CN109917546B - Design method of center symmetrical vortex light beam mask plate capable of being freely regulated and controlled - Google Patents
Design method of center symmetrical vortex light beam mask plate capable of being freely regulated and controlled Download PDFInfo
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Abstract
A design method of a centrosymmetric vortex light beam mask plate capable of being freely regulated and controlled combines a centrosymmetric spiral phase factor, a cone lens transmittance function and a blazed grating to obtain a complex transmittance function of the centrosymmetric vortex light beam mask platet(ii) a The complex transmittance functiontAnd loading the mask plate into a spatial light modulator through a computer to obtain a freely-adjustable centrosymmetric vortex light beam mask plate. The mask plate designed by the invention can realize that the central symmetrical vortex light beam with adjustable light lobe size and light ring radius is generated in the far field of the mask plate; the size of the light lobes on the left side and the right side of the light ring is controlled by a phase reconstruction factor PRF, and the size of the radius of the light ring is controlled by the size of the cone angle of the conical lens, so the method has very important application prospect in the field of particle manipulation.
Description
Technical Field
The invention relates to the field of particle manipulation, in particular to a design method of a freely-adjustable centrosymmetric vortex beam mask plate.
Background
Because the optical vortex carries orbital angular momentum, the optical vortex is widely applied to the fields of particle manipulation, high-capacity optical communication, optical measurement, astronomical observation and the like. In the field of particle manipulation, the light intensity and orbital angular momentum of the vortex beam provide the gradient force and angular optical wrench force, respectively. Therefore, it is very meaningful to develop new techniques for regulating the light intensity and orbital angular momentum distribution.
There is a lot of research work on the regulation of orbital angular momentum of vortex beams, and the most common method is to regulate the topological charge value [ Phys.Rev.A45,8185-81891992 ]. However, the method can only change the size of orbital angular momentum by changing the topological charge value of the vortex beam, but the distribution of the orbital angular momentum cannot be regulated, so that the control of the vortex beam in the field of particle manipulation, particularly the control of complex particles, is limited. To break this limitation, Kovalev yields an asymmetric Bessel mode with crescent-shaped intensity and orbital angular momentum distribution [ opt. lett.39,2395-23982014 ] by adding an off-axis factor to the conventional optical vortex. In 2014, the Zhao Jian Ling project group proposed a spiral power index phase type vortex beam by regulating and controlling a phase gradient factor [ Opt. express 22, 7598-. In 2015, Rodrigo generated a vortex optical field with a three-dimensional spatial structure by beam shaping technique [ optical 2, 812-. Although the light fields generated by the above method have rich spatial mode distributions, their orbital angular momentum is continuous within the light ring. There is also a need in the art of particle manipulation for an asymmetric vortex light field with a separated orbital angular momentum distribution.
In view of the above, there is still a lack of a centrosymmetric vortex beam with controllable optical lobe size and optical ring radius for particle manipulation in the field of particle manipulation, so as to meet the requirement of particle manipulation, especially for cell cluster separation.
Disclosure of Invention
In order to solve the technical problems, the invention provides a design method of a freely-adjustable centrosymmetric vortex light beam mask plate, the mask plate obtained by the method can generate centrosymmetric vortex light beams with controllable light lobe sizes and light lobe radii, and the method has very important application value in the field of particle manipulation.
The technical scheme adopted by the invention for solving the technical problems is as follows:
a design method of a centrosymmetric vortex light beam mask plate capable of being freely regulated and controlled combines a centrosymmetric spiral phase factor, a cone lens transmittance function and a blazed grating to obtain a complex transmittance function t of the centrosymmetric vortex light beam mask plate, wherein the specific expression of the complex transmittance function is as follows:
t＝tαexp[i·(angle(Ec)+P)]
wherein, tαIs a cone lens transmittance function; ecIs a central symmetric spiral phase factor; p is a phase expression of the blazed grating, and angle () is a function for solving the phase of the central symmetric spiral phase factor; and loading the complex transmittance function t into a spatial light modulator through a computer, namely generating a mask plate of the centrosymmetric vortex light beam which can be freely regulated and controlled.
The cone lens transmittance function tαThe expression is as follows:
in the formula, R is a radial parameter in a polar coordinate system, R is a pupil radius of the axicon, n is a refractive index of a material used for the axicon, α is a cone angle of the axicon, and k is a wave vector. The light ring radius of the centrosymmetric vortex light beam can be regulated and controlled by regulating and controlling the cone angle of the cone lens.
The central symmetrical spiral phase factor EcThe expression of (a) is:
wherein, theta is an angular parameter under a polar coordinate system; rect (-) is a function for locally selecting and reconstructing four spiral phases to obtain the needed centrosymmetric spiral phase; ln’For the topological charge of four spiral phases, the relation PRF ═ l is satisfied1＝-l2＝l3＝-l4Where PRF is an arbitrary integer, referred to as the phase reconstruction factor. By regulating the size of the PRF, the sizes of the light lobes on the left side and the right side of the light ring of the generated centrosymmetric vortex light beam can be regulated.
The expression of the blazed grating P is as follows:
and D is the phase period of the blazed grating, and the blazed grating is used for separating the required centrosymmetric vortex light beam and zero-order light spots in the experimental generation of the centrosymmetric vortex light beam.
In operation, parallel light is irradiated on a spatial light modulator input with a central symmetrical vortex light beam phase mask plate, and light beams reflected by the spatial light modulator pass through a Fourier transform lens, so that central symmetrical vortex light beams with adjustable light lobe size and light ring radius can be obtained in a far field.
The invention has the beneficial effects that:
the mask plate designed by the invention can realize that the central symmetrical vortex light beam with adjustable light lobe size and light ring radius is generated in the far field of the mask plate; the size of the light lobes on the left side and the right side of the light ring is controlled by a phase reconstruction factor PRF, and the size of the radius of the light ring is controlled by a cone angle alpha of the conical lens, so the method has very important application prospect in the field of particle manipulation.
Drawings
FIG. 1 is a mask plate for generating a centrosymmetric vortex light beam with controllable light lobe size according to the present invention. The cone angle α of the axicon is 0.06 °, and the phase reconstruction factors PRF are 4, 6, 8, and 10, respectively.
Fig. 2 is a diagram of the reticle shown in fig. 1 generating a centrosymmetric vortex beam with controllable optical lobe size.
FIG. 3 is a mask plate for generating a centrosymmetric vortex light beam with controllable halo radius according to the present invention. The phase reconstruction factor PRF is 4, and the cone angle α of the axicon lens is 0.03 °, 0.04 °, 0.05 °, and 0.06 °, respectively.
FIG. 4 is a centrosymmetric vortex beam with controlled halo radius generated by the reticle shown in FIG. 3.
Detailed Description
Fig. 1 and 3 show a mask plate of an embodiment of a centrosymmetric vortex beam with controllable optical lobe size and optical lobe radius, which is obtained by the following steps: combining a central symmetry spiral phase factor, a cone lens transmittance function and a blazed grating to obtain a complex transmittance function t of the central symmetry vortex beam mask plate, wherein the specific expression of the complex transmittance function t is as follows:
t＝tαexp[i·(angle(Ec)+P)]
wherein, tαIs a cone lens transmittance function; ecIs a central symmetric spiral phase factor; p is the phase expression of the blazed grating, angle (-) is a function for solving the phase of the central symmetrical spiral phase factor, according to the principle of computer-generated holography,firstly, the complex transmittance function t is subjected to modulus squaring, and then the obtained expression is loaded into the spatial light modulator through a computer, so that the mask plate of the centrosymmetric vortex light beam can be generated.
The cone lens transmittance function tαThe expression is as follows:
in the formula, R is a radial parameter in a polar coordinate system, R is a pupil radius of the axicon, n is a refractive index of a material used for the axicon, α is a cone angle of the axicon, and k is a wave vector. The light ring radius of the centrosymmetric vortex light beam can be regulated and controlled by regulating and controlling the cone angle of the cone lens.
The central symmetrical spiral phase factor EcThe expression of (a) is:
wherein, theta is an angular parameter under a polar coordinate system; rect (-) is a function for locally selecting and reconstructing four spiral phases to obtain the needed centrosymmetric spiral phase; ln’For the topological charge of four spiral phases, the relation PRF ═ l is satisfied1＝-l2＝l3＝-l4Where PRF is an arbitrary integer, referred to as the phase reconstruction factor. By regulating the size of the PRF, the sizes of the left and right light lobes on the light ring of the generated centrosymmetric vortex light beam can be regulated.
The expression of the blazed grating P is as follows:
and D is the phase period of the blazed grating, and the blazed grating is used for separating the required centrosymmetric vortex light beam and zero-order light spots in the experimental generation of the centrosymmetric vortex light beam.
In the experiment, the phase reconstruction factor and the cone angle of the cone lens are fixed, the phase period of the blazed grating is adjusted to separate the three diffraction orders until the +1 diffraction order can be screened out by using the diaphragm, and the centrosymmetric vortex beam mask plate with controllable optical lobe size and optical ring radius can be obtained. Fig. 1 shows a phase mask of a centrosymmetric vortex beam with a controllable optical lobe size obtained by setting a cone angle α of a fixed cone lens to 0.06 ° and selecting a phase reconstruction factor PRF from 4 to 10 at intervals of 2. Fig. 3 is a phase mask plate of a centrosymmetric vortex beam with controllable halo radius, which is obtained by selecting a cone angle alpha of a cone lens from 0.03 degrees to 0.06 degrees at intervals of 0.01 degrees, wherein the fixed phase reconstruction factor PRF is 4.
Examples
A mask plate with the size of 512 multiplied by 512 is taken as an example, and a central symmetry vortex beam mask plate is given for laser with the working wavelength of 532 nm. Selecting a conical angle alpha of the conical lens as 0.06 degrees, and taking phase reconstruction factors PRF as 4, 6, 8 and 10 respectively, and finally obtaining a mask plate of the centrosymmetric vortex light beam with the controllable light lobe size according to a mask plate transmittance function in a specific embodiment. Fig. 1 is a phase mask of the centrosymmetric vortex beam of different phase reconstruction factors PRF used in the embodiment. Selecting a phase reconstruction factor PRF of 4, and the cone angles alpha of the conical lenses are respectively 0.03 degrees, 0.04 degrees, 0.05 degrees and 0.06 degrees, and finally obtaining the mask plate of the centrosymmetric vortex light beam with the controllable light ring radius according to the mask plate transmittance function in the specific implementation mode. Fig. 3 is a phase mask of the centrosymmetric vortex beam with different cone angle α of the cone lens used in the embodiment. The central symmetrical vortex beam mask plate capable of being freely regulated and controlled can be realized through a spatial light modulator. Taking a pluto-vis-016 type spatial light modulator of Holoeye, Germany as an example, the proposed centrosymmetric vortex beam mask plate is experimentally verified.
Fig. 2 shows the light intensity distribution of the centrally symmetric vortex beam with controllable optical lobe size obtained by experiment on the focal plane of the lens with numerical aperture NA of 0.04. As can be seen from the figure, as the phase reconstruction factor PRF becomes larger, the optical lobes on the left and right sides of the central symmetric vortex beam become larger gradually. FIG. 4 shows the central symmetric vortex beam with controllable halo radius obtained by experiment. As can be seen from the figure, as the cone angle α of the axicon lens is gradually increased, the radius of the centrally symmetric vortex beam generated in the experiment is gradually increased. This would provide potential applications in the field of particle manipulation, particularly for cell cluster separation.
In summary, the present invention provides a specific design scheme and an implementation scheme of a centrosymmetric vortex beam mask plate capable of being freely adjusted and controlled, and a focusing lens with NA of 0.04 is taken as an example, and a technical implementation route of a centrosymmetric vortex beam mask plate capable of being freely adjusted and controlled is provided for a laser with a working wavelength of 532 nm.
The above-mentioned phase mask for generating a centrosymmetric vortex light beam with controllable light lobe size and light lobe radius only expresses one specific embodiment of the present invention, and is not to be construed as a limitation to the protection scope of the present invention. It should be noted that, for a person skilled in the art, numerous variations and modifications of the details of the embodiments set forth in the present patent can be made without departing from the basic idea of the invention, which falls within the scope of the invention.
The details of the present invention are not known in the art.
Claims (1)
1. A design method of a center symmetrical vortex beam mask plate capable of being freely regulated and controlled is characterized by comprising the following steps:
combining a central symmetry spiral phase factor, a cone lens transmittance function and a phase expression of a blazed grating to obtain a complex transmittance function t of the central symmetry vortex beam mask plate, wherein the specific expression of the complex transmittance function is as follows:
t＝tαexp[i·(angle(Ec)+P)]
wherein, tαIs a cone lens transmittance function; ecIs a central symmetric spiral phase factor; p is a phase expression of the blazed grating, and angle () is a function for solving the phase of the central symmetric spiral phase factor;
loading the complex transmittance function t into a spatial light modulator through a computer to obtain a freely-adjustable centrosymmetric vortex light beam mask plate;
the cone lens transmittance function tαThe expression is as follows:
in the formula, R is a radial parameter under a polar coordinate system, R is a pupil radius of the cone lens, n is a refractive index of a material used by the cone lens, α is a cone angle of the cone lens, k is a wave vector, and the light ring radius of the centrosymmetric vortex light beam can be regulated and controlled by regulating and controlling the cone angle of the cone lens;
the central symmetrical spiral phase factor EcThe expression of (a) is:
wherein, theta is an angular parameter under a polar coordinate system; rect (-) is a function for locally selecting and reconstructing four spiral phases to obtain the needed centrosymmetric spiral phase; ln’For the topological charge of four spiral phases, the relation PRF ═ l is satisfied1＝-l2＝l3＝-l4The PRF is an arbitrary integer and is called as a phase reconstruction factor, and the size of the light lobes on the left side and the right side of the light ring of the generated centrosymmetric vortex light beam can be regulated and controlled by regulating and controlling the size of the PRF;
the expression of the blazed grating P is as follows:
wherein D is the phase period of the blazed grating.
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| CN110472294B (en) * | 2019-07-19 | 2022-09-30 | 河南科技大学 | Design method of mask plate for grafting vortex light beam |
| CN111474708B (en) * | 2020-04-16 | 2022-02-18 | 河南科技大学 | Design method of vortex array mask plate in abnormal annular connection |
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| CN112861274B (en) * | 2021-01-06 | 2022-09-23 | 河南科技大学 | Design method of mask plate of high-order free mode optical vortex array |
| CN113534453B (en) * | 2021-06-29 | 2023-03-24 | 河南科技大学 | Design method of mask plate capable of rotating light beams in rigid body |
| CN114624895B (en) * | 2022-02-21 | 2023-02-10 | 苏州大学 | System and method for generating partial coherence vector power exponent vortex light beam |
| CN115236787B (en) * | 2022-08-12 | 2023-05-16 | 浙江师范大学 | Multi-spiral phase mask plate, multi-spiral light beam generation method and light modulator |
| CN115453752B (en) * | 2022-09-19 | 2023-07-21 | 苏州大学 | Design method of vortex beam mask plate with abnormal radius |
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Application publication date: 20190621 Assignee: Luoyang pingconvex Technology Co.,Ltd. Assignor: HENAN University OF SCIENCE AND TECHNOLOGY Contract record no.: X2021980013091 Denomination of invention: A freely adjustable design method of centrosymmetric vortex beam mask Granted publication date: 20210205 License type: Exclusive License Record date: 20211125 |
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