CN109491081B - Design method of vortex light beam mask plate with oblique line compression phase step - Google Patents
Design method of vortex light beam mask plate with oblique line compression phase step Download PDFInfo
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Abstract
A design method of a vortex beam mask plate with oblique line compression phase step comprises the following steps: combining a complementary function, a plane wave factor and a binary radial cutoff factor to obtain a transmittance function of the vortex beam mask plateTBy selecting different parameter valuesm、KAnda 1introducing said transmittance functionTThe vortex light beam mask plate with the oblique line compression phase step can be obtained. The mask plate manufactured by the design method can generate vortex beams with oblique line compression phase steps. The singular points of the vortex light beam with the oblique line compression phase step are distributed in a spiral shape, and the slope of the compression oblique line controls the helicity of the arrangement of the singular points, so that novel unprecedented light field mode distribution is provided, and the vortex light beam has important application value in the field of particle manipulation.
Description
Technical Field
The invention relates to the field of particle light manipulation, in particular to a design method of a vortex beam mask plate with oblique line compression phase step.
Background
The optical vortex carries orbital angular momentum and has wide application in optically trapping and manipulating tiny particles. Becomes a very important research hotspot in the field of information optics in recent years.
In the study of particle light manipulation, the richness of the vortex beam pattern directly determines the flexibility of light manipulation. One prominent example is the application of fractional vortex beams, which were successfully used in 2005 to achieve particle ordering [ opt. express, 2005, 7726-. Additional examples focus primarily on the generation of asymmetric vortex beams. Rodrigo et al, Jos a in 2015, studied free-form 3D laser traps, a tool that could be used to study the dynamics of light-driven particles, where the trapping of particles by different shaped beams was done. [ Optica, 2015, 812 ] 815. In 2016, alexeya, kovalev et al used an asymmetric laguerre-gaussian beam to manipulate particles to achieve variable acceleration of the particles over the halo [ opt. lett.41,2426(2016) ]. Further studies in 2018, Jos ea, rodrigo et al, achieved a nodal optical steering using three-dimensionally shaped beams.
However, the current asymmetric mode distribution focuses mainly on the modulation of the phase gradient, and the modulation of the phase step also only limits the generation of fractional order vortex beams. The regulation of the phase step is therefore to be investigated further. In summary, a novel optical field for phase step modulation is not yet available to further broaden the mode distribution of the vortex beam.
Disclosure of Invention
The invention aims to solve the defects of the technical problems and provides a design method of a vortex light beam mask plate with a slant line compression phase step. The singular points of the vortex light beam with the oblique line compression phase step are distributed in a spiral shape, and the slope of the compression oblique line controls the helicity of the arrangement of the singular points, so that novel unprecedented light field mode distribution is provided, and the vortex light beam has 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 vortex beam mask plate with oblique line compression phase step,
step one, combining a complementation function, a plane wave factor and a binary radial cutoff factor to obtain a transmittance function T of the vortex beam mask plate, wherein the transmittance function T has an expression as follows:
wherein, (r, theta) is a polar coordinate system variable; w is the beam waist radius of the beam; m is the topological charge value of the vortex light beam of the proposed oblique line compression phase step; im2bw [ exp (-r)2/w2)(2r2/w2)|m|/2]To combine the gray matrix exp (-r)2/w2)(2r2/w2)|m|/2The function is converted into a binary matrix to realize a radial cut-off, and the incident light energy is limited on a circular ring related to the topological charge m; ang (a) ═ atan (a)imag/Areal) Is to solve the angular function of an imaginary number A, wherein ArealAnd AimagRespectively the real part and the imaginary part of the imaginary number A; rem (thetam, f) is a remainder function, represents a remainder obtained by dividing the function thetam by the function f according to bits, and is used for realizing oblique line compression on the phase; f is a step function related to the slope of the slope; 2 pi x/d is a blazed grating item and is used for generating a plane wave factor with a period of d, and the function of the plane wave factor is to concentrate energy into +1 order diffraction;
the expression of the step function f is as follows:
where K is the slope of the slope used; a isjIs the magnitude of the jth phase step; bjThe interval of two adjacent phase steps; k controls the slope of the slope used, a1Controlling the degree of compression of the oblique line to the phase step; the phase gradient of the vortex light beam of the proposed oblique line compression phase step can be regulated by regulating the topological load m; in order to satisfy the phase value range of 0-2 pi, K and a1Satisfies 2 pi K + (m-K) a1/m≤2π；
Step two, selecting different parameter values m, K and a1And bringing the transmittance function T into the mask plate to obtain the vortex beam mask plate with the oblique line compression phase step.
In this embodiment, in the step one, ajAnd bjRepresented by the following recurrence formula:
in practical operation, a flat-top light beam is modulated to serve as an incident light beam of the vortex light beam mask plate, so that a vortex is generated in a far fieldRotating the light beam; the singular points of the vortex light beams are distributed in a spiral shape, and the slope of the compression oblique line controls the spiral degree of the singular point arrangement; by regulating and controlling parameters m, K and a1Vortex beams with different modes and different slope compression phase steps can be obtained.
The invention realizes the phase structure that the phase step is compressed by the oblique line of a specific slope by utilizing the principle of computer holography and through the global design of the phase of the light beam. The resulting phase structure is encoded into a beam complex amplitude expression. Thus, a vortex beam with a ramp-compressed phase step is generated in the far field of the proposed reticle. The singular points of the vortex light beam with the oblique line compression phase step are distributed in a spiral shape, and the slope of the compression oblique line controls the helicity of the arrangement of the singular points, so that novel unprecedented light field mode distribution is provided, and the vortex light beam has important application value in the field of particle manipulation.
The invention has the technical effects that:
the mask plate designed by the invention can generate vortex beams with oblique line compression phase steps in the far field of the mask plate. The topological charge number is determined by a parameter m, the slope of the compression slope used can be determined by a parameter K, and the degree of compression on the phase step can be determined by a parameter a1And (5) controlling. By regulating and controlling parameters m, K and a1Vortex light beams with different modes and different oblique line compression phase steps can be obtained, the richness of vortex light field modes is greatly widened, and therefore the vortex light field mode has very important application prospects in the particle manipulation technology.
Drawings
FIG. 1 is a vortex beam mask for generating a slant line compression phase step according to the present invention. The mask plate parameter is m is 5, K is 0.2 and 0.5 every 0.1, a1＝1.019π。
Fig. 2 is a vortex beam of diagonally compressed phase steps generated by the reticle shown in fig. 1.
Detailed Description
Fig. 1 is a mask blank for a vortex beam with a diagonal compression phase step according to an embodiment of the present invention, and the transmittance function T of the mask blank can be represented as:
wherein, (r, theta) is a polar coordinate system variable; w is the beam waist radius of the light beam, and the value of the specific implementation mode is 10.5 mm; m is the topological charge value of the vortex light beam of the proposed oblique line compression phase step; im2bw [ exp (-r)2/w2)(2r2/w2)|m|/2]To combine the gray matrix exp (-r)2/w2)(2r2/w2)|m|/2The function is converted into a binary matrix to realize a radial cut-off, and the incident light energy is limited on a circular ring related to the topological charge m; ang (a) ═ atan (a)imag/Areal) Is to solve the angular function of an imaginary number A, wherein ArealAnd AimagRespectively the real part and the imaginary part of the imaginary number A; rem (thetam, f) is a remainder function, represents a remainder obtained by dividing the function thetam by the function f according to bits, and is used for realizing oblique line compression on the phase; f is a step function related to the slope of the slope; the 2 pi x/d is a blazed grating term and is used for generating a plane wave factor with a period of d, and the function of the blazed grating factor is to concentrate energy on + 1-order diffraction, and the specific implementation mode is 0.26 mm.
The transmittance function T of the vortex beam mask plate can be obtained by combining a complementary function, a plane wave factor and a binary radial cutoff factor.
The step function f can be represented by the following formula:
where K is the slope of the slope used; a isjIs the magnitude of the jth phase step; bjThe interval of two adjacent phase steps; a isjAnd bjCan be represented by the following recursion equation:
as can be seen from the expression of the function f, the phase step of the proposed vortex beam mask plate with the oblique line compression phase step can be determined by parameters K and a1And (5) regulating and controlling. K controls the slope of the slope used, a1The degree of compression of the slope against the phase step is controlled. Furthermore, the phase gradient of the vortex beam of the proposed ramp compression phase step can be modulated by modulating the topological charge m. In order to satisfy the phase value range of 0-2 pi, K and a1Satisfies 2 pi K + (m-K) a1/m≤2π。
In actual operation, a flat-top light beam is modulated to serve as an incident light beam of the vortex light beam mask plate, so that a vortex light beam is generated in a far field; the singular points of the vortex light beams are distributed in a spiral shape, and the slope of the compression oblique line controls the spiral degree of the singular point arrangement; by regulating and controlling parameters m, K and a1Vortex beams with different modes and different slope compression phase steps can be obtained.
Examples
Hereinafter, a mask plate with 512 × 512 size is taken as an example, and a vortex beam mask plate with oblique line compression phase step is given for laser with an operating wavelength of 532 nm. The mask plate topological load value m is 5, the compression oblique slope K is 0.2-0.5, and the first phase step size value a1And (3) finally obtaining a vortex light beam mask plate with oblique line compression phase step according to the mask plate transmittance function in the specific embodiment, wherein the value of the mask plate transmittance function is 1.019 pi. Fig. 1 shows the vortex beam mask plate with the oblique line compression phase step. The vortex beam mask plate with the oblique line compression phase step can be realized by a spatial light modulator. Taking the PLUTO-VIS-016 phase spatial light modulator from Holoeye, Germany as an example, the pixel size is 8 μm, the filling factor is 93%, and the resolution is 1920 pixels × 1080 pixels. A continuous wave solid laser with a wavelength of 532nm was used in the experiment with a power of 100 mW.
Fig. 2 shows the intensity distribution of the spiral beam mask with diagonal compression phase steps generated by us on the lens focal plane with numerical aperture NA of 0.025. As can be seen from the figure, we obtain the vortex beam with the oblique line compression phase step, and as the compression oblique line slope K is increased from 0.2 to 0.5, the spiral degree of the spiral line where the dark nucleus is located is larger and larger, and the mode distribution of the vortex beam is greatly widened. The experimental result shows that the vortex light beam with the oblique line compression phase step can be obtained through the vortex light beam mask plate with the oblique line compression phase step. This will provide a richer mode of manipulation for optical micro-scale manipulation.
In summary, the present invention provides a specific design scheme and an implementation scheme of a spiral beam mask with a diagonal compression phase step, and provides a technical implementation route of a spiral beam mask with a diagonal compression phase step for a laser with an operating wavelength of 532nm, taking a focusing lens with an NA of 0.025 and a topological charge m of 5 as examples.
The above-mentioned vortex beam mask for generating the slant line compression phase step is only one 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 (3)
1. A design method of a vortex beam mask plate with oblique line compression phase step is characterized in that:
step one, combining a complementation function, a plane wave factor and a binary radial cutoff factor to obtain a transmittance function T of the vortex beam mask plate, wherein the transmittance function T has an expression as follows:
wherein, (r, theta) is a polar coordinate system variable; w is the beam waist radius of the beam; m is the topological charge value of the vortex light beam of the proposed oblique line compression phase step; im2bw [ exp (-r)2/w2)(2r2/w2)|m|/2]To combine the gray matrix exp (-r)2/w2)(2r2/w2)|m|/2The function is converted into a binary matrix to realize a radial cut-off, and the incident light energy is limited on a circular ring related to the topological charge m; ang (a) ═ atan (a)imag/Areal) Is to solve the angular function of an imaginary number A, wherein ArealAnd AimagRespectively the real part and the imaginary part of the imaginary number A; rem (thetam, f) is a remainder function, represents a remainder obtained by dividing the function thetam by the function f according to bits, and is used for realizing oblique line compression on the phase; f is a step function related to the slope of the slope; 2 pi x/d is a blazed grating item and is used for generating a plane wave factor with a period of d;
the expression of the step function f is as follows:
where K is the slope of the slope used; a isjIs the magnitude of the jth phase step; bjThe interval of two adjacent phase steps; k controls the slope of the slope used, a1Controlling the degree of compression of the oblique line to the phase step; the phase gradient of the vortex light beam of the proposed oblique line compression phase step can be regulated by regulating the topological load m; k and a1Satisfies 2 pi K + (m-K) a1/m≤2π；
Step two, selecting different parameter values m, K and a1And bringing the transmittance function T into the mask plate to obtain the vortex beam mask plate with the oblique line compression phase step.
2. The method for designing a vortex beam mask plate with oblique line compression phase steps as claimed in claim 1, wherein: in the step one, ajAnd bjRepresented by the following recurrence formula:
3. the method for generating the vortex beam with oblique line compression phase step by using the mask plate prepared by the design method according to claim 1 is characterized in that:
modulating a flat-top light beam as an incident light beam of the vortex light beam mask plate so as to generate a vortex light beam in a far field; the singular points of the vortex light beams are distributed in a spiral shape, and the slope of the compression oblique line controls the spiral degree of the singular point arrangement;
by regulating and controlling parameters m, K and a1Vortex beams with different modes and different slope compression phase steps can be obtained.
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| CN103941402A (en) * | 2014-03-22 | 2014-07-23 | 中南大学 | Method for generating vortex light with rotation angular momentum and vortex light array with rotation angular momentum |
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| CN103941402A (en) * | 2014-03-22 | 2014-07-23 | 中南大学 | Method for generating vortex light with rotation angular momentum and vortex light array with rotation angular momentum |
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| 不同拓扑荷数的涡旋光束衍射特性研究;宋晓芳;《万方平台--学位论文》;20151231;全文 * |
| 平面光斜入射叉形光栅获取涡旋光束的特性;孟祥君 等;《中国激光》;20130228;第40卷(第2期);全文 * |
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Application publication date: 20190319 Assignee: Luoyang pingconvex Technology Co.,Ltd. Assignor: HENAN University OF SCIENCE AND TECHNOLOGY Contract record no.: X2021980013091 Denomination of invention: A design method of vortex beam mask with oblique compressed phase step Granted publication date: 20201222 License type: Exclusive License Record date: 20211125 |
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