CN103063162A - Method of measuring radius of partial coherent gauss beam wavefront phase - Google Patents

Method of measuring radius of partial coherent gauss beam wavefront phase Download PDF

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CN103063162A
CN103063162A CN201310010442XA CN201310010442A CN103063162A CN 103063162 A CN103063162 A CN 103063162A CN 201310010442X A CN201310010442X A CN 201310010442XA CN 201310010442 A CN201310010442 A CN 201310010442A CN 103063162 A CN103063162 A CN 103063162A
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light beam
width
wave
radius
front phase
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CN103063162B (en
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朱时军
刘琳
陈亚红
蔡阳健
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Suzhou University
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Abstract

The present invention relates to a kind of method for measuring partially coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss associate feature. Light beam to be measured is generated into spheric wave front phase after thin lens focuses, the initial lateral coherent width of light beam is obtained using correlator systematic survey
Figure 201310010442X100004DEST_PATH_IMAGE002
, measured respectively using laser beam analyzer and obtain the initial lateral waist width of light beam With the lateral waist width on exit facet , it is computed processing and obtains Beam Wave-Front phase radius to be measured. The typical partially coherent light beam of measurement provided by the present invention, possess broad application prospect in fields such as free optical communication, biologic medical, nonlinear dielectric, inertial confinement fusions, the measurement method of provided partially coherent Gaussian beam Wave-front phase radius is not needed using expensive Hartmann Wavefront Sensing sensor, measuring condition is simple, as a result reliable, it is low in cost.

Description

A kind of method of measure portion coherent Gaussian beam Wave-front phase radius
Technical field
The present invention relates to a kind of method of measure portion coherent Gaussian beam Wave-front phase radius, be a kind of with the linearly polarized laser bundle with frosted glass plate regulate and control the coherence, with the filtering of G amplitude filter plate, the method for measuring optical field distribution and obtaining the Wave-front phase radius with correlator systematic survey light field coherent width with laser beam analyzer.
Background technology
In recent years, the partial coherence light beam has caused very large concern because it has wide application prospect in fields such as inertial confinement fusion, optical imagery, optical engineering, material heat treatment, nonlinear optics, light scattering, optical communication, remote remote sensing, laser radar, laser scanning and laser captures.Gauss Xie Ermo light beam [E. Wolf and E. Collett, " Partially coherent sources which produce same far-field intensity distribution as a laser; " Opt. Commun. 25,293-296 (1978)] as typical partial coherence light beam, its optical field distribution and light field degree of coherence are Gaussian distribution.The general transmission problem of processing Gauss Xie Ermo light beam with the Wigner distribution function of tradition; Woods and Cai [Q. Lin and Y. Cai, " Tensor ABCDLaw for partially coherent twisted anisotropic Gaussian-Schell model beams; " Opt. Lett. 27,216-218 (2002)] propose to process with Tensor Method the paraxonic transmission problem of Gauss Xie Ermo light beam.
The double velocity correlation characteristic of partial coherence light beam can characterize with cross-spectral density function.For isotropy, do not twist the partial coherence Gauss Xie Ermo light beam of phase place, cross-spectral density can with can be wide by beam waist, lateral coherence width and three parameters of wavefront curvature radius determine.Partial coherence Gauss Xie Ermo light beam is widely applied in fields such as free optical communication, biologic medical, laserresonator, positive and negative refraction rate medium, nonlinear medium, inertial confinement fusion, complicated optical systems.Research find partial coherence Gauss Xie Ermo light beam degree of coherence and spectrum can be with the characteristic of transmission medium different changing, at free optical communication, there is potential using value the aspects such as medical treatment and information transmission processing.
The with a tight waist wide and coherent width of experiment measuring partial coherence light beam has report, but as the important Beam parameters Wave-front phase radius of the another one of partial coherence Gauss Xie Ermo light beam, its measuring method and device but have no report always, many a kind of methods of usefulness are that Hartmann wave front sensor (SHWS) is measured at present, but this method depends on the measurement equipment of complexity, costliness, and measurement expense is high.
Summary of the invention
The object of the invention is to overcome the deficiency that prior art exists, provide a kind of measuring condition simple, reliable results, the measuring method of partially coherent Gaussian beam Wave-front phase radius with low cost.
Realize that the technical scheme of the object of the invention provides a kind of method of measure portion coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss's associate feature, measuring method comprises the steps: light beam to be measured is produced the spherical wave front phase place after thin lens focuses on, and adopts the correlator systematic survey to obtain the initial horizontal of light beam to coherent width , adopt laser beam analyzer to measure respectively the initial horizontal of light beam to waist width With the horizontal waist width on the exit facet
Figure 201310010442X100002DEST_PATH_IMAGE003
, by formula
Figure 712242DEST_PATH_IMAGE004
Obtain the wavefront curvature radius of light beam R
Wherein, kBe wave number, A, B, C and D are the astigmatic system transmission matrix; R 0 Be radius-of-curvature before the primary wave, by formula
Figure 201310010442X100002DEST_PATH_IMAGE005
Obtain, wherein,
Figure 39449DEST_PATH_IMAGE006
The present invention adopts the lateral coherence width of correlator systematic survey light beam, places successively imaging len, beam splitter and correlator system behind the light beam being tested surface, adopts 2 fFormation method carries out association to be surveyed, and the relating value of two-way is carried out Gauss curve fitting, obtains the lateral coherence width of light beam, fFocal length for imaging len.
Measuring method provided by the present invention can be utilized the device of following measure portion coherent Gaussian beam Wave-front phase radius, and this device comprises:
Laser instrument produces a branch of random polarization light beam, obtains a branch of linearly polarized laser bundle through the inclined to one side device of line, successively through focusing on the focusing surface behind a catoptron and the thin lens, produces a branch of partial coherence linear polarized beam with Gaussian statistics association again;
Behind described partial coherence linear polarized beam process collimation lens and G amplitude filter plate, obtain the partially coherent Gaussian beam that a branch of collimation has Gauss's association, it is infinitely great that its wavefront curvature radius is approximately;
After assembling through a condenser lens, have the spherical wave front phase place, spherical wave front phase place radius is measuring object of the present invention again; Connect computing machine with laser beam analyzer and at the difference of light path the partially coherent Gaussian beam light field that produces is measured, measurement result is carried out Gauss curve fitting, obtain the waist width of light beam transversal;
Place successively imaging len, beam splitter and correlator system behind the Gaussian beam being tested surface, the correlator system is connected with computing machine, adopts 2 fFormation method carries out association to the light path difference to be surveyed, and namely being tested surface is placed on imaging len front 2 fThe place, being tested surface will be imaged onto 2 of lens back fThe place, during measurement, a probe D of fixed correlation detector system 2On optical axis, another D that pops one's head in 1In another curb transversal scanning, the relating value of two-way is carried out Gauss curve fitting, obtain the lateral coherence width of light beam;
The present invention is by measuring beam waist width and the incipient beam of light coherent width on the plane of incidence and transmitting a segment distance zAfter the beam waist width, in conjunction with the transmission matrix of optical system
Figure 201310010442X100002DEST_PATH_IMAGE007
,
Figure 450970DEST_PATH_IMAGE008
, fBe the focal length of condenser lens, after machine is processed as calculated, just can obtain the Wave-front phase radius of partially coherent Gaussian beam.
Described laser instrument produces the linearly polarized laser bundle through linear polarizer.
Described focusing surface is a kind of in frosted glass plate, scatterer element or the electro-optic crystal element.
The principle of a kind of partially coherent Gaussian beam Wave-front phase radius measurement method provided by the invention is:
Laser instrument produces a branch of random polarization light beam, produce a branch of linearly polarized laser bundle through the inclined to one side device of line, through focusing on frosted glass plate, scatterer element or the electro-optic crystal element behind a catoptron and a collimation lens, produce a branch of partial coherence linear polarized beam with Gaussian statistics association again; Its association can be expressed as the form of following formula (1):
Figure 201310010442X100002DEST_PATH_IMAGE009
In the formula, Be the light field position vector,
Figure 963171DEST_PATH_IMAGE001
Be the light beam transversal coherent width.
The partial coherence light beam that produces through a thin lens and G amplitude filter plate after, obtain the partially coherent Gaussian beam that a branch of collimation has Gauss's associate feature, it is infinitely great that the wavefront curvature radius of this light beam is approximately.This moment, light beam can characterize with following formula (2):
Figure 201310010442X100002DEST_PATH_IMAGE011
In the formula,
Figure 727076DEST_PATH_IMAGE002
Be the light beam transversal waist width.
The partially coherent Gaussian beam that produces focuses on through another condenser lens 8 again, and the partially coherent Gaussian beam after the focusing has the spherical wave front phase place, spherical wave front phase place radius
Figure 552075DEST_PATH_IMAGE012
Be the object that this patent will be measured, the light field cross-spectral density function can be expressed as the form of following formula (3):
Figure 201310010442X100002DEST_PATH_IMAGE013
The present embodiment is got the G amplitude filter plate from the distance of condenser lens Centimetre, the being tested surface after the focusing from the thin lens distance is l(need not know).Formula (3) can be expressed as the tensor form of following formula (4):
Figure DEST_PATH_IMAGE015
In the formula,
Figure 715782DEST_PATH_IMAGE016
,
Figure DEST_PATH_IMAGE017
It is plane of incidence light field coordinate vector;
Figure 486423DEST_PATH_IMAGE018
Wave number,
Figure DEST_PATH_IMAGE019
Be wavelength;
Figure 708588DEST_PATH_IMAGE020
For
Figure DEST_PATH_IMAGE021
The relevant complex curvature tensor matrix of exponent part is formula (5):
Figure 248285DEST_PATH_IMAGE022
I is in the formula
Figure DEST_PATH_IMAGE023
The rank unit matrix.
After the transmission of astigmatism ABCD optical system, the cross-spectral density function of partial coherence Gauss Xie Ermo light beam can be expressed as following formula (6) form:
Figure 163283DEST_PATH_IMAGE024
The value of Det representing matrix determinant in the formula;
Figure DEST_PATH_IMAGE025
,
Figure 409501DEST_PATH_IMAGE026
Figure DEST_PATH_IMAGE027
Be respectively the arbitrary coordinate vector on the exit facet.
Figure 169778DEST_PATH_IMAGE028
Be the partial coherence complex curvature tensor on the exit facet, following tensor A BCD formula (7) arranged:
Figure DEST_PATH_IMAGE029
In the formula
Figure 829560DEST_PATH_IMAGE030
With
Figure DEST_PATH_IMAGE031
The form that following formula (8) are arranged:
Figure 649880DEST_PATH_IMAGE032
Figure DEST_PATH_IMAGE033
With Be the astigmatic system transmission matrix.
The form of formula (9) below partial coherence complex curvature tensor matrix on exit facet can also be expressed as:
Figure DEST_PATH_IMAGE035
In the formula ,
Figure 847271DEST_PATH_IMAGE036
,
Figure DEST_PATH_IMAGE037
Represent respectively the horizontal waist width on the exit facet, lateral coherence width and radius-of-curvature.Can be obtained by formula (7):
Convolution (5), (7) and (9) can obtain respectively the relational expression of following formula (11), (12) and (13):
Figure DEST_PATH_IMAGE039
Figure 71022DEST_PATH_IMAGE040
In the formula:
Figure 450399DEST_PATH_IMAGE042
Convolution (11)～(14), the wavefront curvature radius that can obtain incipient beam of light is expressed as formula (15):
Figure DEST_PATH_IMAGE043
From following formula, can obtain: choose a primary face and an exit facet; The Wave-front phase radius of initial Gaussian light beam can be by measuring the horizontal waist width on the exit facet, and horizontal waist width and lateral coherence width on the primary face obtain.Formula (15) is two values, which is right? can be checked by following mode: if measured ,
Figure 325524DEST_PATH_IMAGE001
With
Figure 888093DEST_PATH_IMAGE044
, substitution formula (15) can obtain two wavefront curvature values; To obtain again
Figure 934808DEST_PATH_IMAGE002
,
Figure 220427DEST_PATH_IMAGE001
With two Value substitution formula (11) just can obtain two lateral coherence width values on the exit facet, and what one of them was identical or close with measured value just is effective value, the wavefront curvature radius value that this moment is corresponding
Figure 744261DEST_PATH_IMAGE012
Be effective value.
Compared with prior art, the invention has the beneficial effects as follows: focus on the spot size that rotates on the frosted glass plate by thin lens, can regulate and control the coherence of generating portion coherent light beam, the spot size of light beam can be controlled by the G amplitude filter plate; This method does not need to use expensive Hartmann Wavefront Sensing sensor, just can obtain the wavefront curvature radius of partial coherence light beam, and measuring condition is simple, reliable results, and also cost is low.Partially coherent Gaussian beam particularly as typical partial coherence light beam, has widely application prospect in fields such as free optical communication, biologic medical, nonlinear medium, inertial confinement fusions.
Description of drawings
Fig. 1 is the structural representation of a kind of partially coherent Gaussian beam waist width measurement mechanism of providing of the embodiment of the invention;
Fig. 2 is the structural representation of a kind of partially coherent Gaussian beam coherent width measurement mechanism of providing of the embodiment of the invention;
Fig. 3 is a kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the embodiment of the invention to provide, and records incipient beam of light optical field distribution and Gauss curve fitting figure with a tight waist;
Fig. 4 is a kind of partially coherent Gaussian beam coherent width measurement mechanism that adopts the embodiment of the invention to provide, and records incipient beam of light lateral coherence width fitted figure;
Fig. 5 is a kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the embodiment of the invention to provide, and records light beam in transmission Centimetre the time optical field distribution figure;
Fig. 6 is a kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the embodiment of the invention to provide, and records light beam in transmission
Figure 984880DEST_PATH_IMAGE046
Millimeter,
Figure DEST_PATH_IMAGE047
Millimeter,
Figure 531531DEST_PATH_IMAGE048
Millimeter,
Figure DEST_PATH_IMAGE049
The optical field distribution figure at millimeter place;
Among the figure: 1, laser instrument; 2, the inclined to one side device of line; 3, catoptron; 4, thin lens; 5, frosted glass plate; 6, collimation lens; 7, G amplitude filter plate; 8, condenser lens; 9, laser beam analyzer; 10, computing machine; 11, imaging len; 12, beam splitter; 13, correlator system.
Embodiment
Below in conjunction with drawings and Examples technical solution of the present invention is further described.
Embodiment 1
Referring to accompanying drawing 1, it is the structural representation of a kind of partially coherent Gaussian beam waist width measurement mechanism of providing of the present embodiment; Laser instrument 1 produces a branch of random polarization light beam, produces a branch of linearly polarized laser bundle through the inclined to one side device 2 of line, through focusing on the frosted glass plate 5 behind a catoptron 3 and the thin lens 4, produces the partial coherence linear polarized beam with Gaussian statistics association again; Behind the partial coherence light beam process collimation lens 6 and G amplitude filter plate 7 that produces, obtain the partially coherent Gaussian beam of a branch of collimation, it is infinitely great that the wavefront curvature radius of this light beam is approximately.The partial coherence Gauss Xie Ermo light beam that produces is 25 centimetres condenser lens 8 focusing through a focal length, and the partially coherent Gaussian beam after the gathering has the spherical wave front phase place, and the radius of spherical wave front phase place is the parameter that this patent will be measured.Described G amplitude filter plate from condenser lens 8 distances is f, the being tested surface after the focusing from condenser lens 8 is lConnect computing machine 10 with laser beam analyzer 9 and at the difference of light path the partially coherent Gaussian beam light field that produces is measured, measurement result is carried out Gauss curve fitting, can obtain the waist width of light beam transversal.
Referring to accompanying drawing 2, it is the structural representation of a kind of partially coherent Gaussian beam lateral coherence width of measuring device of providing of the present embodiment; Laser instrument 1 produces a branch of random polarization light beam, produces a branch of linearly polarized laser bundle through the inclined to one side device 2 of line, through focusing on the frosted glass plate 5 behind a catoptron 3 and the thin lens 4, produces the partial coherence linear polarized beam with Gaussian statistics association again; Behind the partial coherence light beam process collimation lens 6 and G amplitude filter plate 7 that produces, obtain the partially coherent Gaussian beam that a branch of collimation has Gauss's association, it is infinitely great that the Wave-front phase radius of this light beam is approximately.The partially coherent Gaussian beam that produces is 25 centimetres condenser lens 8 focusing through a focal length, and the partially coherent Gaussian beam after the focusing has the spherical wave front phase place, and the radius of spherical wave front phase place is the parameter that the present invention need to measure.Described G amplitude filter plate from condenser lens 8 distances is f, the being tested surface after the gathering from condenser lens 8 is l(need not know).Consist of 2 with imaging len 11 at last fImaging optical path, light beam obtains two imaging surfaces after beam splitter 12 equal strength 1:1 beam splitting, place respectively the detecting head D of correlator system 13 at two imaging surfaces 1And D 2, the correlator system connects 10, two optical path signals of computing machine and meets calculating through interconnected system, obtains the relating value of two-way light, and relating value is carried out Gauss curve fitting, just can obtain the coherent width of imaging surface.
Concrete measuring method is: imaging len 11 is imaged onto lens opposite side 2 with being tested surface fPlace beam splitter 12 light beam be divided into the equicohesive two-beam of 1:1 at dotted line face place behind imaging len, again with two detecting head D of correlator system 1And D 2(the dotted line face is 2 from imaging len 11 distances at dotted line face place after placing again beam splitter f).When measuring coherent width, with detecting head D 1Be fixed on the center of light beam, another detecting head D 2Along light beam xDirection moves horizontally, and correlator is done two paths of signals and met calculating, obtains the relating value of two-way light, and relating value is carried out Gauss curve fitting, just can obtain the lateral coherence width of light beam.
Referring to accompanying drawing 3, it is a kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the present embodiment to provide, and records the incipient beam of light optical field distribution and (schemes a) and Gauss curve fitting figure with a tight waist (figure b); As can be seen from the figure experimental result well meets Gauss curve fitting, obtains the incipient beam of light waist width to be
Figure 820474DEST_PATH_IMAGE050
Millimeter;
Referring to Fig. 4, it is a kind of partially coherent Gaussian beam coherent width measurement mechanism that adopts the present embodiment to provide, and records incipient beam of light lateral coherence width fitted figure; As can be seen from the figure experimental result well meets Gauss curve fitting, obtains the incipient beam of light coherent width to be
Figure DEST_PATH_IMAGE051
Millimeter.
Referring to Fig. 5, it is a kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the present embodiment to provide, and records light beam in transmission
Figure 718154DEST_PATH_IMAGE045
Centimetre the time optical field distribution figure; As can be seen from the figure experimental result well meets Gauss curve fitting, obtains the beam waist width to be
Figure 136366DEST_PATH_IMAGE052
Millimeter.
With the initial horizontal that obtains to waist width
Figure 881730DEST_PATH_IMAGE050
Millimeter, initial horizontal is to coherent width
Figure 196037DEST_PATH_IMAGE051
Millimeter, exit facet
Figure DEST_PATH_IMAGE053
The horizontal waist width of centimeters
Figure 581013DEST_PATH_IMAGE052
The transmission matrix of millimeter and optical system
Figure 101119DEST_PATH_IMAGE007
,
Figure 465104DEST_PATH_IMAGE008
Substitution theoretical formula (15):
Figure 248514DEST_PATH_IMAGE043
Convolution (11):
Figure 25846DEST_PATH_IMAGE039
Can obtain the wavefront curvature radius of incipient beam of light after the calculating
Figure 959430DEST_PATH_IMAGE054
Centimetre.
By formula (13)
Figure 974659DEST_PATH_IMAGE041
Obtain the wavefront curvature radius of light beam R
Be checking measurements result's accuracy, can choose different transmission ranges and measure waist width, repeatedly calculate the accuracy of coming the checking measurements value with regard to the way of mean value.A kind of partially coherent Gaussian beam waist width measurement mechanism that adopts the present embodiment to provide records respectively light beam in transmission
Figure 397812DEST_PATH_IMAGE046
Centimetre,
Figure 865703DEST_PATH_IMAGE047
Centimetre,
Figure 942592DEST_PATH_IMAGE048
Centimetre,
Figure 77907DEST_PATH_IMAGE049
The optical field distribution figure of centimeters, its result utilizes Gauss curve fitting referring to accompanying drawing 6, obtains respectively corresponding waist width
Figure DEST_PATH_IMAGE055
Millimeter, Millimeter,
Figure DEST_PATH_IMAGE057
The millimeter and Millimeter.Equally, calculating the phase place radius according to formula (15) is respectively: Centimetre,
Figure 856529DEST_PATH_IMAGE060
Centimetre, Centimetre,
Figure 206870DEST_PATH_IMAGE062
Centimetre.Calculate phase place radius mean value
Figure DEST_PATH_IMAGE063
Centimetre.With following error amount expression formula formula (16) error of calculation:
Figure 362038DEST_PATH_IMAGE064
Obtain error amount
Figure DEST_PATH_IMAGE065
Can find out from error amount, the present invention is feasible according to the measuring method of Theoretical Design, has reliability.

Claims (2)

1. the method for a measure portion coherent Gaussian beam Wave-front phase radius, partially coherent Gaussian beam to be measured has Gauss's associate feature, it is characterized in that measuring method comprises the steps: light beam to be measured is produced the spherical wave front phase place after thin lens focuses on, adopt the correlator systematic survey to obtain the initial horizontal of light beam to coherent width
Figure 201310010442X100001DEST_PATH_IMAGE001
, adopt laser beam analyzer to measure respectively the initial horizontal of light beam to waist width
Figure 284435DEST_PATH_IMAGE002
With the horizontal waist width on the exit facet
Figure 201310010442X100001DEST_PATH_IMAGE003
, by formula
Figure 513160DEST_PATH_IMAGE004
Obtain the wavefront curvature radius of light beam R
Wherein, kBe wave number, A, B, C and D are the astigmatic system transmission matrix; R 0 Be radius-of-curvature before the primary wave, by formula
Figure 201310010442X100001DEST_PATH_IMAGE005
Obtain, wherein,
2. the method for a kind of measure portion coherent Gaussian beam Wave-front phase radius according to claim 1, it is characterized in that: the lateral coherence width that adopts correlator systematic survey light beam, behind the light beam being tested surface, place successively imaging len, beam splitter and correlator system, adopt 2 fFormation method carries out association to be surveyed, and the relating value of two-way is carried out Gauss curve fitting, obtains the lateral coherence width of light beam, fFocal length for imaging len.
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CN106990694A (en) * 2017-03-29 2017-07-28 苏州大学 A kind of non-iterative phase recovery device and method under partially coherent optical illumination
CN108427204A (en) * 2018-04-03 2018-08-21 苏州大学 A kind of method and system generating isotropism Twisted Gaussian Xie Ermo light beams

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Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN106990694A (en) * 2017-03-29 2017-07-28 苏州大学 A kind of non-iterative phase recovery device and method under partially coherent optical illumination
CN108427204A (en) * 2018-04-03 2018-08-21 苏州大学 A kind of method and system generating isotropism Twisted Gaussian Xie Ermo light beams
CN108427204B (en) * 2018-04-03 2023-08-25 苏州大学 Method and system for generating isotropic distorted Gaussian Shell mode light beam

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