CN107065046A - A kind of Bessel-Gaussian beam mask plate based on Mittag Leffler functions - Google Patents
A kind of Bessel-Gaussian beam mask plate based on Mittag Leffler functions Download PDFInfo
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- CN107065046A CN107065046A CN201710508791.2A CN201710508791A CN107065046A CN 107065046 A CN107065046 A CN 107065046A CN 201710508791 A CN201710508791 A CN 201710508791A CN 107065046 A CN107065046 A CN 107065046A
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- bessel
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- G—PHYSICS
- G02—OPTICS
- G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
- G02B5/00—Optical elements other than lenses
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- G—PHYSICS
- G21—NUCLEAR PHYSICS; NUCLEAR ENGINEERING
- G21K—TECHNIQUES FOR HANDLING PARTICLES OR IONISING RADIATION NOT OTHERWISE PROVIDED FOR; IRRADIATION DEVICES; GAMMA RAY OR X-RAY MICROSCOPES
- G21K1/00—Arrangements for handling particles or ionising radiation, e.g. focusing or moderating
Abstract
One kind is based onMittag‑LefflerThe Bessel-Gaussian beam mask plate of function, utilize information optical principle, with reference to Mittag Leffler modulation functions, Bessel-Gaussian beam and plane wave complex amplitude, obtain interference light intensity figure, the interference recording process of principle of holography is realized, the interference light intensity figure is the mask plate designed by the present invention.Beneficial effect of the present invention：The invention provides a kind of Bessel-Gaussian beam mask plate based on Mittag Leffler functions, the pattern that can produce any smooth valve number using the mask plate is distributed, and has important application value in fields such as multiparticle captures.
Description
Technical field
The present invention relates to mask plate technical field, specifically a kind of Bei Sai based on Mittag-Leffler functions
That-Gaussian beam mask plate.
Background technology
1987, J. Durnin proposed a kind of light beam of free space salt free ligands, i.e. bessel beam
【J.Opt.soc.Am.A,1987,651-654】, it is in unbounded free space transmission, and vertical with transmission direction is each flat
Optical field distribution is always identical on face, and the cross direction profiles of electric-field intensity are concentrated, and main lobe width keeps constant in transmitting procedure.It is this
Light beam is in addition to possessing the directionality of general laser beam, monochromaticjty, high brightness and the characteristic of coherence, also with salt free ligands
Feature, non-diffraction beam refers to light field and is not subjected to diffraction extension, and this characteristic causes the extensive concern of researcher.
Bessel beam is a preferable mathematical modeling, it is impossible to experimentally produced.Because preferable high-order shellfish plug
Your light beam carries the energy of infinity, violates law of conservation of energy.In order to produce bessel beam, 1987 in an experiment
Year, F. Gori et al. propose Bessel-Gauss beams first【Opt. Commun, 1987, 491-494】.Bezier-height
This light beam is on bessel beam plus the modulation of a Gaussian profile distribution, so that its energy is restricted to limited model
Enclose.Such light beam easily can be produced experimentally, and it also has the spy of bessel beam to a certain extent
Property.In order to further widen the application value of bessel beam, 1996, K. V. Spulveda et al. proposed high-order shellfish
Sai Er light beams【J. Opt. B: Quantum Semiclass, 2002, S82-S89】Then, bessel beam is obtained rapidly
It is widely applied.The orbital angular momentum of high-order bessel beam has been solved in K. V. Spulveda in 2002 et al., and will
This light beam is applied to optical tweezer son research【J. Opt. B: Quantum Semiclass, 2002, S82-S89】.In 2006,
Y. the bessel beam that the application such as Matsuoka is produced by axicon, have studied punching energy threshold with austenite stainless steel plate
Relation between thickness, the coning angle of light beam【Appl. Phys. A, 2006,23-430】., the research such as Milne in 2007
Motion of the silicon dioxide microsphere in bessel beam【Opt. Express, 2007,13972-13987】.
However, in many application scenarios such as multiparticle capture, the rich accuracy controlling to particle of beam mode is outstanding
To be important.
The content of the invention
The technical problems to be solved by the invention are to provide a kind of Bessel-Gauss based on Mittag-Leffler functions
Light beam mask plate, applied to fields such as multiparticle captures.
The present invention is for the technical scheme that is used of solution above-mentioned technical problem：One kind is based onMittag-LefflerFunction
Bessel-Gauss beams mask plate, the transmittance function of described mask plate meets relational expression：
Wherein,MLForMittag-LefflerFunction, its expression formula is, wherein,iFor imaginary unit,L
For the parameter relevant with optical field distribution,,CGather for plural number,Represent wave number,nRepresent refraction
Rate,Represent optical wavelength,Represent gamma function；
BGFor Bessel-Gaussian beam expression formula, it is specially, whereinIt is M rank Bessel functions,For the parameter related to Bessel function,For radial direction parameter,For angular ginseng
Amount,For the waist width of corresponding fundamental-mode gaussian beam,For vortex phase,mRepresent topological charge number；
E p For plane wave factor electric field expression formula, it is specially, whereinE 0 For initial complex amplitude,zFor
Propagation distance.
The beneficial effects of the invention are as follows：The invention provides a kind of Bezier-height based on Mittag-Leffler functions
This light beam mask plate, the pattern that can produce any smooth valve number using the mask plate is distributed, and has weight in fields such as multiparticle captures
The application value wanted.
Brief description of the drawings
Fig. 1 is MittagLeffler- Bessel-Gauss beams mask plates resulting when L of the present invention is respectively 2；
Fig. 2 is MittagLeffler- Bessel-Gauss beams mask plates resulting when L of the present invention is respectively 6；
Fig. 3 is L when being 2, planar lightfield strength theory simulation drawing of 512 × 512 masks on f=50mm lens focal planes；
Fig. 4 is L when being 6, planar lightfield strength theory simulation drawing of 512 × 512 masks on f=50mm lens focal planes.
Embodiment
One kind is based onMittag-LefflerThe Bessel-Gauss beams mask plate of function, the transmission of described mask plate
Rate function meets relational expression：
Wherein,MLForMittag-LefflerFunction, its expression formula is, wherein,iFor imaginary unit,L
For the parameter relevant with optical field distribution,,CGather for plural number,Represent wave number,nRepresent refraction
Rate,Represent optical wavelength,Represent gamma function；
BGFor Bessel-Gaussian beam expression formula, it is specially, whereinIt is M rank Bessel functions,For the parameter related to Bessel function,For radial direction parameter,For angular ginseng
Amount,For the waist width of corresponding fundamental-mode gaussian beam,For vortex phase,mRepresent topological charge number；
E p For plane wave factor electric field expression formula, it is specially, whereinE 0 For initial complex amplitude,zFor
Propagation distance.
The electric field expression formula of MittagLeffler- Bessel-Gauss beams of the present invention is generated in an experiment
Come, specifically：According to calculating holographic technique, the complex amplitude expression formula of simulationInterfere with plane wave Ep, afterwards modulus
The squared interference light intensity figure that obtains realizes the interference recording process of principle of holography.The interference light intensity figure is designed by the present invention
Mask plate.
Different L values are chosen in experiment successively, the different Bezier height crossed through MittagLeffler FUNCTION MODULATIONs are obtained
This light beam, L is taken successively difference be worth to the different Bessel-Gaussian beams crossed through Mittag Leffler FUNCTION MODULATIONs.Figure
1 and Fig. 2 is that L is taken as MittagLeffler- Bessel-Gauss beams mask plates resulting when 2,6.
Embodiment
Below withIt is 532nm for operation wavelength, providing one kind can produce exemplified by mask
The mask of MittagLeffler- Bessel-Gaussian beams.If the underlying topology electric charge value for encoding vortex phase is m=2；
The underlying parameter value of MittagLeffler functions is as follows,,b=1, L=2,6,10；Bessel function
Underlying parameter value is as follows.In functionValue by(x,y)（- 25.6 to 25.6 values are at intervals of 0.1）Conversion
.According to formula, we are to be somebody's turn to doThe transmitance distribution of mask plate, Fig. 1, Fig. 2 give L and are respectively
Black portions represent that intensity is 0 in the intensity distribution of 2 and 6 mask plates, figure, and white portion represents that intensity is 1, this continuous light
The mask plate being distributed by force can be realized by a spatial light modulator, with Beijing Lei Zhiwei photoelectricity technology corporation, Ltd.s
Exemplified by LWGL532-100mW-SLM model spatial light modulators, its power is 50mW, and wavelength is 532nm.
As shown in Figure 3, Figure 4, our theoretical modelingsMask plate existsf=50mmOn the lens focal plane of focal length
Distribution of light intensity distribution.Our theoretical modeling result shows that the mask plate obtained by technical scheme, which is produced, appoints
The pattern distribution of meaning light valve number, has important application value in fields such as multiparticle captures.
Mask plate after generation FUNCTION MODULATION described above only expresses a kind of embodiment of the present invention, can not
Therefore it is interpreted as limiting the scope of the invention.It should be pointed out that for the person of ordinary skill of the art,
On the premise of basic thought of the present invention is not departed from, the specific implementation details that can also be proposed to this patent make some deformations
And improvement, these belong to protection scope of the present invention.
Claims (1)
1. one kind is based onMittag-LefflerThe Bessel-Gauss beams mask plate of function, it is characterised in that：Described mask
The transmittance function of plate meets relational expression：
Wherein,MLForMittag-LefflerFunction, its expression formula is, wherein,iFor imaginary unit,L
For the parameter relevant with optical field distribution,,CGather for plural number,Represent wave number,nRepresent refraction
Rate,Represent optical wavelength,Represent gamma function；
BGFor Bessel-Gaussian beam expression formula, it is specially, whereinIt is M rank Bessel functions,For the parameter related to Bessel function,For radial direction parameter,For angular parameter,For the waist width of corresponding fundamental-mode gaussian beam,For vortex phase,mRepresent topological charge number；
E p For plane wave factor electric field expression formula, it is specially, whereinE 0 For initial complex amplitude,zTo pass
Broadcast distance.
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Cited By (5)
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| CN107589480A (en) * | 2017-10-24 | 2018-01-16 | 首都师范大学 | A kind of diaphragm and method for suppressing the vibration of finite size Beams axial intensity |
| CN107621701A (en) * | 2017-09-07 | 2018-01-23 | 苏州大学 | Produce the method and system of double index Bessel-Gaussian beams |
| CN108037584A (en) * | 2017-12-27 | 2018-05-15 | 河南科技大学 | A kind of design method of the mask plate of V-type light beam |
| CN108681084A (en) * | 2018-04-03 | 2018-10-19 | 河南科技大学 | A kind of design method for the angular Airy beam mask plate that can freely regulate and control |
| CN112861274A (en) * | 2021-01-06 | 2021-05-28 | 河南科技大学 | Design method of mask plate of high-order free mode optical vortex array |
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Cited By (10)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN107621701A (en) * | 2017-09-07 | 2018-01-23 | 苏州大学 | Produce the method and system of double index Bessel-Gaussian beams |
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| CN107589480A (en) * | 2017-10-24 | 2018-01-16 | 首都师范大学 | A kind of diaphragm and method for suppressing the vibration of finite size Beams axial intensity |
| CN107589480B (en) * | 2017-10-24 | 2023-08-04 | 首都师范大学 | Diaphragm and method for inhibiting axial light intensity oscillation of diffraction-free light beam with limited size |
| CN108037584A (en) * | 2017-12-27 | 2018-05-15 | 河南科技大学 | A kind of design method of the mask plate of V-type light beam |
| CN108037584B (en) * | 2017-12-27 | 2020-05-15 | 河南科技大学 | Design method of mask plate of V-shaped light beam |
| CN108681084A (en) * | 2018-04-03 | 2018-10-19 | 河南科技大学 | A kind of design method for the angular Airy beam mask plate that can freely regulate and control |
| CN108681084B (en) * | 2018-04-03 | 2020-07-24 | 河南科技大学 | Design method of freely-adjustable angular Airy beam mask plate |
| CN112861274A (en) * | 2021-01-06 | 2021-05-28 | 河南科技大学 | Design method of mask plate of high-order free mode optical vortex array |
| 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 |
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Application publication date: 20170818 Assignee: Henan Yunyi Software Technology Co., Ltd. Assignor: Henan University of Science and Technology Contract record no.: X2019980000349 Denomination of invention: Bessel-Gaussian beam mask plate based on Mittag-Leffler function Granted publication date: 20190503 License type: Common License Record date: 20191031 |
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