CN105607275B - Generate the method and device of radial polarisation cosine gaussian schell model light beam - Google Patents
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- 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 present invention relates to a kind of method and devices for generating radial polarisation cosine gaussian schell model light beam, and method includes: to expand to laser, and the associate feature of light beam is modulated by spatial light modulator, obtains the light beam with cosine Gauss associate feature；Spatial polarization regulation is carried out to light beam, obtains radial polarized light beam；The space correlation characteristic for reducing radial polarized light beam obtains noncoherent cosine Gauss and is associated with light beam；Noncoherent cosine Gauss is associated with the cosine Gauss that light beam obtains linear polarization through lens focus after the filtering of G amplitude filter plate and is associated with Gaussian beam；The cosine Gauss of linear polarization is associated with Gaussian beam and obtains radial polarisation cosine gaussian schell model light beam by radial polarisation photoconverter.The invention proposes a kind of production method of novel light beam, by further push special coherence beam transmission, imaging and in terms of research, expand light beam type.
Description
Technical field
The present invention relates to polarization cosine gaussian schell model light beam, especially a kind of generation radial polarisation cosine gaussian schell models
The method and device of light beam.
Background technique
In the application of optics and laser, coherence and polarizability are two key properties of laser beam.Previous people
Polarization characteristic and coherence to laser beam are mostly individually to study, and in recent years, partially coherent vector beam causes people
Extensive attention.Vector beam is also referred to as electromagnetic beam, and for scalar light beam, electromagnetic beam can describe more multiple light courcess letter
Breath.
Since radial polarized light beam has special polarization properties, relative to even polarization light field, partially such as linear polarization, ellipse
Vibration, circular polarization, radial polarisation polarization state distribution be it is heterogeneous, electric field oscillation have perfect rotational symmetry characteristic, and
Light field center intensity is zero, has received widespread attention it.It is theoretical and experimental studies have found that, radial polarized light beam is compared to generally
Even light beam has some new features, and such as the minimum light spot area of " tightly focused " radial polarized light beam is up to 0.16 λ2, than same
Under the conditions of linearly polarized light it is small by nearly 50%.In addition, also can get very strong long-range salt free ligands axial electric field component and be easier
Excitating surface plasmon etc..The production method of radial polarized light beam can be divided mainly into outside intracavitary generation and chamber and generate two
Kind: intracavitary production method is by learning element in intracavitary placement, such as conscope, birefringence element and liquid crystal polarized selector
Deng, selected by these elements or change light beam polarization state generate radial polarized light beam.Rule is generated outside chamber mainly to pass through
Mode-interference superposition utilizes some particular polarization mode conversion elements, such as radial polarizer, LCD space light modulator, phase
Delay element, polarizationselective light fibre and sub-wave length grating etc. obtain radial polarized light beam.
Coherent optical theory has obtained sufficient research, but only a few correlation function between in the past few decades
It is suggested, for describing the coherence of light beam, such as Xie Ermo association, Bezier association, Laguerre association.Table is studied in recent years
It is bright, it, can be by the associate feature of design regulation light beam come Effective Regulation beche-de-mer without spike under the conditions of meeting the authenticity of beam configuration
Number characteristic.2011, Lajuen et al. proposed non-homogeneous associated light beam, its degree of coherence distribution is related with spatial position,
Research shows that Self-focusing can occurs in it；2012, Sahin et al., which was proposed, to generate the part phase of flat-top light intensity in far field
Dry light beam；It 2013, can be ground in the particular associative partially coherent light beam that far field generates hollow light spot from theoretical and experimental
Study carefully.Research constructs the laser beam with coherence's non-uniform Distribution, and furtheing investigate, there is the light beam of special coherence distribution to exist
Transmission is imaged and has become a big research hotspot with the new mechanism and new phenomenon of matter interaction etc..
However, the correlation that not yet discovery generates radial polarisation cosine gaussian schell model beam method in existing literature is recorded.
Summary of the invention
The purpose of the present invention is to provide a kind of method and devices for generating radial polarisation cosine gaussian schell model light beam.
Realize the technical solution of the object of the invention are as follows: a method of radial polarisation cosine gaussian schell model light beam is generated,
The following steps are included:
Step 1 expands laser, and the associate feature of light beam is modulated by spatial light modulator, is obtained with cosine
The light beam of Gauss associate feature；
Step 2 carries out spatial polarization regulation to the light beam that step 1 obtains, and obtains radial polarized light beam；
Step 3, the space correlation characteristic for reducing radial polarized light beam obtain noncoherent cosine Gauss and are associated with light beam；
Step 4, noncoherent cosine Gauss are associated with light beam and obtain line after lens focus and the filtering of G amplitude filter plate
The cosine Gauss of polarization is associated with Gaussian beam；
Step 5, the cosine Gauss of linear polarization are associated with Gaussian beam and are obtained more than radial polarisation by radial polarisation photoconverter
String gaussian schell model light beam.
A kind of device generating radial polarisation cosine gaussian schell model light beam, including laser generator, beam expander, reflection
Mirror, spatial light modulator, computer, circular aperture, linear polarizer, frosted glass plate, thin lens, G amplitude filter plate and radial direction
Polarization converter；
The laser that the laser generator generates is expanded by beam expander, passes through space light modulation after reflecting mirror
Device is modulated, and the spatial light modulator is connect with computer, and computer obtains plane wave and cosine Gauss wave interference
Raster holographic pattern is loaded into spatial light modulator；Modulated light beam selects First order diffraction pattern through circular aperture, obtains
Cosine Gauss is associated with light beam；Cosine Gauss, which is associated with light beam, reduces the space of laser beam by linear polarizer and the frosted glass plate of rotation
Coherence obtains noncoherent cosine Gauss and is associated with linearly polarized light beam；Noncoherent cosine Gauss is associated with linearly polarized light beam through thin
The cosine association Gaussian beam that linear polarization is obtained after lens, G amplitude filter plate, finally by radial polarisation converter to line
The polarization state of the cosine association Gaussian beam of polarization is modulated, and obtains the cosine gaussian schell model light beam with radial polarisation.
Compared with prior art, remarkable result of the invention are as follows: it is high that the invention proposes a kind of generation radial polarisation cosine
The method of Si Xieermo light beam, it is determined that the selection condition of light beam optical parameter can be changed by the manipulation to spatial light modulator
Become the cosine order n of this light beam, focus characteristics of the light beam of different rank coherence distribution in transmission process are different, formed
Various spot shapes generate the novel phenomenon such as beam splitting, theoretical consistent with experimental result.
Detailed description of the invention
Fig. 1 is a kind of generation provided by the invention and the device signal of measurement radial polarisation cosine gaussian schell model light beam
Figure.
Fig. 2 (a), Fig. 2 (b) and Fig. 2 (c) are theoretical modeling radial polarisation cosine gaussian schell model light beam different rank n=
0,1,2 normalized intensity distribution and one-dimensional section profile line schematic diagram.
Fig. 3 (a), Fig. 3 (b), Fig. 3 (c) and Fig. 3 (d) are respectively theoretical modeling radial polarisation cosine gaussian schell model light beam
In Yuan ChangDegree of coherence distribution profile figure.
Fig. 4 (a) is the one-dimensional normalized intensity distribution map of light beam source field experiment measurement, Fig. 4 (b), Fig. 4 (c), Fig. 4 (d) point
It Wei not total light intensity two-dimensional silhouette figure, x-polarisation direction intensity two-dimensional silhouette figure, y-polarisation direction intensity two-dimensional silhouette figure.
Fig. 5 (a) is the one-dimensional degree of coherence distribution map of light beam source field experiment measurement, and Fig. 5 (b), Fig. 5 (c), Fig. 5 (d) are respectivelyTwo-dimensional silhouette figure.
Specific embodiment
In conjunction with Fig. 1, a kind of method of generation radial polarisation cosine gaussian schell model light beam of the invention, including following step
It is rapid:
Step 1 expands laser, and the associate feature of light beam is modulated by spatial light modulator, is obtained with cosine
The light beam of Gauss associate feature；
Step 2 carries out spatial polarization regulation to the light beam that step 1 obtains, and obtains radial polarized light beam；
Step 3, the space correlation characteristic for reducing radial polarized light beam obtain noncoherent cosine Gauss and are associated with light beam；
Step 4, noncoherent cosine Gauss are associated with light beam and obtain line after lens focus and the filtering of G amplitude filter plate
The cosine Gauss of polarization is associated with Gaussian beam；
Step 5, the cosine Gauss of linear polarization are associated with Gaussian beam and are obtained more than radial polarisation by radial polarisation photoconverter
String gaussian schell model light beam.
2 × 2 rank cross-spectral density matrix of radial polarisation cosine gaussian schell model light beamMatrix element be expressed asSource associate feature is expressed as
r1=(x1,y1) and r2=(x2,y2) it is source position vector；w0For source waist width；σgFor the relevant length in source
Degree；It is light field position vector, AxAnd AyIt is the amplitude of light field electric field component in the x and y direction, δ respectivelyxxAnd δyyIt is x points respectively
The coherent width of amount and y-component auto-correlation function, δxy=δyxIt is electric field x-component and the mutual coherent width of y-component, Bxx=Byy=1,For light field x-component and y-component multiple association coefficient, φxyBetween electric field x-component and y-component
Phase difference, qαβFor the degree of coherence of each matrix element, n is positive real number.
In conjunction with Fig. 1, a kind of device generating radial polarisation cosine gaussian schell model light beam, including laser generator 1, expansion
Beam device 2, reflecting mirror 3, spatial light modulator 4, computer 13, circular aperture 5, linear polarizer 6, frosted glass plate 7, thin lens L1、
G amplitude filter plate 8 and radial polarisation converter 9；
The laser that the laser generator 1 generates is expanded by beam expander 2, passes through spatial light after reflecting mirror 3
Modulator 4 is modulated, and the spatial light modulator 4 is connect with computer 13, and computer 13 is by plane wave and cosine high bass wave
Obtained raster holographic pattern is interfered to be loaded into spatial light modulator；Modulated light beam selects single order through circular aperture 5 and spreads out
Pattern is penetrated, cosine Gauss is obtained and is associated with light beam；Cosine Gauss is associated with light beam and is dropped by linear polarizer 6 and the frosted glass plate 7 of rotation
The spatial coherence of low laser beam obtains noncoherent cosine Gauss and is associated with linearly polarized light beam, wherein light beam is by frosted glass
Spot diameter be much larger than frosted glass plate coarse scale；Noncoherent cosine Gauss is associated with linearly polarized light beam through thin lens L1、
The cosine association Gaussian beam that linear polarization is obtained after G amplitude filter plate 8, finally by radial polarisation converter 9 to linear polarization
Cosine association Gaussian beam polarization state be modulated, obtain the cosine gaussian schell model light beam with radial polarisation.
As shown in figure 1 shown in right side of dotted line part, device further includes beam splitter 10, the first lens L2, the second lens L3, light beam
Analyzer 11 and CCD12, wherein CCD is charge coupled cell, and the cosine gaussian schell model light beam of radial polarisation passes through beam splitter
10 carry out 50:50 beam splitting, are divided into equal strength light, and light beam is f by focal length2Lens L2Focusing, pass through light beam in focal point
Analyzer 11 obtains the intensity distribution of radial polarisation cosine gaussian schell model light beam；Another light beam passes sequentially through the second lens L3With
CCD12, wherein the second lens L3Distance with CCD12 is the second lens L3Twice of focal length, CCD12 are fixed on a certain of light beam
Signal and ccd signal, which are done, at point, on laser beam analyzer 11 meets calculating, obtains the relating value of two-way light, relating value is intended
It closes, the associate feature for obtaining light beam certain point and light field is distributed.
Further, the laser generator 1 is He-Ne laser.
The present invention is described further with reference to the accompanying drawings and embodiments.
Embodiment
Partially coherent partial polarization general theory will be based in the present embodiment, 2 × 2 rank cross spectrums of random electromagnetic light beam are close
Spend matrixMatrix may be expressed as:
ExAnd EyRespectively indicate electric field component on the direction x and y.
The general expression of the cross spectrum density matrix array element of radial polarisation cosine gaussian schell model light beam may be expressed as:
Source correlation function is expressed as
Wherein r1=(x1,y1) and r2=(x2,y2) it is source position vector；w0For source waist width；σgFor the relevant length in source
Degree；AxAnd AyIt is the amplitude of light field electric field component in the x and y direction, δ respectivelyxxAnd δyyIt is x-component and y-component auto-correlation function respectively
Coherent width, δxy=δyxIt is electric field x-component and the mutual coherent width of y-component, Bxx=Byy=1,
It is light field x-component and y-component multiple association coefficient, φxyIt is the phase difference between electric field x-component and y-component, qαβIt characterizes each
The degree of coherence of matrix element, n is positive real number, and as n=0, beam dogradation is common radial polarisation Xie Ermo beam models.
To determine that the achievable optical parameter of model foundation, above-mentioned beam models need to meet following three conditions:
Condition 1, the realization condition of electromagnetic beam with cosine Gauss correlation function；
Condition 2, the cosine Gauss that polarization characteristic is radial polarisation are associated with the realization condition of light beam；
Condition 3, the far field beams condition for meeting cosine association radial polarized light beam.
To meet condition 1 in the present embodiment, the realization condition of the electromagnetic beam with cosine Gauss correlation function, by formula
(2) it is written as
QxxAnd QyyFor the diagonal entry of cross spectrum density matrix, it is scalar auto-correlation function, can be obtained by formula (4)
Be to diagonal matrix member it is non-negative, that is, be only required to be off diagonal element and meet condition.For general electromagnetic beam
For, it is only necessary to meet nonnegativity condition:
The meaning of ξ is spatial frequency domain coordinate,WithFor the arbitrary function about point ξ, * representative function
Complex conjugate, α, β are corresponding with cross spectrum density matrix element；
For qαβ(r1-r2) Fourier transformation, and since cross spectrum density matrix is Hermitian conjugate, this hasCondition should be met by bringing (5) formula into and obtaining optical parameter:
Consideration is obtained into the polarization properties of array beams in the present embodiment, the polarization state at any point can use polarization in light field
Ellipse describes, and is based on partially coherent partial polarization general theory, by cross spectrum density matrix can be inclined with light field any point
Shake elliptical three important parameters, and oval deflection may be expressed as:
The long axis and short axle of polarization ellipse can be indicated by cross spectrum density matrix are as follows:
To meet condition 2, polarization characteristic is that the cosine Gauss of radial polarisation is associated with the realization condition of light beam, needs to meet light
Field any point is linear polarization, and the polarization ellipse deflection of light field is radially distributed:
ε is meant that the ellipticity of polarization ellipse, range are 0≤ε≤1, takes 0 as line, takes 1 as circle, other values indicate
It is oval；
In conjunction with (7), (8), (9) formula obtains optical parameter to meet condition:
Bxy=Byx=1 (10)
It is further obtained according to condition (6):
δxx=δxy=δyx=δyy=δ0 (11)
Need to guarantee that the radial polarisation cosine gaussian schell model light beam generated meets beam condition in far field in the present embodiment.
In free space at far field a bit(ρ is distance of the light source to light field,For unit direction vector at far field) spectrum it is close
Spend function expression:
WhereinFor the four-dimensional welfare leaf transformation in source,Indicate two dimension
Spatial frequency vector,Indicate unit trivectorThe two-dimentional unit vector projected in the plane of source,Indicate beDirection
Angle, i.e., by source plane origin be directed toward far field point of observation ρ direction and source plane normal angle.By formula
(2) it brings formula (7) into and obtains the spectral density function in source:
Wherein parameter replacement has
In order to meet condition 3, far-field intensity distribution is that can ignore in the range other than in the narrow angle about the direction z
Disregard, i.e. the initial parameter of light beam needs to meet condition:
Assuming that the consistent A of the source amplitude of x with y electric field componentx=Ay=1, then it finally obtains more than the source for meeting above-mentioned condition
String is associated with 2 × 2 rank cross-spectral density matrix of radial polarized light beamMatrix element be represented by
Source relevance is expressed as
As shown in Figure 1, left-half is the generation device that cosine Gauss is associated with radial polarisation light, He-Ne laser 1 is generated
Beam of laser first passes through beam expander 2 and expands to it, is modulated by spatial light modulator 4 to it after reflecting mirror 3,
The raster holographic pattern that plane wave and cosine Gauss wave interference obtain is loaded into spatial light modulator, space by computer 13
Optical modulator plays the role of phase grating, selects First order diffraction pattern by circular aperture 5 later, obtains cosine Gauss pass
Join light beam.The spatial coherence of laser beam is reduced by linear polarizer 6 and the frosted glass plate 7 of rotation later, we set light
Beam is much larger than the coarse scale of frosted glass plate by the spot diameter on frosted glass, and it is inclined to obtain noncoherent cosine Gauss association line
Shake light beam.Beam Propagation f later1Distance reaches thin lens L1Height is associated with the cosine for obtaining linear polarization after G amplitude filter plate 8
This light beam is most modulated afterwards through polarization state of the radial polarisation converter 9 to light beam, finally obtains the cosine with radial polarisation
Gaussian schell model light beam.
Above-mentioned spatial light modulator is LCD space light modulator, and LCD space light modulator is a kind of programmable photoelectricity
Type diffraction optical element, LCD space light modulator are modulated laser beam, substantially inclined using the optically-active of liquid crystal molecule
Vibration property and birefringence.Liquid crystal molecule direction can change under the action of external electric field, and knots modification size has with applied voltage
It closes.Molecular orientation changes the refractive index for directly affecting liquid crystal material, realizes to light wave modulation.It can real-time control using computer
Different pixels applied voltage size can dynamically realize that required output intensity is distributed with it.
Fig. 1 right half part is the experiment schematic diagram for measuring radial polarisation cosine gaussian schell model light beam, the light that source generates
Beam carries out 50:50 beam splitting by beam splitter 10, is divided into equal strength light by beam splitter, light beam is f by focal length2Lens L2's
It focuses, obtains the intensity distribution of radial polarisation cosine gaussian schell model light beam, another light beam in focal point laser beam analyzer 11
For the instrumentation plan of degree of coherence.
The specific measurement method of degree of coherence are as follows: the optical path of above-mentioned measurement light intensity is changed to it is consistent with another beam optical path, i.e., two
Optical path tested surface and lens L3Distance and lens between CCD at a distance from be 2f3.It, will when measuring degree of coherence distribution
CCD is fixed at the certain point of light beam, and signal and ccd signal, which are done, on laser beam analyzer meets calculating, obtains the association of two-way light
Value, relating value is fitted, and the associate feature that can obtain light beam certain point and light field is distributed.
Fig. 2 is normalized intensity point of the numerical simulation radial polarisation cosine gaussian schell model light beam in source different rank n
Butut and one-dimensional section profile line schematic diagram, vertical and horizontal coordinate respectively indicate the transverse and longitudinal coordinate of light field under cartesian coordinate system, weighing apparatus
The size of light field is measured, the intensity distribution in its source is unrelated with the coherence of light beam as the result is shown, meets the basic of partially coherent light
Theory, parameter are chosen for λ=632.8nm, w0=1mm, δxx=δyy=δxy=δyx=δ0=0.6mm.
By formula (17) and (18), general theory is polarized according to partially coherent, it is relevant using the vector beam of Tervo et al.
Degree definition
Wherein Tr is the mark of matrix, i.e., the sum of moral element on matrix leading diagonal；
Fig. 3 is degree of coherence distribution map and one of the numerical simulation single order radial polarisation cosine gaussian schell model light beam in source
Section profile line schematic diagram is tieed up,Indicate the related chi square function between each electric field component, transverse and longitudinal coordinate in Fig. 3
Indicate light field coherence length under cartesian coordinate system, abscissa indicates the coherence length of light field x-axis direction, and ordinate indicates light field
The coherence length in the direction y, Fig. 3 (b), Fig. 3 (c), Fig. 3 (d) are point of the light field coherence length in electric field oscillation direction xx, xy, yy
Amount.As seen from the figure, the array distribution of matrix symmetric is obeyed in degree of coherence distribution, and with the increase of distance, it is high that cosine is presented in coherence
This distribution.
It by focal length is f that Fig. 4, which is the light beam that generates of source,2Lens L2Focusing, it is direct in focal point laser beam analyzer
The intensity distribution of radial polarisation cosine gaussian schell model light beam is obtained, and obtains to obtain the electric field side x and y with polarizing film limit is to the rear
To intensity distribution, testing beam waist that the data measured are fitted is w0=0.96mm, is consistent with Fig. 2, reason
By almost the same with experimental result.
Fig. 5 is the degree of coherence distribution map for measuring single order radial polarisation cosine gaussian schell model light beam, and Fig. 5 (a) fixes CCD
In (the x of light beam2=0.2mm, y2=0.2mm) at point, with another point (x1,y1=0mm) coincidence measurement is done, obtain two-way light
Relating value is fitted by relating value, and obtained coherence length is δ0Cosine Gauss is obeyed in=0.12mm, one-dimensional degree of coherence distribution
Type distribution.The distribution profile and Fig. 3 of the measurement display degree of coherence of Fig. 5 (b)-Fig. 5 (d) are almost the same, in summary the present embodiment
Produce radial polarisation cosine gaussian schell model light beam.
Claims (4)
1. a kind of device for generating radial polarisation cosine gaussian schell model light beam, which is characterized in that including laser generator
(1), beam expander (2), reflecting mirror (3), spatial light modulator (4), computer (13), circular aperture (5), linear polarizer (6), hair
Sheet glass (7), thin lens (L1), G amplitude filter plate (8) and radial polarisation converter (9)；
The laser that the laser generator (1) generates is expanded by beam expander (2), passes through space after reflecting mirror (3)
Optical modulator (4) is modulated, and the spatial light modulator (4) connect with computer (13), computer (13) by plane wave with
The raster holographic pattern that cosine Gauss wave interference obtains is loaded into spatial light modulator (4)；After spatial light modulator (4) modulation
Light beam select First order diffraction pattern through circular aperture (5), obtain cosine Gauss be associated with light beam；It is logical that cosine Gauss is associated with light beam
The spatial coherence for crossing frosted glass plate (7) the reduction laser beam of linear polarizer (6) and rotation, obtains noncoherent cosine Gauss and closes
On line light beam；Noncoherent cosine Gauss is associated with linearly polarized light beam through thin lens (L1), after G amplitude filter plate (8)
Cosine to linear polarization is associated with Gaussian beam, is associated with Gauss light finally by cosine of the radial polarisation converter (9) to linear polarization
The polarization state of beam is modulated, and obtains the cosine gaussian schell model light beam with radial polarisation.
2. the device according to claim 1 for generating radial polarisation cosine gaussian schell model light beam, which is characterized in that device
It further include beam splitter (10), the first lens (L2), the second lens (L3), laser beam analyzer (11) and CCD (12), radial polarisation
Cosine gaussian schell model light beam carries out 50:50 beam splitting by beam splitter (10), is divided into equal strength light, and light beam is f by focal length2
Lens (L2) focusing, obtain the strong of radial polarisation cosine gaussian schell model light beam by laser beam analyzer (11) in focal point
Degree distribution；Another light beam passes sequentially through the second lens (L3) and CCD (12), wherein the second lens (L3) and the distance of CCD (12) be
Second lens (L3) twice of focal length, CCD (12) is fixed at the certain point of light beam, signal and CCD on laser beam analyzer (11)
Signal does coincidence counting, obtains the relating value of two-way light, relating value is fitted, and obtains being associated with for light beam certain point and light field
Characteristic distribution.
3. the device according to claim 1 for generating radial polarisation cosine gaussian schell model light beam, which is characterized in that light beam
It is greater than the coarse scale of frosted glass plate by the spot diameter on frosted glass.
4. the device according to claim 1 for generating radial polarisation cosine gaussian schell model light beam, which is characterized in that described
Laser generator (1) is He-Ne laser.
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