A Design Method for a Mask Template that Can Rotate a Light Beam Parallel to the Optical Axis

Abstract

The present invention discloses a design method for a mask capable of rotating a light beam parallel to the optical axis. The present invention proposes a light beam that can be rotated parallel to the optical axis. By segmenting the shaped light beam and separately modulating additional Fourier phase shifts, and then superimposing them to obtain the hologram transmittance function of the light beam, combining the hologram transmittance function and a blazed grating, a mask capable of rotating a light beam parallel to the optical axis can be obtained. Using this mask, a light beam that can be rotated parallel to the optical axis can be generated. The rotation angle, beam size, and rotation radius of the light beam generated by this technology can all be arbitrarily modulated, thereby realizing longitudinal micro-manipulation of particles. This technology solves the problem that structured light beams cannot achieve longitudinal micro-manipulation of particles, and theoretically can endow structured light beams with the ability to support multi-particle longitudinal micro-manipulation in three-dimensional space. This technology is easy to operate and use, providing great potential for the future development of structured optical tweezers.

Description

Technical Field

[0001] The present invention relates to the field of three-dimensional optical tweezers and particle manipulation, and specifically to a design method for a mask capable of rotating a light beam parallel to the optical axis. Background Art

[0002] Since the 1970s, the optical tweezer technology invented by A. Ashkin has brought revolutionary changes to many fields such as condensed matter physics, biology, and nanomaterials [Phys. Rev. Lett. 24, 156 (1970)]. Thanks to the development of structured light beams [Phys. Rev. Lett. 102, 230601 (2009)], the trapping force of optical tweezers has gradually evolved from the gradient force of a single Gaussian beam to the "wrench force" that combines optical orbital angular momentum, spin angular momentum, etc. [Nature 561, 79 (2018)]. Structured light beams play an increasingly important role in the field of optical tweezers due to their rich wavefront distribution and strong plasticity of the light intensity distribution. Nevertheless, some operations are beyond the capabilities of structured optical tweezers, such as rotating particles parallel to the optical axis.

[0003] To solve this technical problem, it is necessary to develop three-dimensional optical tweezers that can operate freely in three-dimensional space. Initially, researchers thought of adjusting the focusing position of the light beam to achieve three-dimensional manipulation of holographic optical tweezers. Although it can achieve point-manipulation three-dimensional manipulation, it has deficiencies such as a small capture range and a single capture method [Opt. Express 28, 12729 (2020)]. Since changing the focusing position also relies on parametric equations and rotation matrices, it is difficult to achieve rotation parallel to the optical axis in three-dimensional space. Another type of three-dimensional operation is the tractor beam, but the tractor beam can only push and pull. There is no way to achieve a complete circular motion parallel to the optical axis [Rep. Prog. Phys. 83, 032401 (2020)]. Another new method for achieving 3D motion involves using recently developed deformable structured light beams [Optica 10, 379 (2023)]. It allows free customization of the transport trajectory along parametric equations. Although there are alternative methods that do not rely on parametric equations, the limitations of deformable structured light beams still exist. That is, it cannot achieve a complete flip of the light beam, so it is impossible to manipulate particles to rotate parallel to the optical axis. Additionally, spatiotemporal vortices may be a feasible solution, but due to their strict requirements for experimental equipment and environmental conditions, it limits the practical implementation of their large-scale application [Nat. Photonics 14, 350 (2020)].

[0004] In summary, in the field of optical tweezers, there is a lack of a direct, reliable, and convenient technology to achieve the parallel rotation of particles along the optical axis. Based on this, the innovation of this invention patent lies in that the beam that can rotate parallel to the optical axis is obtained by synergistically combining the three-dimensional circular trajectory equation with the beam grafting technology and the Fourier phase shift technology. This beam allows for the generation of selectable and adjustable trapping points and enables 360° flipping. We demonstrated the efficacy of this beam in particle manipulation by showing that polystyrene particles can be induced to move in a circular path parallel to the optical axis, successfully achieving longitudinal micro-manipulation of particles. And only one of the usage methods is demonstrated here, which can also provide technical support for tasks such as customizing complex trajectories. Summary of the Invention

[0005] The object of the present invention is to solve the deficiencies of the above technical problems, and provides a mask for generating a beam that can rotate parallel to the optical axis. Then, by loading this mask through a spatial light modulator, a beam that can rotate parallel to the optical axis is generated, and a method for manipulating particles using this beam to achieve longitudinal micro-manipulation of particles is provided.

[0006] Technical Solution: A design method for a mask of a beam that can rotate parallel to the optical axis,

[0007] Combining the amplitude, phase of the beam that can rotate parallel to the optical axis with a blazed grating to obtain the complex transmittance function of the mask of the beam that can rotate parallel to the optical axis, and the expression is:

[0008] T = circ(ρ)exp{j[angle(G(η,ξ)) + P0]}

[0009] where circ(·) is the circular domain function, angle(·) is the function for taking the phase angle, G(·) is the complex amplitude, ρ is the polar coordinate radial variable, exp(·) is the exponential function with the natural constant e as the base, j is the imaginary unit, and P0 is the phase of the blazed grating;

[0010] The electric field expression of the beam that can rotate parallel to the optical axis is:

[0011]

[0012] where, is the Fourier transform function, (x,y) are the coordinates before Fourier transform, (η,ξ) are the coordinates after Fourier transform, G1(x,y,t1), G2(x,y,t2), G3(x,y,t3) …… G k (x,y,t k ) is the complex amplitude of the beam used for superposition, and t1 + t2 + t3 + …… + t k = 2π, U1, U2, U3, ……, U kis the Fourier phase shift factor, responsible for giving each part of the light beam a corresponding displacement to maintain it as a whole, where k is an arbitrary integer; among which G k (x, y, t k ) is expressed as:

[0013]

[0014] Among which Φ k (x, y, t k ) and ψ k (x, y, t k ) are phase terms that can rotate the light beam parallel to the optical axis. c0(t k ) determines the shape of the light beam, which is three-dimensional circular. c′0(t k ) represents the derivative of c0(t k ). The Fourier phase shift factor U k is expressed as:

[0015] U k = exp{2πj[(η + Δη k )x + (ξ + Δξ k )y]}

[0016] Among which Δη k and Δξ k correspond to the displacement amounts in the x and y directions respectively. Loading the complex transmittance function onto the spatial light modulator, the mask for the light beam that can rotate parallel to the optical axis is obtained.

[0017] Preferably, the expression of the phase P0 of the blazed grating is: P0 = 2πx / d; where d is the period of the blazed grating and x is the abscissa before Fourier transform.

[0018] A method for generating a light beam that can rotate parallel to the optical axis using the mask prepared by this design method. Irradiate a parallel light beam onto the spatial light modulator loaded with the mask for the light beam that can rotate parallel to the optical axis. After being modulated by the spatial light modulator, a light beam that can rotate parallel to the optical axis is generated.

[0019] A method for realizing longitudinal micro-manipulation of particles, including the following steps:

[0020] Step 1): Generate a light beam that can rotate parallel to the optical axis;

[0021] Step 2): Plan the particle manipulation trajectory. Load the mask for the light beam that can rotate parallel to the optical axis onto the spatial light modulator and continuously refresh it to realize longitudinal micro-manipulation of particles.

[0022] First, the present invention utilizes the principle of computer-generated holography to obtain an amplitude-modulated phase mask for rotating a light beam parallel to the optical axis through computer coding. Then, by loading such a mask on a spatial light modulator, a light beam that can rotate parallel to the optical axis can be generated. Furthermore, longitudinal micro-manipulation of particles is achieved, so it has important application value in the field of cell manipulation. The technical solution adopted by the present invention to solve the above technical problems is as follows:

[0023] First of all, based on the beam shaping technology, we can know that the electric field expression of a light beam that can rotate parallel to the optical axis is:

[0024]

[0025] where is the Fourier transform function, (x, y) are the coordinates before Fourier transform, and (η, ξ) are the coordinates after Fourier transform. G1(x, y, t1), G2(x, y, t2), G3(x, y, t3)……G k (x, y, t k ) is the complex amplitude of the light beam used for superposition, and t1 + t2 + t3 + …… + t k = 2π. U1, U2, U3, ……, U k are Fourier phase shift factors responsible for giving each part of the light beam a corresponding displacement to maintain it as a whole. Among them, G k (x, y, t k ) can be expressed as:

[0026]

[0027] where Φ k (x, y, t k ) and ψ k (x, y, t k ) are the phase terms of the light beam, and c0(t k ) determines the shape of the light beam, and a three-dimensional circle is used in this technology. U k can be expressed as:

[0028] U k = exp{2πj[(η + Δη k )x + (ξ + Δξ k )y]}

[0029] where Δη k and Δξ k correspond to the displacement amounts in the x and y directions respectively, and j is the imaginary unit.

[0030] The phase expression of the blazed grating is P0 = 2πx / d. Here, d is the period of the blazed grating, and its function is to generate the above-mentioned electric field expression capable of rotating the beam parallel to the optical axis through diffraction grading in the experiment.

[0031] A mask for rotating a beam parallel to the optical axis is characterized in that coordinate transformation technology, grafting technology, and arbitrary curve shaping technology are used to generate the amplitude, phase, and a blazed grating of the beam. The specific expression of its complex transmittance function is:

[0032] T = circ(ρ)exp{j[angle(G(η,ξ)) + P0]}

[0033] Where circ(·) is the circular domain function, and ρ is the polar coordinate radial variable. The mask described by this complex transmittance function is a mask for rotating a beam parallel to the optical axis.

[0034] After that, this mask is loaded through a spatial light modulator to generate a beam that can rotate parallel to the optical axis. The specific method is to design the motion trajectory of the particle in advance, and then generate the mask according to the parameters of the motion trajectory. Finally, the mask is loaded into the spatial light modulator, and parallel light is used for illumination to generate a beam that can rotate parallel to the optical axis. Then, through the optical tweezer device, the beam that can rotate parallel to the optical axis is coupled into the microscope objective for focusing, so as to manipulate the polystyrene microspheres in the sample chamber.

[0035] Advantageous effects:

[0036] The mask designed by the present invention can generate a beam that can rotate parallel to the optical axis. By adopting beam grafting, Fourier phase shift, and beam shaping technologies, a part of the annular beam rotates parallel to the optical axis, so as to drive the particle to rotate parallel to the optical axis. The beam exhibits adjustable and diverse properties, and longitudinal micro-manipulation of the particle can be realized. This technology solves the long-existing problem that the structured beam cannot rotate parallel to the optical axis for a long time. This method is easy to implement, operate, and use, and provides great potential for the future development of structured optical tweezers. Description of the drawings

[0037] Figure 1 For the case where the curve parameter of the beam that can rotate parallel to the optical axis is circular and the topological charge value m is 30, masks with tilt angles of 0, π / 2, π, 3π / 2, and 2π are obtained.

[0038] Figure 2 is Figure 1 The beam that can rotate parallel to the optical axis generated by the shown mask.

[0039] Figure 3It is a continuously generated beam with an inclination angle that continuously changes from 0 to 2π and can rotate parallel to the optical axis. After being focused by a microscope objective, it manipulates the longitudinal rotation of particles. Detailed implementation mode

[0040] Figure 1 It is a mask template of the beam that can rotate parallel to the optical axis generated by the present invention. The detailed implementation mode is as follows:

[0041] First of all, based on the beam shaping technology, we can know that the electric field expression of the beam that can rotate parallel to the optical axis is:

[0042]

[0043] Among them, is the Fourier transform function, (x, y) are the coordinates before Fourier transform, and (η, ξ) are the coordinates after Fourier transform. G1(x, y, t1), G2(x, y, t2), G3(x, y, t3) …… G k (x, y, t k ) is the complex amplitude of the beam used for superposition, and t1 + t2 + t3 + …… + t k = 2π. U1, U2, U3, ……, U k are Fourier phase shift factors responsible for giving each part of the beam corresponding displacements to maintain it as a whole. Among them, G k (x, y, t k ) can be expressed as:

[0044]

[0045] Among them, Φ k (x, y, t k ) and ψ k (x, y, t k ) are the phase terms of the beam, c0(t k ) determines the shape of the beam, and a three-dimensional circle is used in this technology. U k can be expressed as:

[0046] U k = exp{2πj[(η + Δη k )x + (ξ + Δξ k )y]}

[0047] Among them, Δη k and Δξ k correspond to the displacement amounts in the x and y directions respectively, and j is the imaginary unit.

[0048] The phase expression of the blazed grating is P0 = 2πx / d. Where d is the period of the blazed grating, and its function is to generate the above-mentioned electric field expression that can rotate the beam parallel to the optical axis through diffraction grading in the experiment.

[0049] A mask for rotating a beam parallel to the optical axis, characterized in that coordinate transformation technology, grafting technology and arbitrary curve shaping technology are used to generate the amplitude, phase and a blazed grating of the beam. The specific expression of its complex transmittance function is:

[0050] t = circ(ρ)exp{j[angle(G(η,ξ)) + P0]}

[0051] Where circle(·) is the circular domain function and ρ is the polar coordinate radial variable. The mask described by this complex transmittance function is a mask for rotating a beam parallel to the optical axis according to the present invention. Then, by loading this mask into a spatial light modulator, a beam that can rotate parallel to the optical axis is generated. The specific method is to design the motion trajectory of the particles in advance, and then generate the mask according to the parameters of the motion trajectory. Finally, the mask is loaded into the spatial light modulator, and parallel light is used to irradiate to generate a beam that can rotate parallel to the optical axis. Then, through an optical tweezer device, the beam that can rotate parallel to the optical axis is coupled into the microscope objective for focusing, so as to manipulate the polystyrene microspheres in the sample chamber. In the experiment, when the curve parameter of the beam that can rotate parallel to the optical axis is circular and the number of segments is 6, a beam that can rotate parallel to the optical axis with a continuously changing tilt angle from 0 to 2π is obtained.

[0052] Example 1:

[0053] Taking a mask with a size of 1024pixel×1024pixel as an example, a mask for rotating a beam parallel to the optical axis is given for a laser with a working wavelength of 532nm. When the parameters of the mask for rotating a beam parallel to the optical axis are circular and the number of segments is 6, a beam that can rotate parallel to the optical axis with a continuously changing tilt angle from 0 to 2π is obtained. According to the complex transmittance function of the mask in the specific implementation manner, the mask for rotating a beam parallel to the optical axis is finally obtained. Figure 1 That is, the mask samples of the beam that can rotate parallel to the optical axis at different tilt angles used in the example have tilt angles of 0, π / 2, π, 3π / 2, and 2π respectively. Such a mask for rotating a beam parallel to the optical axis can be realized by a spatial light modulator. Taking the Zhongke Weixing FSLM-2K39-P02 phase spatial light modulator as an example, its pixel size is 4.5μm and the resolution is 1920pixel×1080pixel. In the experiment, a continuous wave solid laser with a wavelength of 532nm and a power of 600mW is used.

[0054] Figure 2As shown, it is the beam that can rotate parallel to the optical axis generated in the embodiment. It can be seen from the figure that we have obtained a beam that can rotate parallel to the optical axis. Due to the rotation to the vertical direction, the beam is defocused in the focal plane.

[0055] After that, through the optical tweezer device, the beam that can rotate parallel to the optical axis is coupled into the microscope objective for focusing, so as to manipulate the polystyrene microspheres in the sample chamber. The microscope objective used in the experiment is a Nikon oil immersion objective with a magnification of 100 times and a numerical aperture NA of 1.49. The polystyrene microspheres are single-dispersed polystyrene microspheres from Tianjin BEXCEL with a diameter of 2 μm. Figure 3 As shown, it is the beam that can rotate parallel to the optical axis with a continuously changing tilt angle from 0 to 2π generated continuously. After being focused by the microscope objective, it manipulates the particles to rotate longitudinally.

[0056] In summary, the present invention proposes a specific design scheme and implementation plan for the mask template of the beam that can rotate parallel to the optical axis. Taking the curve shape as a circle and the tilt angle as the beam that can rotate parallel to the optical axis with a continuous change from 0 to 2π, a technical implementation route for longitudinal rotation of particles is proposed for a laser with a working wavelength of 532 nm.

[0057] The method for realizing longitudinal micro-manipulation of particles described above only represents a specific implementation manner of the present invention and should not be construed as a limitation on the protection scope of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the basic idea of the present invention, several deformations and improvements can be made to the specific implementation details proposed in this patent, and these all belong to the protection scope of the present invention.

Claims

1. A design method for a mask that can rotate a light beam parallel to the optical axis, characterized in that: By combining the amplitude, phase of the light beam that can rotate parallel to the optical axis with a blazed grating, the complex transmittance function of the mask that can rotate the light beam parallel to the optical axis is obtained, and the expression is: T = circ(ρ)exp{j[angle(G(η,ξ)) + P0]} Wherein, circ(·) is the circular domain function, angle(·) is the function for taking the phase angle, G(·) is the complex amplitude function, ρ is the polar coordinate radial variable, exp(·) is the exponential function with the natural constant e as the base, j is the imaginary unit, and P0 is the phase of the blazed grating; The electric field expression of the light beam that can rotate parallel to the optical axis is: Among them, is the Fourier transform function, (x, y) are the coordinates before Fourier transform, (η, ξ) are the coordinates after Fourier transform, G1(x, y, t1), G2(x, y, t2), G3(x, y, t3) …… G k (x, y, t k ) is the complex amplitude of the light beam used for superposition, and t1 + t2 + t3 + …… + t k = 2π, U1, U2, U3, ……, U k are the Fourier phase shift factors, responsible for giving each part of the light beam a corresponding displacement to remain as a whole, k is an arbitrary integer; among them G k (x, y, t k ) is expressed as: where Φ k (x, y, t k ) and ψ k (x, y, t k ) are phase terms for a beam that can be rotated parallel to the optical axis, c0(t k ) determines the shape of the beam, which is three-dimensional circular, c′0(t k ) represents the derivative of c0(t k ), and the Fourier phase shift factor U k is expressed as: U k = exp{2πj[(η + Δη k )x+(ξ + Δξ k )y]} where Δη k and Δξ k correspond to the displacement amounts in the x and y directions respectively. Loading the complex transmittance function onto the spatial light modulator gives a mask that can rotate the beam parallel to the optical axis.

2. The design method of a mask for rotating a light beam parallel to the optical axis according to claim 1, characterized in that: The expression of the phase P0 of the blazed grating is: P0 = 2πx / d; where d is the period of the blazed grating and x is the abscissa before Fourier transform.

3. A method for generating a light beam that can be rotated parallel to the optical axis using a mask prepared by the design method according to any one of claims 1-2, characterized in that: By irradiating a parallel light beam on a spatial light modulator loaded with a mask that can rotate a light beam parallel to the optical axis, and after being modulated by the spatial light modulator, a light beam that can rotate parallel to the optical axis is generated.

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