CN111474708B - Design method of vortex array mask plate in abnormal annular connection - Google Patents
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- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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- G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
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Abstract
A design method of a vortex array mask plate in abnormal annular connection is characterized in that two reconstructed spiral phase factors and two cone lens complex transmittance functions are combined to obtain a complex transmittance function of the vortex array mask plate in abnormal annular connection, and the complex transmittance function is loaded into a spatial light modulator through a computer, so that the required mask plate of the vortex array in abnormal annular connection with controllable local vortex distribution on an optical ring and unchanged vortex total number can be generated. And the mask plate is used for generating an abnormally annular connected vortex array with controllable vortex distribution and invariable total number of vortices on the light ring, so as to meet the requirements of particle manipulation field, especially the requirement of simultaneously capturing particles with different sizes.
Description
Technical Field
The invention relates to the field of particle manipulation, in particular to a design method of an abnormal annular connected vortex array mask plate.
Background
Because the optical vortex carries orbital angular momentum, the optical vortex has wide application in the aspects of particle capture, optical tweezers and the like. Therefore, the optical lens becomes an important research hotspot in the field of optics, and attracts the wide attention of researchers. The vortex array provides an additional degree of freedom for regulation because it carries a plurality of vortices, and becomes an important research hotspot in the application of multi-particle capture in the field of micromanipulation. In these applications, the vortex distribution of the vortex array is of great research interest.
The vortex array beam, connected by optical intensity, is typically generated by the coaxial superposition of two or more spatially structured beams. In 2007, S.Franke-Arnold et al generated a toroidal optical vortex array [ Opt.express, 2007, 8619-8625 ] that could be used for atomic cooling by the coaxial interferometric superposition of two Laguerre-Gaussian beams with specific topological charge values. In 2013, Vaity et al superimposed two gaussian beams using a mach-zehnder interferometer to produce a vortex array beam with high energy [ appl. opt.2013,6652-6656 ]. In 2017, Ma et al obtained a vortex array beam [ an. phys-Berlin 2017,1700285 ] with a flexibly adjustable vortex number by superimposing two concentric perfect vortex beams. In 2018, Li et al generated a vortex array with a rich structure based on holographic beam shaping technology, and the vortex distribution on the halo of the vortex array could be distributed along any curved trajectory [ Opt.Ex 2018, 9798-. However, the vortices of the vortex array generated by the above scheme are uniformly distributed on the light ring. There is also a need in the art of particle manipulation for an array of vortices that can achieve an abnormal annular connection that controls the vortex distribution over a local area of the optical ring without changing the total number of vortices on the ring.
In view of the above, there is still a lack of vortex array beams with controlled local vortex distribution and constant total number of vortices on the ring for particle manipulation in the field of particle manipulation, which can meet the requirement of particle manipulation, especially for simultaneous capture of different sizes of particles.
Disclosure of Invention
In order to solve the above-mentioned disadvantages, the present invention provides a method for designing an abnormal ring-connected vortex array mask plate, and the mask plate is used to generate an abnormal ring-connected vortex array with controllable local vortex distribution and constant total number of vortices on a halo, so as to meet the requirements of particle manipulation field, especially simultaneous capture of particles of different sizes.
The invention is based on a computer-generated holographic method, and constructs a vortex array of abnormal annular connection in a far field. The vortex array connected in the abnormal ring shape can flexibly regulate and control the distribution condition of local vortex on the light ring, and the total number of the vortex is kept unchanged, so that the vortex array has important application value in the field of particle manipulation.
The technical scheme adopted by the invention is as follows:
a design method of an abnormal annular connected vortex array mask plate is provided, wherein a complex transmittance function of the abnormal annular connected vortex array mask plate is obtained by combining two reconstructed spiral phase factors and two cone lens complex transmittance functions, and the specific expression of the complex transmittance function is as follows:
wherein the content of the first and second substances,
is a polar coordinate system, rho is a radial variable of the polar coordinate system,
for polar coordinate system angular variables, exp (-) is an exponential function with a natural constant e as the base, i is an imaginary unit, k is the wave number of the proposed vortex array beam of the abnormal annular connection, n is the refractive index of the cone lens material, αaAnd alphabCone angle factors of two conical lenses, psiaAnd ΨbTwo reconstructed helical phase factors respectively;
and loading the complex amplitude transmittance function into the spatial light modulator through a computer to generate a required mask plate of an abnormally annularly connected vortex array with controllable local vortex distribution on the light ring and unchanged total vortex number.
The reconstructed helical phase factor psiaAnd ΨbThe expressions are respectively:
wherein n' ═ 1 and 2 are numbers; rect () rectangular function; m isan’And mbn’For two reconstructed helical phase factors ΨaAnd ΨbThe local area topology load parameter of (1) satisfies the relation | ma1+ma2|＝|mb1+mb2L, |; the total number of the array vortexes satisfies the relation N ═ N1+N2＝|mb1-ma1|/2+|mb2-ma2I/2, where N denotes the total number of vortices on the halo, N1Indicating the number of vortices in the lower half of the annulus, N2Indicating the number of vortices in the upper half of the annulus. By separately regulating man’And mbn’Can regulate and control the local vortex distribution of the generated abnormal annular connected vortex array.
In an experiment, parallel light beams are irradiated on a spatial light modulator loaded with a vortex array mask plate in abnormal annular connection, and the light beams reflected after being modulated by the spatial light modulator can generate vortex array light beams in abnormal annular connection with controllable local vortex distribution and unchanged vortex total number on the light ring in a far field through a convex lens.
The invention has the technical effects that:
the mask plate designed by the invention can generate a vortex array beam which is in abnormal annular connection and has controllable local vortex distribution and invariable total vortex number on the light ring in a far field of the mask plate. The number of the vortexes of the lower semi-ring and the upper semi-ring of the vortex in the light ring is respectively determined by two reconstructed spiral phase factors psiaAnd ΨbLocal area topology load parameter difference | mb1-ma1I/2 and | mb2-ma2I/2. The increase or decrease of the number of the local vortices on the halo enables the corresponding decrease and increase of the dark nucleus area of the local vortices, and can realize the capture of particles with different sizes at the same time, thus having very important application prospect in the particle manipulation technology.
Drawings
FIG. 1 is a vortex array mask plate for producing abnormal annular connections with controllable local vortex distribution and constant total number of vortices on a ring of light according to the present invention. The local topology load parameters of the reconstructed spiral phase factor are respectively ma1Sequentially taking 1, m from 4 at intervals of 1a2Sequentially taking 7 m from 4 at intervals of 1b1＝mb2＝-4。
Fig. 2 is a vortex array beam of an abnormal annular connection generated using the mask plate shown in fig. 1.
Detailed Description
Fig. 1 is a mask plate of an abnormally annularly connected vortex array with controllable local vortex distribution and constant total vortex number on a light ring, which is generated by the invention, and the specific expression of a complex transmittance function is as follows:
wherein the content of the first and second substances,
is a polar coordinate system, rho is a radial variable of the polar coordinate system,
for polar coordinate system angular variables, exp (-) is an exponential function with a natural constant e as the base, i is an imaginary unit, k is the wave number of the proposed vortex array beam of the abnormal annular connection, n is the refractive index of the cone lens material, αaAnd alphabCone angle factors of two conical lenses, psiaAnd ΨbTwo reconstructed helical phase factors, respectively.
And loading the complex amplitude transmittance function into the spatial light modulator through a computer to generate a mask plate of an abnormally annularly connected vortex array on the required light ring, wherein the local vortex distribution on the light ring is controllable, and the total number of vortices is kept unchanged.
The reconstructed helical phase factor psiaAnd ΨbThe expressions are respectively:
wherein n' ═ 1 and 2 are numbers; rect () rectangular function; m isan’And mbn’For two reconstructed helical phase factors ΨaAnd ΨbThe local area topology load parameter of (1) satisfies the relation | ma1+ma2|＝|mb1+mb2L, |; the total number of the array vortexes satisfies the relation N ═ N1+N2＝|mb1-ma1|/2+|mb2-ma2I/2, where N denotes the total number of vortices on the halo, N1Indicating the number of vortices in the lower half of the annulus, N2Indicating the number of vortices in the upper half of the annulus. By separately regulating man’And mbn’Can regulate and control the local vortex distribution of the generated abnormal annular connected vortex array.
The cone angle factor alpha of two cone lenses is firstly given in the experimentaAnd alphabBy continuously adjusting alphaaAnd alphabThe proposed vortex array beam of abnormal annular connection is generated. Reconstructing a helical phase factor local topology charge parameter mbn’Taking a fixed value, and reconstructing a helical phase factor local topology load parameter man’And sequentially taking different topological charge values to obtain vortex array beams which are in abnormal annular connection and have controllable local vortex distribution and constant vortex total number on the light ring. FIG. 1 shows that the local topological charge parameters of the reconstructed helical phase factor are ma1Sequentially taking 1, m from 4 at intervals of 1a2Sequentially taking 7 m from 4 at intervals of 1b1＝mb2Mask plate for vortex array of abnormal annular connection obtained-4.
Examples
A mask plate with the size of 512 multiplied by 512 is taken as an example, and a vortex array which is connected with an abnormal ring and has controllable local vortex distribution and constant vortex total number on a light ring is given for laser with the working wavelength of 532 nm. The cone angle factors of the mask conical lens are respectively alphaa0.07rad and αbWhen the local topological load parameter of the reconstructed spiral phase factor is 0.08rad, the local topological load parameter is ma1Sequentially taking 1, m from 4 at intervals of 1a2Sequentially taking 7 m from 4 at intervals of 1b1＝mb2And 4, finally obtaining the vortex array mask plate which is in abnormal annular connection and has controllable local vortex distribution and constant vortex total number on the halo according to the mask plate transmittance function in the specific implementation mode. Fig. 1 shows the masks generated under the different local topology load parameter values. The vortex array mask plate with the abnormal annular connection, which is controllable in local vortex distribution on the light ring and constant in total number of vortices, can be realized by one spatial light modulator. Take the pluto-vis-016 type spatial light modulator from Holoeye, Germany as an exampleThe vortex array mask plate which is in abnormal annular connection and has controllable local vortex distribution and constant vortex total number on the light ring is provided for experimental verification.
As shown in fig. 2, we have experimentally generated the light intensity distribution on the focal plane of the convex lens with numerical aperture NA of 0.025 and focal length of 200mm in the mask plate of the vortex array connected in the abnormal ring shape with controllable local vortex distribution and constant total vortex number on the halo. As can be seen from the figure, we obtain the vortex array beam of the abnormal annular connection with the non-uniform distribution of dark nuclei on the light ring, and the total number of the vortex arrays meets the relation N-N1+N2＝|mb1-ma1|/2+|mb2-ma2I/2-8 remains unchanged, and N is also present1Indicating the number of vortices in the lower half of the annulus, N2Indicating the number of vortices in the upper half of the annulus. The experimental result shows that the vortex array mask plate for abnormal annular connection provided by the invention can obtain vortex array beams for abnormal annular connection, wherein the local vortex distribution on the light ring is controllable, and the total number of the vortices is unchanged. This will provide a richer variety of manipulation modes for the field of particle manipulation, especially for simultaneous capture of particles of different sizes.
In summary, the present invention provides a specific design scheme and an implementation scheme of an abnormally annularly connected vortex array mask plate with controllable local vortex distribution and constant total number of vortices on a halo, and uses cone angle factors of complex transmittance functions of a focusing lens and a conical lens with NA of 0.025 to respectively take alphaa0.07rad and αbFor example, 0.08rad provides a technical implementation route of an abnormally annularly connected vortex array mask plate with controllable local vortex distribution on a light ring and invariable total vortex number for laser with the working wavelength of 532 nm.
The above-mentioned mask plate for generating an abnormal annular connection with controllable local vortex distribution and constant total number of vortices on a halo only represents one specific embodiment of the present invention, and is not to be construed as limiting the 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.
Claims (2)
1. A design method of a vortex array mask plate in abnormal annular connection is characterized in that: combining the two reconstructed spiral phase factors and the two cone lens complex transmittance functions to obtain a complex transmittance function of the vortex array mask plate in the abnormal annular connection, wherein the specific expression of the complex transmittance function is as follows:
wherein the content of the first and second substances,
is a polar coordinate system, rho is a radial variable of the polar coordinate system,
for polar coordinate system angular variables, exp (.) is an exponential function with a natural constant e as the base, i is an imaginary unit, k is the wave number of the proposed vortex array beam in abnormal annular connection, n is the refractive index of the cone lens material, and alphaaAnd alphabCone angle factors of two conical lenses, psiaAnd ΨbTwo reconstructed helical phase factors respectively;
loading the complex transmittance function of the vortex array mask plate in abnormal annular connection into a spatial light modulator through a computer to generate the required mask plate of the vortex array in abnormal annular connection, wherein the local vortex distribution on the light ring is controllable, and the total number of the vortices is kept unchanged;
the two reconstructed helical phase factors ΨaAnd ΨbThe expressions are respectively:
wherein n' ═ 1 and 2 are numbers; rect () rectangular function; m isan’And mbn’For two reconstructed helical phase factors ΨaAnd ΨbThe local area topology load parameter of (1) satisfies the relation | ma1+ma2|＝|mb1+mb2L, |; the total number of the array vortexes satisfies the relation N ═ N1+N2＝|mb1-ma1|/2+|mb2-ma2I/2, where N denotes the total number of vortices on the halo, N1Indicating the number of vortices in the lower half of the annulus, N2Indicating the number of vortices in the upper half of the annulus.
2. A method for generating a vortex array beam with an abnormal annular connection by using a mask plate prepared by the design method of claim 1, wherein the method comprises the following steps:
parallel light beams are irradiated on a spatial light modulator loaded with a vortex array mask plate in abnormal annular connection, and the light beams reflected after being modulated by the spatial light modulator can generate vortex array light beams in abnormal annular connection with controllable local vortex distribution and unchanged vortex total number on the light ring in a far field through a convex lens.
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Application publication date: 20200731 Assignee: Luoyang pingconvex Technology Co.,Ltd. Assignor: HENAN University OF SCIENCE AND TECHNOLOGY Contract record no.: X2022980024383 Denomination of invention: A Design Method of Vortex Array Mask with Anomalous Annular Connection Granted publication date: 20220218 License type: Exclusive License Record date: 20221215 |
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