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GaussianTEM00He-NeLaserModeanditsParameters

YanhongYang

9April2012

ENGR533Optoelectronics

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CollegeofEngineeringandScience

CollegeofEngineeringandScience

GaussianTEM00He-NeLaserModeanditsParameters

Reportfromalaboratoryexperimentconductedon22March2012

aspartofELEN533001Optoelectronics

YanhongYang

102-13-631

9thApril2012

Abstract:

Gaussianbeamisveryimportantmodelinlaseroptics.“ManylasersemitbeamsthatapproximateaGaussianprofile,inwhichcasethelaserissaidtobeoperatingonthefundamentaltransversemode,or"TEM00mode"ofthelaser'sopticalresonator.”FromWikipedia,

/wiki/Gaussian_beam

.

Inthisreport,authorcalculatesbeamwaistanddiversityangleinTEM00modeHe-Nelaser.InGaussianbeam,theshouldbesameinHorizontalandVerticaldata,howeveritisdifferent.Theauthorgivessomereasonstoexplain.Becauseoftheequipmentlimited,theexperimentcouldnotgivetheexactlypositionofthewaistbeam.However,itcanbecalculated.

TableofContents

Abstract:

i

TableofContents

ii

1. Introduction

1

2. Theory

1

3. ExperimentalSetup

2

4. EquipmentUsed

2

5. Procedure

2

6. Data

3

7. AnalysisofData

4

8. DiscussionofResults

4

9. Conclusions

5

10. References

5

Introduction

Usuallythecross-sectionofamplitudeofelectricalfielddistributioninlaserresonatorcomplieswiththeGaussianfunction.ItisknownastheGaussianbeam.Generally,thelaserresonatordon’tshootexactlyGaussiandistributionbeam.However,theTEM00modeispurelyGaussianbeam.Inthatway,thisexperimentweobservetheintensitydistributionoftheHe-Nelaser.ItisverysimulartoGaussianfunction.AndalsoweusetheGaussianbeamknowledgecalculatethebeamwaistanddivergenceangleinTEM00modeoftheHe-Nelaser.

IntherestofthereportwediscussthereasonofdifferenceinHorizontalandVerticalcalculation.Also,weanalyseandcalculatetheactualpositionofthebeamwaistofHe-Nelaser.

Theory

InGaussianbeamtheamplitudeiscomplexamplitude.

(1)

Inequation(1)

Where

(2)

(3)

(4)

Fromequation(1)wecanseparatelycalculatetheintensityofxdirectionandydirection.

(5)

(6)

Incasewecanfindtwodifferentdistanceszasand.Alsoatthewdistanceinxdirectionwehavetheintensityfall

ento(13.5%).That’sourand.

Fromequation(3)wecaneasilyfindthat

(7)

(8)

Solvingthesystemofequations(7)and(8)

(9)

Alsowecandeterminethedivergenceangle

(10)

ExperimentalSetup

CCDCamera

PC

He-Nelasershouldbeprovideda1250VDC4mApower,andCCDcameraneedsanACadapter.

He-Nelaser

USB

Light

Filter

Figure1.diagramoftheexperimentalsetup

EquipmentUsed

SingleTEM00modeHe-Nelaser(JDSUniphase)withemissionwavelength632.8nmwith0.5mWpower.

TheHe-Nelaserprovidesalongitudinalofanoutputopticalpowerof0.5mW.

LaserbeamprofilerLBP-USBUVLaserBeamprofiler190-1100nm,USB2.0interface(withneutraldensityfilters,CCDcamera,andinterface)

Thesystemiscombinedwithfilters,CCDcamera,USBandinterface.Cameraprovides190-1100nmwavelengthrangeforopticsourceinput.TheLBPcananalysethecontinuouswavelight.

Thesystemreceivestheinputpowerandrestoresthedistributionofthepowerintwodimension(x,yaxis).Italsogivestheaccurateintensityin640×480distinguishabilityand6.47mmwide×4.83mmhigh.

Procedure

WefixthepositionoftheCCDcameraandchangetheHe-Nelasertochangethezaxis.

Movethelasertofurtherpositionandwritedownthedistanceofthelaseras.ObservethedataanddistributiondisplayedonthePCscreen.Thenlockitandsavethedata.

Movethelaserandwritedownthedistanceas.Observethedataanddistributionofthebeam.Thenlockitandsavethedata.

Analyzedataandcompletetheexperimentreport.

Data

Becauseofthespacelimitedonlylisttheimportantdatainthediagram.

No.

Horizontal(%)

Vertical(%)

62

11.38

12.94

63

12.15

13.68

64

12.94

14.24

65

13.46

14.98

149

100.00

99.95

159

96.51

100.00

231

13.87

23.65

232

13.29

22.95

244

6.80

13.74

245

6.28

13.08

No.

Horizontal(%)

Vertical(%)

10

13.60

18.47

11

12.15

19.41

143

99.14

100.0

146

100.00

99.29

284

13.63

18.85

285

12.99

18.79

297

8.60

13.60

298

8.25

12.94

Table1.datafrom=815mmdatafrom=1385mm

While,theHorizontalScaleis9.0515um,andVerticalScaleis8.3um.

Figure2.=815mmthephotoofthedistributionoftheIntensity

Figure2.isthephotowegotformthesoftware.ItshowsthedistributionoftheIntensityisGaussianBeam,anditgivestheshapeoftheHorizontalintensityandVerticalintensitydistribution.Thephotoin=1385mmisverysimilar.

AnalysisofData

WeusetheHorizontaldatatocalculate.For=815mm,wehave=(232-65)×9.0515nm(i.e.=755.80um).For=1385mm,wealso=(284-10)×9.0515um(i.e.=1240.06nm).While,λ=632.8um,π=constant=3.14,andintheairn=constant=1.

Fromequation(9)and(10),easilywecanget=230.37um=0.87mrad.

DiscussionofResults

ThedifferenceinHorizontalandVerticalcalculation.

IntheanalysisweuseHorizontaldatatocalculate,nowinsamewayweusetheVerticaldatatocalculate.In=1385mm,welostsomedata.BecausewehaveVertical(%)=18.47inNo.10andVertical(%)=19.41inNo.11,weassumeit’slinearinshortpointoftheGaussiandistribution.ThenwegetVertical(%)=13.40inNo.8.SamewaywithcalculationofHorizontaldatawecanget=243.11um=0.83mrad.

ThedifferencecalculationbetweenHorizontalandVerticalmightbecausedbyfollows.First,theHe-NelaserisnotexactlyGaussianbeam,andthedistributioninx,yaxisislittlebitdifferent.Second,theequipmentmaycauselittleerrorindatagathering.

Theactualpositionofthebeamwaist.

Infact,theHe-Nelaserdon’tshootthelightfromexactl