CN108121067B - Design method of multi-notch elliptical perfect vortex light beam mask plate - Google Patents

Design method of multi-notch elliptical perfect vortex light beam mask plate Download PDF

Info

Publication number
CN108121067B
CN108121067B CN201711443997.8A CN201711443997A CN108121067B CN 108121067 B CN108121067 B CN 108121067B CN 201711443997 A CN201711443997 A CN 201711443997A CN 108121067 B CN108121067 B CN 108121067B
Authority
CN
China
Prior art keywords
elliptical
mask plate
notch
perfect vortex
design method
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201711443997.8A
Other languages
Chinese (zh)
Other versions
CN108121067A (en
Inventor
台玉萍
马海祥
李新忠
李贺贺
唐苗苗
王静鸽
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Henan University of Science and Technology
Original Assignee
Henan University of Science and Technology
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Henan University of Science and Technology filed Critical Henan University of Science and Technology
Priority to CN201711443997.8A priority Critical patent/CN108121067B/en
Publication of CN108121067A publication Critical patent/CN108121067A/en
Application granted granted Critical
Publication of CN108121067B publication Critical patent/CN108121067B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/0012—Optical design, e.g. procedures, algorithms, optimisation routines
    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B27/00—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00
    • G02B27/09—Beam shaping, e.g. changing the cross-sectional area, not otherwise provided for
    • G02B27/0938—Using specific optical elements
    • G02B27/0988—Diaphragms, spatial filters, masks for removing or filtering a part of the beam

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Exposure And Positioning Against Photoresist Photosensitive Materials (AREA)

Abstract

The invention discloses a design method of a multi-notch elliptical perfect vortex beam mask plate, which comprises the following steps: step one, the topological loads under two elliptical coordinate systems are differentInteger order helical phase factor Ev1、Ev2Combine to obtain Ev1+Ev2To E, forv1+Ev2Obtaining an angle (E) by phase calculationv1+Ev2) (ii) a Step two, obtaining a spiral phase factor E of the perfect vortex of the multi-notch ellipsev，EvThe expression of (a) is: ev＝exp[i·angle(Ev1+Ev2)]Wherein angle () represents a function of phase of the complex number; helical phase factor EvComplex transmittance function t of elliptic cone lensaCombining to obtain an optical electric field expression taEv(ii) a Step three, according to the computer holographic technology, the photoelectric field expression t is madeaEvAnd plane wave EpAfter interference, a module is calculated and a square is taken to obtain an interference light intensity image, and the interference light intensity image is the multi-gap elliptical perfect vortex beam mask plate t. The mask plate designed by the invention can generate an elliptical perfect vortex beam with any gap.

Description

Design method of multi-notch elliptical perfect vortex light beam mask plate
Technical Field
The invention relates to the field of particle light manipulation and optical testing, in particular to a design method of a multi-notch elliptical perfect vortex beam mask plate.
Background
Vortex beams have wide application in optically trapping, manipulating small particles, and the like. Becomes a very important research hotspot in the field of information optics in recent years. But the size of the central dark spot of a conventional vortex beam increases with increasing topological charge value. However, in applications where optical vortex-related trapping and manipulation of particles is desired, it is often desirable to achieve both large topological charge and a smaller central dark spot. To address this problem, Andrey s.ostrovsky et al, 2013, proposed the concept of perfect swirl (perfect swirl) whose bright ring radius is independent of the topological charge value [ opt.lett.38,5342013 ]. But this method produces additional stray light rings with perfectly vortex beams. In 2015, Pravin value et al obtained integer order perfect vortices without additional halo by fourier transforming the bessel-gaussian beam [ opt. lett.40, 5972015 ].
On the other hand, the fractional order vortex beam can carry more information and provide more fine particle operation due to the gap, which becomes a hot topic of competitive research of many researchers in the field of vortex optics. In order to realize generation of fractional order vortex light beams, in 2017, Michael Mazilu and other spiral phase picture-based designs, a multi-notch perfect vortex [ Optica 4,3302017 ] is provided. However, their technical means make the multi-gap perfect vortex generated by them need to perform picture processing on the phase diagram of the vortex term every time the parameter is changed, rather than formula implementation, so that it is difficult to implement wide application in industry. In addition, the elliptical light beam is not distributed in a circular symmetry manner, so that the method provided by the document [ Optica 4,3302017 ] cannot generate a multi-notch light beam. Therefore, due to technical limitations, perfect vortexing of multi-gap ellipses has not been reported yet, making fine manipulation of some special morphology particles difficult to achieve.
In summary, in the field of vortex beam research, there is still a lack of a mask design for a particle-steering multi-gap elliptical perfect vortex beam to generate a multi-gap fractional order elliptical perfect vortex beam.
Disclosure of Invention
The invention aims to provide a design method of a multi-notch elliptical perfect vortex beam mask plate for solving the problems in the prior art.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: a design method of a multi-notch elliptical perfect vortex beam mask plate comprises the following steps:
step one, performing integral-order spiral phase factor E with different topological loads under two elliptical coordinate systemsv1、Ev2Combine to obtain Ev1+Ev2To E, forv1+Ev2Obtaining an angle (E) by phase calculationv1+Ev2)；
Step two, obtaining a spiral phase factor E of the perfect vortex of the multi-notch ellipsev，EvThe expression of (a) is:
Ev＝exp[i·angle(Ev1+Ev2)]
where angle () denotes a function of the phase of the complex number;
helical phase factor EvComplex transmittance function t of elliptic cone lensaCombining to obtain an optical electric field expression taEv；
Step three, according to the computer holographic technology, the photoelectric field expression t is madeaEvAnd plane wave EpAfter interference, a module is calculated and a square is taken to obtain an interference light intensity image, and the interference light intensity image is the multi-gap elliptical perfect vortex beam mask plate t.
Further, the complex transmittance function expression of the mask t is as follows:
t＝circ(r)|taexp[i·angle(Ev1+Ev2)]+Ep|2
wherein r is an elliptical coordinate system radial variable, and the transformation relationship between the elliptical coordinate system radial variable and a cartesian coordinate system (x, y) is Mx ═ rcos (θ), My ═ rsin (θ), θ is an angular parameter of the elliptical coordinate system, and M is a constant; circ (r) describes an elliptical diaphragm, expressed as:
Figure BDA0001527142560000021
which serves as a boundary condition for limiting the mask.
Further, the helical phase factor Ev1And helical phase factor Ev2Are respectively:
Ev1(θ)＝exp(ilθ)
Ev2(θ)＝exp[i(l+m)θ]
wherein l is a helical phase factor Ev1The topological load of (1); l +m is helical phase factor Ev2The topological load of (1); the parameters l and m are integers, and i is an imaginary unit; evThe topological charge number of (2l + m)/2, m is the gap number;
elliptic cone lens transmittance function taThe expression is as follows:
Figure BDA0001527142560000022
in the formula, a is an elliptical cone lens parameter, R is an elliptical cone lens pupil radius, and R is an elliptical coordinate system radial variable.
Further, the plane wave factor electric field EpThe expression of (a) is:
Ep＝E0exp(-ikz)
where i is the imaginary unit, k is the wavevector, and z is the propagation distance.
Further, the helical phase factor Ev1The topological load parameter is 1, and the gap number m is sequentially taken from 1 to 5 at intervals of 1.
Further, the elliptical cone lens parameter a is taken as 12.
Compared with the prior art, the invention has the beneficial effects that:
the mask plate designed by the invention can generate an elliptical perfect vortex beam with any gap. Has very important application value in the field of particle manipulation. The invention utilizes the principle of computer holography and generates multi-notch elliptic perfect vortex beams in a far field through the computation simulation of the complex amplitude of the beams. The multi-notch elliptical perfect vortex light beam can enable the elliptical perfect vortex optical rotation ring to have any number of notches, and therefore the multi-notch elliptical perfect vortex optical rotation ring has important application value in the field of particle manipulation.
The mask plate designed by the invention can realize that the perfect vortex of any notch ellipse can be generated in the far field of the mask plate. The number of gaps is determined by the parameter m. The gap for controlling the perfect vortex of the multi-gap ellipse is a breakpoint for controlling the orbital angular momentum density of the perfect vortex light beam of the multi-gap ellipse, so the method has very important application prospect in the particle manipulation technology.
Drawings
FIG. 1 is a mask plate for generating multi-notch elliptical perfect vortex beams according to the present invention. Helical phase factor Ev1The topological load parameter is 1, and the gap number m is sequentially taken from 1 to 5 at intervals of 1.
Fig. 2 is a multi-gap elliptical perfect vortex beam generated by the reticle simulation shown in fig. 1.
Detailed Description
FIG. 1 is a mask plate of an embodiment of a multi-notch elliptical perfect vortex beam generated by the present invention, wherein a specific expression of a transmittance function is as follows:
t＝circ(r)|taexp[i·angle(Ev1+Ev2)]+Ep|2
wherein r is a radial variable of an elliptical coordinate system, and a transformation relationship between r and a cartesian coordinate system (x, y) is Mx ═ rcos (θ), y ═ rsin (θ), θ is an angular parameter of the elliptical coordinate system, M is a constant, and a value in the specific embodiment of the present patent is 2; t is taIs an elliptic cone lens transmittance function; ev1、Ev2Integer order spiral phase factors with different topological charges in an elliptic coordinate system; epIs a plane wave factor electric field expression; angle (.) represents a function that takes the phase of the complex number; circ (r) describes an elliptical diaphragm, expressed as:
Figure BDA0001527142560000031
used as a boundary condition for limiting the proposed multi-gap elliptical perfect vortex beam mask plate.
The transmittance function (t) of the elliptic cone lensa) The expression is as follows:
Figure BDA0001527142560000032
in the formula, a is an elliptical cone lens parameter, and the value in the specific embodiment of the patent is 12; and R is the pupil radius of the elliptical cone lens.
The helical phase factor (E)v1、Ev2) The expressions are respectively:
Ev1(θ)＝exp(ilθ)
Ev2(θ)＝exp[i(l+m)θ]
wherein l is a helical phase factor Ev1The topological load of (1); l + m is helical phase factor Ev2The topological load of (2). The parameters l and m are integers. Then Ev＝exp[i·angle(Ev1+Ev2)]Constitute the spiral phase factor of the perfect vortex of the multi-notch ellipse. (2l + m)/2 is the topological charge number of the multi-gap fractional order helical phase factor; m is the number of gaps.
The electric field of the plane wave is expressed as:
Ep＝E0exp(-ikz)
where z is the propagation distance. According to the computer-generated holography technique, the electric field expression taEvAnd plane wave EpAnd after the interference, the mode is solved and the square is taken to obtain an interference light intensity pattern, so that the interference recording process of the holographic principle is realized. The interference light intensity pattern is the mask plate t designed by the invention.
In the experiment, E is fixed firstv1And (3) taking the value of the topological charge parameter l, and then selecting different parameters m to obtain the multi-notch elliptic perfect vortex beam mask plate with the notch number of m. FIG. 1 shows the helical phase factor Ev1And (3) selecting 1 as the topological load parameter, and sequentially taking 1 as the interval to obtain the multi-notch elliptical perfect vortex beam mask plate when the notch number m is taken from 1 to 5.
Example (b):
taking a mask plate with the size of 512 × 512 as an example, a multi-notch elliptical perfect vortex beam mask plate with controllable notch number is given for laser with the working wavelength of 532nm, the parameters of the elliptical cone lens of the mask plate are 12, and the phase factor E isv1And (3) selecting 1 as the topological load parameter, sequentially taking 1 as the interval to take 5 from 1 for the gap number m, and finally obtaining the multi-gap elliptical perfect vortex beam mask plate according to the mask plate transmittance function in the specific implementation mode. FIG. 1 shows a multi-gap elliptical perfect vortex beam mask plate under 1-5 gaps. The multi-notch elliptic perfect vortex beam mask plate can pass through a spaceAn inter-light modulator. Taking a pluto-vis-016 type spatial light modulator of Holoeye, Germany as an example, the proposed multi-notch elliptical perfect vortex beam mask plate is experimentally verified.
As shown in fig. 2, we have experimentally obtained the light field intensity distribution of the multi-notch elliptical perfect vortex beam mask plate on the lens focal plane with NA of 0.025 numerical aperture. As can be seen from the figure, we have obtained a multi-notch elliptical perfect vortex beam with a notch number of m. The experimental result shows that the multi-notch elliptical perfect vortex light beam mask plate provided by the invention can obtain the multi-notch elliptical perfect vortex light beam with any number of notches. 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 multi-notch elliptical perfect vortex beam mask plate, and provides a technical implementation route of the multi-notch elliptical perfect vortex beam mask plate for a laser with a working wavelength of 532nm, taking 12 as an example of parameters of a focusing lens and an elliptical cone lens with an NA of 0.025.
The mask plate for generating the multi-notch elliptical perfect vortex beam is only used for expressing one specific embodiment of the invention, and is not to be construed as limiting the protection scope of the 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 previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (7)

1. A design method of a multi-notch elliptical perfect vortex beam mask plate is characterized by comprising the following steps:
step one, performing integral-order spiral phase factor E with different topological loads under two elliptical coordinate systemsv1、Ev2Combine to obtain Ev1+Ev2To E, forv1+Ev2Obtaining an angle (E) by phase calculationv1+Ev2)；
Step two, obtaining a spiral phase factor E of the perfect vortex of the multi-notch ellipsev，EvThe expression of (a) is:
Ev＝exp[i·angle(Ev1+Ev2)]
where angle () denotes a function of the phase of the complex number;
helical phase factor EvComplex transmittance function t of elliptic cone lensaCombining to obtain an optical electric field expression taEv；
Step three, according to the computer holographic technology, the photoelectric field expression t is madeaEvAnd plane wave EpAfter interference, a module is calculated and a square is taken to obtain an interference light intensity image, and the interference light intensity image is the multi-gap elliptical perfect vortex beam mask plate t.
2. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 1, characterized in that: the complex transmittance function expression of the mask t:
t＝circ(r)|taexp[i·angle(Ev1+Ev2)]+Ep|2
wherein r is an elliptical coordinate system radial variable, and the transformation relationship between the elliptical coordinate system radial variable and a cartesian coordinate system (x, y) is Mx ═ rcos (θ), My ═ rsin (θ), θ is an angular parameter of the elliptical coordinate system, and M is a constant; circ (r) describes an elliptical diaphragm, expressed as:
Figure FDA0001527142550000011
which serves as a boundary condition for limiting the mask.
3. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 1, characterized in that: helical phase factor Ev1And helical phase factor Ev2Are respectively:
Ev1(θ)＝exp(ilθ)
Ev2(θ)＝exp[i(l+m)θ]
wherein l is a helical phase factor Ev1The topological load of (1); l + m is helical phase factor Ev2The topological load of (1); the parameters l and m are integers, and i is an imaginary unit; evThe topological charge number of (2l + m)/2, m is the gap number.
4. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 1, characterized in that: elliptic cone lens transmittance function taThe expression is as follows:
Figure FDA0001527142550000012
in the formula, a is an elliptical cone lens parameter, R is an elliptical cone lens pupil radius, and R is an elliptical coordinate system radial variable.
5. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 2, characterized in that: plane wave factor electric field EpThe expression of (a) is:
Ep＝E0exp(-ikz)
where i is the imaginary unit, k is the wavevector, and z is the propagation distance.
6. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 1, characterized in that: helical phase factor Ev1Selecting the topological load parameter as l ═1, the number of notches m is taken from 1 to 5 at intervals of 1 in sequence.
7. The design method of the multi-notch elliptical perfect vortex beam mask plate according to claim 1, characterized in that: the elliptical cone lens parameter a is 12.
CN201711443997.8A 2017-12-27 2017-12-27 Design method of multi-notch elliptical perfect vortex light beam mask plate Active CN108121067B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201711443997.8A CN108121067B (en) 2017-12-27 2017-12-27 Design method of multi-notch elliptical perfect vortex light beam mask plate

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201711443997.8A CN108121067B (en) 2017-12-27 2017-12-27 Design method of multi-notch elliptical perfect vortex light beam mask plate

Publications (2)

Publication Number Publication Date
CN108121067A CN108121067A (en) 2018-06-05
CN108121067B true CN108121067B (en) 2020-09-15

Family

ID=62232132

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201711443997.8A Active CN108121067B (en) 2017-12-27 2017-12-27 Design method of multi-notch elliptical perfect vortex light beam mask plate

Country Status (1)

Country Link
CN (1) CN108121067B (en)

Families Citing this family (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN108761783B (en) * 2018-08-10 2020-07-24 河南科技大学 Design method of tightly-arranged perfect vortex array mask plate with controllable structure
CN109683339B (en) * 2019-01-11 2020-11-03 中国科学院西安光学精密机械研究所 Phase mask plate for realizing bright nuclear vortex light beam and light path system
CN109870890B (en) * 2019-01-11 2020-06-26 中国科学院西安光学精密机械研究所 Integer order vortex light beam phase mask plate with fractional order vortex contour and light path system
CN109828370B (en) * 2019-01-24 2021-01-08 河南科技大学 Design method of mirror symmetry optical vortex optical trap mask plate
CN115453752B (en) * 2022-09-19 2023-07-21 苏州大学 Design method of vortex beam mask plate with abnormal radius

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103984103A (en) * 2014-02-18 2014-08-13 上海大学 Method for generating vortex light beam by use of calculation hologram
CN106560738B (en) * 2016-06-02 2019-06-11 河南科技大学 A kind of generation device and production method of perfection IG vortex beams
CN107238933B (en) * 2017-07-07 2023-08-25 苏州大学 Method and system for generating a local fractional order Bessel vortex beam

Also Published As

Publication number Publication date
CN108121067A (en) 2018-06-05

Similar Documents

Publication Publication Date Title
CN108121067B (en) Design method of multi-notch elliptical perfect vortex light beam mask plate
CN106933027B (en) Design method of annular vortex array mask plate with controllable vortex number
Chen et al. Generation and characterization of a perfect vortex beam with a large topological charge through a digital micromirror device
Kazanskiy et al. Binary beam splitter
CN109917546B (en) Design method of center symmetrical vortex light beam mask plate capable of being freely regulated and controlled
Mikuła et al. Imaging with extended focal depth by means of lenses with radial and angular modulation
Lopez-Mariscal et al. Observation of the experimental propagation properties of Helmholtz-Gauss beams
Yu et al. Three-dimensional Dammann vortex array with tunable topological charge
Zhao et al. Shaping diffraction-free Lommel beams with digital binary amplitude masks
Bañas et al. GPC light shaper for speckle-free one-and two-photon contiguous pattern excitation
CN110472294B (en) Design method of mask plate for grafting vortex light beam
WO2023279424A1 (en) System for generating polygonal partially coherent vortex beam, and method
Shaw et al. Scanning holographic optical tweezers
Liu et al. Generalized photon sieves: fine control of complex fields with simple pinhole arrays
Aksenov et al. Properties of vortex beams formed by an array of fibre lasers and their propagation in a turbulent atmosphere
Golbandi et al. Controlling and shaping topological charge by means of spiral petal-like zone plate
Fang et al. Accelerating polygon beam with peculiar features
Cheng et al. Generation of Bessel-beam arrays for parallel fabrication in two-photon polymerization
Yang et al. Controlling spacing of double-ring perfect optical vortex using the Fourier transform of Bessel beam with axicon phase
Hu et al. High-speed generation of singular beams through random spatial multiplexing
Zhao et al. Autofocusing self-imaging: symmetric Pearcey Talbot-like effect
CN109683339B (en) Phase mask plate for realizing bright nuclear vortex light beam and light path system
Liu et al. Effect of the astigmatic phase on the intensity of nonsingular beams during propagation
CN111474708B (en) Design method of vortex array mask plate in abnormal annular connection
Soifer et al. Diffractive micro-optical element with nonpoint response

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
EE01 Entry into force of recordation of patent licensing contract
EE01 Entry into force of recordation of patent licensing contract

Application publication date: 20180605

Assignee: Luoyang pingconvex Technology Co.,Ltd.

Assignor: HENAN University OF SCIENCE AND TECHNOLOGY

Contract record no.: X2021980013091

Denomination of invention: A design method of multi notch elliptical perfect vortex beam mask

Granted publication date: 20200915

License type: Exclusive License

Record date: 20211125