CN105974600A - Method for realizing beam tight focusing through vortex beams - Google Patents
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- CN105974600A CN105974600A CN201610579589.4A CN201610579589A CN105974600A CN 105974600 A CN105974600 A CN 105974600A CN 201610579589 A CN201610579589 A CN 201610579589A CN 105974600 A CN105974600 A CN 105974600A
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- 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
- G02B27/58—Optics for apodization or superresolution; Optical synthetic aperture systems
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- 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
- G02B27/28—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising
- G02B27/286—Optical systems or apparatus not provided for by any of the groups G02B1/00 - G02B26/00, G02B30/00 for polarising for controlling or changing the state of polarisation, e.g. transforming one polarisation state into another
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Abstract
The invention provides a method for realizing beam tight focusing through vortex beams, relates to the method for beam tight focusing, and provides the method for realizing beam tight focusing through the vortex beams for solving the problems in the prior art that the aperture of an optical system is limited by the size of equipment and the focusing effect better than the Rayleigh diffraction limit cannot be acquired. The method is realized by the steps that firstly azimuth polarized light is incident to a spiral phase plate; secondly, the phase of the azimuth polarized light is linearly modulated according to the annular azimuth of being within the interval of 0-2pi by utilizing the spiral phase plate so that spatial phase coding is completed and the vortex beams are formed; and thirdly the vortex beams of the known phase code are enabled to pass through a focusing lens of high value aperture so that focusing light spots better than the Rayleigh diffraction limit are formed. The method for realizing beam tight focusing through the vortex beams is suitable for the field of beam tight focusing and super-resolution imaging.
Description
Technical field
The present invention relates to the use of the method that vortex beams realizes light beam tightly focused.
Background technology
Light beam tightly focused has high application valency at aspects such as optical storage of data, offset printing and super-resolution imagings
Value.And the method for current optical focus is limited by classical diffraction limit.Under limiting at this, the hot spot after light beam focuses on is big
Little have a minima, and radius is 0.61 λ2/D.Wherein λ is optical wavelength, and D is optical system numerical aperture.Can from formula
Go out, will expect that less hot spot needs increase numerical aperture or reduce wavelength.In actual applications, numerical aperture and wavelength
It is all limited, it is impossible to unlimited increase numerical aperture or reduction wavelength, how under conditions of numerical aperture and wavelength are certain
Obtain less hot spot and become problem demanding prompt solution.It is thus desirable to find a kind of condition certain with wavelength in vertical aperture
Under, break through diffraction limit, it is achieved the method that more small light spot focuses on.
Summary of the invention
The size that the invention aims to solve prior art focal beam spot is limited by numerical aperture and optical wavelength
The problem that cannot obtain the focusing effect being better than Rayleigh diffraction limit, and the one proposed utilizes vortex beams to realize light tightens poly-
Burnt method.
Above-mentioned goal of the invention is achieved through the following technical solutions:
The described device utilizing vortex beams to realize light beam tightly focused specifically includes orientation polarized light piece, 0～2 spirals of π
Phase-plate and high numerical aperture condenser lens.
Step one, orientation polarized light is made to incide spiral phase plate；
Step 2, utilize spiral phase plate that the phase place of orientation polarized light is carried out in the interval of 0～2 π by angular orientation
Linear modulation, thus complete phase encode and form vortex beams；
Step 3, the vortex beams making known phase encode are better than Rayleigh diffraction limit by aperture focusing lens, formation
Focal beam spot；
The described electric vector incided on aperture focusing lens by vortex beams is distributed:
Wherein, θ is the angle between light beam and optical axis；A2For comprising the function of the characteristic information of lens；K is wave vector, and n is
Refractive index；For polar angle coordinate；r2For the light beam radial coordinate after lens；For the light beam polar angle coordinate after lens；
z2Coordinate for the direction of propagation；NA is lens numerical aperture；N is the index of refraction in lens；A1For light beam vibration amplitude
?；I is imaginary part unit；With optical axis as z-axis, any two direction is x and y-axis sets up coordinate system；px, py, pzIt is x, y and z respectively
Polarization base vector on three directions of axle；Aperture focusing lens NA > 1；
The integration abbreviation of formula (2) is obtained:
In formula,For beam phase,
V1=Jm-1(krsinθ)+Jm+1(krsinθ)
V2=Jm-1(krsinθ)-Jm+1(krsinθ)
It is solid angle that Ω is first,
Jm+1For m+1 rank Bezier Gaussian function
M is the topological Numbers of vortex light；
A is integral constant；
R is radial coordinate.
Invention effect
The present invention relates to super-resolution imaging technical field, particularly relate to one and utilize vortex beams to realize light beam tightly focused
Method.The focal beam spot breaking through classical diffraction limit can be obtained.The invention discloses one utilizes vortex beams to realize light
The method of bundle super-resolution tightly focused, belongs to high-resolution imaging technical field.It solving in light beam focusing, hot spot focuses on
Size is by the restricted problem of classical diffraction limit.The present invention make particular polarization light produce vortex light by spiral phase plate
Bundle, the condenser lens through large-numerical aperture realizes focusing on afterwards.The focal beam spot of vortex phase modulation is adjusted than without phase place
The phase specific area of system reduces nearly half, breaches classical diffraction limit.The present invention proposes one and realizes light beam based on vortex beams
The method of tightly focused, it is possible to obtain break through the focal beam spot of classical diffraction limit.Can be realized target by light beam tightly focused
Super-resolution imaging.The present invention is by utilizing spiral phase plate that incident illumination carries out phase code, saturating with high-NA afterwards
Mirror focuses on, and compared with prior art, the present invention can break through classical diffraction limit, it is achieved Figure of description is shown in focusing less to light beam
2。
Accompanying drawing explanation
Fig. 1 is that light beam super-resolution tightly focused schematic diagram is put in detailed description of the invention one proposition；Wherein, (1) is orientation polarization
Mating plate, (2) are the spiral phase plate of 0-2 π, (3) high numerical aperture condenser lens
Fig. 2 is the different polarization big logotype of light focal beam spot that detailed description of the invention one proposes.
Detailed description of the invention
Detailed description of the invention one: a kind of method utilizing vortex beams to realize light beam tightly focused of present embodiment, specifically
Prepare according to following steps:
The described device utilizing vortex beams to realize light beam tightly focused specifically includes the spiral phase of orientation polarized light piece, 0-2 π
Position plate (VPP-1c) and high numerical aperture condenser lens such as Fig. 1 (GCL-010213)；
Step one, orientation polarized light is made to incide spiral phase plate；
Step 2, utilize spiral phase plate that the phase place of orientation polarized light is carried out in the interval of 0～2 π by angular orientation
Linear modulation, thus complete phase encode and form vortex beams；
Step 3, the vortex beams making known phase encode are better than Rayleigh diffraction limit by aperture focusing lens, formation
Focal beam spot；
General thought is that polarized light focuses on by realizing more small light spot after lens compared with other light with the light of phase code,
The effect reached is hot spot less (breakthrough diffraction limit)
The described electric vector incided on aperture focusing lens by vortex beams is distributed:
Wherein, θ is the angle between light beam and optical axis；A2For comprising the function of the characteristic information of lens；K is wave vector, and n is
Refractive index；For polar angle coordinate；r2For the light beam radial coordinate after lens；For the light beam polar angle coordinate after lens；
z2Coordinate for the direction of propagation；NA is lens numerical aperture；N is the index of refraction in lens；A1For light beam vibration amplitude
?；I is imaginary part unit；With optical axis as z-axis, any two direction is x and y-axis sets up coordinate system；px, py, pzReact light beam
Polarization characteristic, px, py, pzIt is the polarization base vector on tri-directions of xyz respectively；Aperture focusing lens NA > 1；
The integration abbreviation of formula (2) is obtained:
In formula,For beam phase,
V1=Jm-1(krsinθ)+Jm+1(krsinθ)
V2=Jm-1(krsinθ)-Jm+1(krsinθ)
V1And V2For intermediate variable；
It is solid angle that Ω is first,
Jm+1For m+1 rank Bezier Gaussian function；
M is the topological Numbers of vortex light；
A is integral constant；
R is radial coordinate；
Experiment can be made by regulation spatial light modulator the topological Numbers m=1 of vortex light, and then make V1、V2In shellfish
Sai Er function becomes zeroth order, has:
V1=J0(krsinθ)+J2(krsinθ)≈J0(krsinθ)
V2=J0(krsinθ)-J2(krsinθ)≈J0(krsinθ)
So vortex light makes Bessel function become 0 rank, and the characteristic of 0 rank Bessel function is the function compared with other rank
Having more preferable focusing effect, make light intensity concentrate on center (tightly focused), and the function on other rank is hollow, light intensity is dispersed in week
Enclose
Said method is carried out experimentation, experiment is respectively adopted linear polarization, circular polarization, radial polarisation and orientation polarization
For incident illumination；Wherein orientation polarized light carries out phase code with through spiral phase plate；The hot spot of experimental result vortex beams is big
Little is 0.147 λ2, radial polarisation light is 0.17 λ2, circularly polarized light 0.229 λ2, line polarized light is 0.26 λ2；And diffraction limited spot
Size is 0.36 λ2, result shows that vortex beams can effectively reduce the size of focal beam spot, breaks through diffraction limit, inclined with other
The light that shakes has compared more preferable focusing effect.
Present embodiment effect:
Present embodiment relates to super-resolution imaging technical field, particularly relates to one and utilizes vortex beams to realize light to tighten
The method focused on.The focal beam spot breaking through classical diffraction limit can be obtained.Present embodiment discloses one and utilizes vortex light
The method of Shu Shixian light beam super-resolution tightly focused, belongs to high-resolution imaging technical field.It solve in light beam focusing,
Hot spot focuses on the size restricted problem by classical diffraction limit.Present embodiment make particular polarization light pass through spiral phase plate
Producing vortex beams, the condenser lens through large-numerical aperture realizes focusing on afterwards.It is better than the focal beam spot of Rayleigh diffraction limit
Ratio reduces nearly half without the phase specific area of phase-modulation, breaches classical diffraction limit.Present embodiment proposes a kind of base
In the method that vortex beams realizes light beam tightly focused, it is possible to obtain break through the focal beam spot of classical diffraction limit.Tightened by light
Focusing can realize the super-resolution imaging to target.Present embodiment carries out phase place volume by utilizing spiral phase plate to incident illumination
Code, focuses on by high numerical aperture lens afterwards, and compared with prior art, present embodiment can break through classical diffraction limit, it is achieved
Figure of description 2 is shown in focusing less to light beam.
Detailed description of the invention two: present embodiment is unlike detailed description of the invention one: utilize spiral phase in step 2
The phase place of orientation polarized light is existed by position plate by angular orientationInterval in carry out linear modulation.Other step and parameter
Identical with detailed description of the invention one.
Detailed description of the invention three: present embodiment is unlike detailed description of the invention one or two: phase described in step 2
Position coding forms the detailed process of vortex beams:
The electric vector of incident orientation polarized light isElectric vector after spiral phase plateFor:
In formula:For azimuthal coordinate function；E is exponential function；
The PHASE DISTRIBUTION understood on beam cross-section by above formula changes along with radial angle, has vortex characteristic；Make
Orientation polarized light becomes vortex beams.Other step and parameter are identical with detailed description of the invention one or two.
Detailed description of the invention four: present embodiment is unlike one of detailed description of the invention one to three: A in step 31
For the term amplitude of light beam, then:
Wherein, β0Ratio for lens radius with waist radius；J1For first-order bessel function.Other step and parameter and tool
One of body embodiment one to three is identical.
Detailed description of the invention five: present embodiment is unlike one of detailed description of the invention one to four: A in step 32
Comprise lens arrangement letter feature, then:
Wherein, V () is that the depolarization bent by lens is shaken the Jacobian matrix of generation (attributes of lens).Other step and ginseng
Number is identical with one of detailed description of the invention one to four.
Claims (7)
1. one kind utilizes the method that vortex beams realizes light beam tightly focused, it is characterised in that described utilize vortex beams to realize light
Tighten the device of focusing specifically include orientation polarized light piece, 0～2 π spiral phase plate and high numerical aperture condenser lens, the party
Method specifically follows the steps below:
Step one, orientation polarized light is made to incide spiral phase plate；
Step 2, utilize spiral phase plate that the phase place of orientation polarized light is carried out linearly by angular orientation in the interval of 0～2 π
Modulation, thus complete phase encode and form vortex beams；
Step 3, the vortex beams making known phase encode pass through aperture focusing lens, are formed and are better than the poly-of Rayleigh diffraction limit
Burnt hot spot；
The described electric vector incided on aperture focusing lens by vortex beams is distributed:
Wherein, θ is the angle between light beam and optical axis；A2For comprising the function of the characteristic information of lens；K is wave vector, and n is refraction
Rate；For polar angle coordinate；r2For the light beam radial coordinate after lens；For the light beam polar angle coordinate after lens；z2For
The coordinate of the direction of propagation；NA is lens numerical aperture；N is the index of refraction in lens；A1For light beam vibration amplitude item；i
For imaginary part unit；With optical axis as z-axis, any two direction is x and y-axis sets up coordinate system；px, py, pzIt is x, y and z axes three respectively
Polarization base vector on individual direction；Aperture focusing lens NA > 1；
The integration abbreviation of formula (2) is obtained:
In formula,For beam phase,
V1=Jm-1(krsinθ)+Jm+1(krsinθ)
V2=Jm-1(krsinθ)-Jm+1(krsinθ)
V1And V2For intermediate variable；
It is solid angle that Ω is first；
Jm+1For m+1 rank Bezier Gaussian function；
M is the topological Numbers of vortex light；
A is integral constant；
R is radial coordinate.
A kind of method utilizing vortex beams to realize light beam tightly focused, it is characterised in that: step 2
Middle utilize spiral phase plate that the phase place of orientation polarized light is existed by angular orientationInterval in carry out linear modulation.
A kind of method utilizing vortex beams to realize light beam tightly focused, it is characterised in that: step 2
Described in phase code formed vortex beams detailed process be:
The electric vector of incident orientation polarized light isElectric vector after spiral phase plateFor:
In formula:For azimuthal coordinate function；E is exponential function.
A kind of method utilizing vortex beams to realize light beam tightly focused, it is characterised in that: step 3
Middle A1For the term amplitude of light beam, then:
Wherein, β0Ratio for lens radius with waist radius；J1For first-order bessel function.
A kind of method utilizing vortex beams to realize light beam tightly focused the most according to claim 1 or claim 2, it is characterised in that: step
A in rapid three1For the term amplitude of light beam, then:
Wherein, β0Ratio for lens radius with waist radius；J1For first-order bessel function.
A kind of method utilizing vortex beams to realize light beam tightly focused, it is characterised in that: step 3
Middle A2Comprise lens arrangement letter feature, then:
Wherein, V () is that the depolarization bent by lens is shaken generation Jacobian matrix.
7. according to a kind of method utilizing vortex beams to realize light beam tightly focused described in claim 1,2 or 4, it is characterised in that:
A in step 32Comprise lens arrangement letter feature, then:
Wherein, V () is that the depolarization bent by lens is shaken generation Jacobian matrix.
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|---|---|---|---|---|
| CN106990547A (en) * | 2017-05-16 | 2017-07-28 | 南开大学 | The super surface of dolphin shape cellular circular array |
| CN107390381A (en) * | 2017-08-30 | 2017-11-24 | 济南大学 | A kind of method and apparatus that the rotation direction polarization vector light beam with vortex phase is produced based on axial cone mirror |
| CN108227220A (en) * | 2017-12-26 | 2018-06-29 | 上海大学 | Complex light vortex production method |
| CN108593995A (en) * | 2017-12-26 | 2018-09-28 | 上海大学 | Light swirl pattern all-fiber current sensor |
| CN108983443A (en) * | 2018-08-20 | 2018-12-11 | 德州学院 | Metasurface for generating diffraction-free optical vortex lattice and design method thereof |
| CN109142273A (en) * | 2018-09-07 | 2019-01-04 | 深圳大学 | A kind of refractive index micrometering system |
| CN109239915A (en) * | 2018-09-29 | 2019-01-18 | 南京理工大学 | A method of it generating hamburger pouch-type and focuses light field |
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| CN110955054A (en) * | 2019-11-26 | 2020-04-03 | 中国科学院光电技术研究所 | Method for generating nano-optical needle based on angular polarized light |
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| CN114236817A (en) * | 2021-12-23 | 2022-03-25 | 中国科学院物理研究所 | Design method of multi-focus super surface based on vortex beam orbital angular momentum |
| CN114624895A (en) * | 2022-02-21 | 2022-06-14 | 苏州大学 | System and method for generating partial coherence vector power exponent vortex light beam |
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