and expanding element 2 to expand the beam emitted by the laser 1 to generate a plane wave. The polarization direction of the expanded beam is determined using a polarizer 3 and a first half-wave plate 4. Then, the beam is split into horizontal and vertical polarization components by a polarization beam splitter cube 6. These components illuminate the left and right sections of the spatial light modulator, respectively. The ratio of the two components is adjusted by rotating the first half-wave plate. Since the spatial light modulator is only sensitive to the horizontal polarization component, a second half-wave plate 8 is placed between the reflector 7 and the spatial light modulator 9 to convert the vertically polarized beam into a horizontally polarized beam before illuminating the screen. The screen displays a phase hologram loaded by a computer connected to the spatial light modulator. After modulation by the spatial light modulator, the two beams are recombined by the polarization beam splitter cube 6. These two components are then reflected by the beam splitter cube 5, and the linear polarization basis is converted to a circular polarization basis by a quarter-wave plate 10. Finally, a Fourier lens 11 combines the two scalar beams carrying orthogonal basis vectors into a vector beam, and a camera 12 records the generated vector beam on the focal plane.

[0014] The method for generating a custom arbitrary-shaped vector beam using the system described above involves using two parallel beams with orthogonal polarization generated by a continuous-wave solid-state laser and a half-wave plate to illuminate a spatial light modulator of a custom arbitrary-shaped structural beam hologram loaded with different topological charges. The beam is modulated by the spatial light modulator and then coaxially superimposed by a quarter-wave plate and a Fourier lens to generate a custom arbitrary-shaped vector beam with uniform intensity. Based on this model and the principle of computational holography, the phase hologram generated by computer calculation is as follows: First, the electric field expression for a scalar beam with an arbitrary shape can be customized: Where a(x,y) is the amplitude. Let x(t), y(t) be the phase distribution along the preset trajectory [x(t), y(t)]; x(t) and y(t) are the analytical expressions of the customized trajectory, which can be expressed as follows using the current model and Fourier series: Where N is the number of rounds, Re() represents the real part of the complex number, Im() represents the imaginary part of the complex number, and c k The radius and initial rotation angle of each current cycle are determined, and can be written as: Where, f(g) = x g +iy g , g represents the g-th key point, (x,y) are the coordinates of each key point on the curve, and ω=2πk / N is the rotational speed of this round; Based on computational holography, a hologram is generated in the front focal plane of a lens, and its complex amplitude can be expressed as: In the formula: E(x) d ,y d H(x) represents the target field, which can be directly obtained from E(x,y) by simply replacing the coordinate variables with the target plane coordinate system; j ,y j () indicates the incident field; x j and y j x represents the coordinates of the j-th pixel on the spatial light modulator; d and y d H(x) represents the spatial coordinates of the d-th focal point in the target; λ is the laser wavelength; f is the focal length of the focusing lens; mathematically, H(x) j ,y j ) indicates that it has a weighting factor E(x) d ,y d The summation of individual plane waves. Therefore, to increase the beam generation speed, summation is usually used instead of integration: D represents the total number of foci. To achieve a uniform intensity distribution, a random phase Ψ is introduced at each foci. d =q*Rand(0,1), where 0≤q≤2π represents the modulation depth, and Rand(0,1) is a uniformly random number in the range [0,1]. Based on the above, the modulation function of the complex amplitude phase function is used to obtain the hologram of a beam with a custom arbitrary shape. T = angle[H(x) j ,y j )] Here, angle() is the phase function. Two holograms with the same preset shape but different topological charges are loaded onto the left and right halves of the screen of the spatial light modulator, respectively. Figure 2 This involves generating a beam phase hologram with amplitude and phase distributed along a preset shape resembling a hat or glove, and topological charge values ​​of 1, -1 and 2, -1, respectively. This yields two scalar beams of the same preset shape but carrying different topological charges. After generating the scalar beams, any vector beam of arbitrary shape can be described as the superposition of two orthogonally circularly polarized scalar beams with topological charges m and n, respectively, and can be expressed as: in and These represent the unit vectors for right-handed and left-handed circularly polarized states, respectively. and Let E be the complex amplitude of the scalar beam described above. The polar angle and azimuth angle are denoted by 2θ and 2α, respectively, and they control E... R and E L The amplitude ratio and phase difference between them. The polarization distribution of this vector light field is mainly determined by the topological charge m, n and θ, α. That is, by adjusting parameters such as the topological charge and the initial phase, the vector light field of the corresponding polarization state can be obtained. Figure 3 It is to utilize Figure 2 The beams generated by phase holograms with hat and glove shapes and different topological charge values ​​are shown, and vector beams are produced by coaxial superposition of them through the proposed system. Experimental Example

[0015] To verify the effectiveness of this invention, a phase hologram of a customizable arbitrary structure vector beam is presented for a laser with a working wavelength of 532 nm. The parameters of this customizable arbitrary structure vector beam phase hologram are two different curves, one for a hat and one for gloves. Figure 2 This refers to the customizable arbitrary structure vector beam phase holograms with different topological charge values ​​under different curves used in the embodiments. Such customizable arbitrary structure vector beam phase holograms can be realized using a spatial light modulator. Taking the HDSLM38R phase spatial light modulator from Shanghai Ruilike as an example, its pixel size is 3.8μm, fill factor is >90%, and resolution is 4096 pixels × 2160 pixels. The generated hologram is input into the spatial light modulator via a personal computer. The Fourier lens has a focal length of 300mm. The camera is a professional CMOS camera, Basler acA1600-60gc, with a resolution of 2 megapixels and a pixel size of 4.5 × 4.5μm. 2 .

[0016] Figure 3 As shown, this is the vector beam with an arbitrary structure generated in the embodiment. The inset in the sub-figure represents a preset geometric shape. As can be seen from the figure, we obtained a vector beam with a preset arbitrary structure, and the structured light shape in the experiment is highly consistent with the preset trajectory. Therefore, it has very important application prospects in the fields of particle manipulation and micromaterial shaping.

[0017] In summary, this invention proposes a system and method for generating vector beams based on arbitrary structures, and takes two curved shapes as examples to realize vector light fields with light intensity distributions in the shapes of hats and gloves.

[0018] The parts not described in detail in this embodiment are existing technologies.

[0019] The above-described system and method for generating customizable vector beams with arbitrary structures merely illustrates 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 system for generating vector beams based on arbitrary structures, characterized in that: The generation system consists of a laser (1), a collimating beam expander (2), a polarizer (3), a first half-wave plate (4), a beam splitter cube (5), a polarization beam splitter cube (6), a mirror (7), a second half-wave plate (8), a spatial light modulator (9), a quarter-wave plate (10), a Fourier lens (11), and a camera (12). The beam emitted by the laser (1) passes sequentially through the collimating and expanding element (2), polarizer (3), first half-wave plate (4), beam splitting cube (5), and polarization beam splitting cube (6). The beam is split into a horizontally polarized beam and a vertically polarized beam by the polarization beam splitting cube (6). The horizontally polarized beam directly illuminates the spatial light modulator (9). The vertically polarized beam passes sequentially through the reflector (7) and second half-wave plate (8) before illuminating the spatial light modulator (9). The two beams after modulation are combined again by the polarization beam splitting cube (6) and then reflected by the beam splitting cube (5). The reflected beam is converted from linearly polarized to circularly polarized by the quarter-wave plate (10). Then, the two scalar beams carrying orthogonal basis vectors are combined into a vector beam by the Fourier lens (11) and the vector beam is generated on the focal plane by the camera (12).

2. The system for generating vector beams based on arbitrary structure according to claim 1, characterized in that: A computer is also provided. After the beam passes through the polarization beam splitting cube (6), it is split into two beams and illuminates the screen. The screen is a phase hologram loaded by the computer connected to the spatial light modulator (9). After being modulated by the spatial light modulator (9), the two beams are recombined through the polarization beam splitting cube (6).

3. A method for generating a vector beam of a customized arbitrary shape using the system of claim 2, characterized in that: Two parallel beams with orthogonal polarization, generated by a continuous-wave solid-state laser and a half-wave plate, are respectively irradiated onto a spatial light modulator of a custom arbitrary-shaped beam hologram loaded with different topological charges. After being modulated by the spatial light modulator and coaxially superimposed by a quarter-wave plate and a Fourier lens, a custom arbitrary-shaped vector beam with uniform intensity can be generated.

4. The method according to claim 3, characterized in that: The method for obtaining a hologram of a beam with a custom arbitrary shape involves the following steps: S1. Electric field expression for scalar beams of arbitrary shapes: Where a(x,y) is the amplitude. Let x(t), y(t) be the phase distribution along the preset trajectory [x(t), y(t)]. x(t) and y(t) are the analytical expressions of the customized trajectory; S2. A hologram is generated in the front focal plane of the lens based on computational holography, and its complex amplitude can be expressed as: In the formula: E(x) d ,y d H(x) represents the target field; j ,y j () indicates the incident field; x j and y j x represents the coordinates of the j-th pixel on the spatial light modulator; d and y d λ represents the spatial coordinates of the d-th focal point in the target; λ is the laser wavelength; f is the focal length of the focusing lens. S3. Based on the above, the phase function of the complex amplitude is taken to obtain the modulation function of the customized arbitrary-shaped beam hologram. The customized arbitrary-shaped beam hologram can then be obtained by computer. T=angle[H(x j ,y j )] Here, angle() is the phase function.

5. The method according to claim 4, characterized in that: In step S1, x(t) and y(t) are expressed as: Where N is the number of rounds, Re() represents the real part of the complex number, Im() represents the imaginary part of the complex number, and c k This determines the radius and initial rotation angle of each current wheel.

6. The method according to claim 5, characterized in that: c k Represented as: Where, f(g) = x g +iy g , g represents the g-th key point, (x,y) are the coordinates of each key point on the curve, and ω=2πk / N is the rotational speed of this round.

7. The method according to claim 4, characterized in that: In step S2, H(x j ,y j ) indicates that it has a weighting factor E(x) d ,y d To increase the beam generation speed, the summation of individual plane waves can be used instead of integration, where the summation is the sum of the individual plane waves. D represents the total number of foci, which are uniformly distributed in intensity, with a random phase Ψ introduced at each foci. d =q*Rand(0,1), where 0≤q≤2π represents the modulation depth, and Rand(0,1) is a uniform random number in the range [0,1].

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