BRILLOUIN SCATTERING FROM A GAS SUBJECT TO A TEM PERATURE GRADI ENT: OPTICAL CONSIDERATIONS

BRILLOUIN SCATTERINGFROMA GASSUBJECT TOA TEMPERATURE GRADIENT:OPTICAL

CONSIDERAT IONS

By

ChinHengChao

B.Sc.(Hons.)MemorialUniversityof Newfoundland

A THESISSUBMIlTED INPARTIAL FULFILLMENTOF TI·IE REQUIREMENTSFORTHE DEGREEOF MASTEROF SCIENCE

DEPARTMENT OFPHYSICSANDPHYSICALOCEANOGRAPHY MEMORIALUNIVERSITY OFNEWFOUNDLAND

AUGUST1996

ST.JOHN'S NEWFOUNDLAND

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Abstract

This thesisdescribesan attemp t to use the Brillo uinlight scatteringtechniq ueto observenonequil ibrium effec ts ingaseoussulphurhexa fluoridesubjec t to a tempera ture gradient.Due to theinherent geometryofthe experime ntalsetup, animagin g fi breoptic probe wasinvestigatedas ameans ofscatt ered light collectio n. 111Csr~gas washouse d in a moderate pressu regascell.The scattered ligh tcollec tedwas analyze dwitha Fabry-Perot interfe rom eter.A computersim ula tion ofthebehav iouroftemperature, dens ityund refractiveind exfor gaseousSF6subjec t to a temperaturegrad ientwas performed using a 2 dimensiona l nonc on vecti veheatflowmodel. A computersimulationofthescatteredmy pathsfrom the gas cell to the opticalfibre intheimagin gfibreoptic probewasatsc performed.The soundspeedinSF6atapressure of1.28MPa and a temperatureof20°Cwas measured to be133 ±6ms''.Soun d speeds in SF6for pressures from 0.44Mllllto1.83MPa were alsomeasured . These sound speedsshowed alargernon linearityinitscha ngedwith differentpressuresthanthatcalculatedfrom theory. Noncq uil ibriumBrillou in spect raforSF~

wereobservedat pressures of 0.89 1 MPa and1.35MPawith temperaturegradients of about 15 .3Kern"and 18.9Kerr!•respectively.TIleBrillouin compo ne nts atnoncqui librium showe dan intensityincreaseof about16% whe ncompare d to theircoun terpartslit equili brium.

Ack nowlwgcmcn ts

Iwish 10 thank mysupervisors, Dr.MJ.CjcurerandDr.H.Kiefte for sharing with methc:ircxpcrtisc in therlCldoflighlscatteringand for theirguidancethroughout the course of this research andthe preparationofthis thesis.I wouldalsowish to tbankDr.le.Lewis forsuggestingthemethodused inthecomput er simulationof thetemperature anddensity gradient sin this thesis.

Iwould wishtothank Mr.ToddAndrewforsharingwith mehis knowledgeon light scaucri ng nndallotherswho hoveassisted me inthecompletionof thisproject.

Wh ile engagedin this workI wassupportedbyaMemorialUniversityGradu ate Fellowshi p which I gratefull yacknowledge.

i i

Tableof Contents

Abstract

Acknowledge ments

Tabl e ofContents List ofFigu res I.lntruduction

1.1NenequllibriumFluid 1.2BrillouinScatteringinaGas

1.3Theoryof'LightScatteringin a NcncquilibriurnFluid 1.3.1SoundBending

1.4 ScatteringGeometry 2.ExperimentalMelhod

2.llntroduclion 2.2lnputOpties 2.3 ReferenceOptics 2.4 CollectionOpucs 2.5 InputEnd

2.5.\ImagingFibre OpticProbe 2.5.2OutputEnd 2.6The GasScatteringCell

iii

iii vi

10 14

,.

14

I.

18 19 19 27

31

34 34 35

38 3.Simu la tio nofScatt er edRayPathsina SF₆Gas

witha DensityGradient 3.1Introduction 3.21bcSulphurHexafluorideGas

3.3 ComputerSimulationofthcDensity Distribution in aTemperatureGradient

3.4 RaytracingThroughtheDensityGradientand the

Imaging FibreOptic Probe 44

3.4.1RaytracingThroughtheDensityGradient 44 3.4.2 RaytracingThroughtheImagingFibreOptic Probe 47 4. ExperimentalResults

4.1Introduction 4.2 Results S.Diseus sion

5.1Discussion 5.2Concl usion Blbllo graphy

Ap pend hA

PhysicalPropertiesofSulphurHexafluoride Ap pe ndix B

PropagativeModesin anOpticalFibre

53 53 53 65 65 68 71 74

76

iv

AppendixC

InelasticLightScattering AppendixD

ProgramFlowchartsandSourceCodes

79

8J

ListofFigures

1. Brillouinintensityeffects for fluidindifferent noncquilibriumconditions 2. Simplesoundbending

3. Totalsound bending 4.Computersimulation of sound speed 5.Cavity modes in a lasingmediumlinewidth 6. Horizontalandvertical amplitudeprofile oflaserbeam 7.Argon ion lascr lightpro perties

8.lnput.Reference andInputEnd ofCollectionOptics 9.Guiding Iightlhrough theopticalfibre 10.111eImagingFibre OpticProbe II.Transmittance curve fora fusedsilica singlefibre 12.Modesseen fromopticalfibre

13.Imagedistancesat variousobjectdistances 14. Magnificationfactorforvarious objectdistances 15. Coupling light raysatmaximum efficiency 16. Output sectionofCollection Optics 17.GasSeattering Cel1 18.vapeurpressure curve ofSF₆ 19.2-0nonconvecuveheatflowmodel 20.Densitydistributionasa function ofheight

vi

II

14 I;

16 17 19 20 22 23 24 24 25 26 32 35 38 42

21.Densitydistributionas a function of'tempemtare ..l2

22.Temperaturedistribution as a functionof height 43

23.Refractiveindex distributionas a functionofhcig ht 43 24.Axial cross sectional geometry ofgasscaucringcellnndaperture 44 25. Computersimulationoutputscattered raypaths throughadens itygradi"'nt 45 26.Computersimulation output:sceueredmypathsthroughthe:lpcrtUR: 46

27.Transferfunctioncoordinates ·n

28. Vector diagram forlightrefraction 49

29.Computersimu.~~lionoutput: scatteredraypathsthroughinmgingfibre

optic probe 51

30.Simulatedfrequencydistribution ofcollectedscuncredlight 52 31.ABrillouinspectrum collectedfor Sf',gasin anequilibriume..rete 54 32.TheBrillouinspectrum foroneorder ofinterference 54

33.LinewidthofaBrillouincomponent 55

34.ChangesinXcpeaksposition asFSRchanges 56

35.Frequency shift(channels)versusplatesseparationpier 57 36.Changesinthecharacteristics ofX-peaksaspressureis changed 59 37.158⁰backscatterBrillouin shiftsfor differentpressures 60 38.Frequency shiftsofX-peaksandbackscatterpeaks for differentpressures 61 39.Sound speedsin gaseous SF, fordifferentpressures 61

vii

62

63 40.Brillo uinspectrumof bothequilibrium andnoneq uiJibrium stales:

Pressures from 0.919 MPato 0.891MPa

41.Brillouinspecuumof both equilibrium and nonequilibrium stales:

Pressuresfrom 1.38 MPato1.35 MPa

41.Equilibri umand noncquilibriumconditionswithrespectto

thevapourpressurecurve 64

A.IDifferentprcpngativemodes 77

A.2Th e rirsr rcnL1'..modes 77

A.JEIT(.~1oflihrc diamctcrouwavespeedfortheHEll>TE ,uand TM'Q^{modes 78}

AAInelast ic lightscattering 80

A.5Vectoradditionofwave vectorsininelastic lightscauering 81

A.6Rotatio nofaperture'scoordinnte 107

viii

To the memoryof my father, Mr.ChooPengYoong

Chapter I

Introduction

t.INon eq u ilib riumfluid

Although systemsinequilibrium ingeneralDecwellstudied, prog ressintheanalysis ofsystemsin nonequ ilibriumstatesisoften sloweitherbeca use ofthelackor atheory10 properlyexp lain existin gexperime nta ldataorthelackof experimenta levidence10suppo rt andverifyresults Hu mtheoriesthat attempttoexplainthesebehaviours.In thisthesis,Iwill discussan attemptto observenonequilibriumeffectsina gassubject to atemperature gradi en tbyinvestigating changes intheinteractions between light and soundwaves (pho no ns)asthe gasgoesfrom an equilibri um\0a noncqu ilibriumstate.Brillouin (light) scauc rmgtechniqueswill be used in thisexperimenttoprobefor these effects in a scattering geometrythat isdifferentfrom previousexperiments of this nature.

1.2Brillou in SC:ltfcr ingin a gas

SPOIllMCOUSmicroscopic fluctuations alwaysexist in anysystemwhose temperature isaboveabsolutezero. These microscopicfluctuationsdissipateinthesame wayasexternal perturbationsdo.Localfluctuationsinteractwith eachothertoproducecollective fluctuationswithadistributionof wavelengths and frequencies.By studying thesecollective thermalIluctutnions,we canextractimportant thermodynamic propertiesand transport coefficientsliketheratioof specificheatsy•theadiabatic sound velocity.isothermal compressibility X.thermaldiffuslvity,thermalconductivityand coefficientsof viscosity.

Thesethermalfluctuationsare also calledthermal soundwaves.

Sincethesethermalfluctuations presentthemselvesin a distributionofwavelengths, different techniquesmayberequiredto study fluctuations atregionswith different wavelengths and frequencies.At low frequencies and longwavelengths,thesethermal fluctuations behavelike a continuum andcanbe modeled by hydrodynamictheory.But at wavelengths that arecomparableto themolecularmean freepath. localmolecularstructure

ofthefluidbecomesimponanc.and1hefluctuationsno longerbehavelike a continuum.This is themoleculardynamic regime.Thehydrodynamicregimeischaracterizeby low wavenumberk andfrequencyw.andalso by a parameterj-It1(45].

.v-

J,JJ where1is the wavelengthof fluctuationsandJisthemeanfreepath.Themolecular dynamicn.,;inlo.: is characterizedbyhigherkand wand)'-I.For)' llI.we havefreeparticlemotions.

Tostudy the behaviourofthennalfluctuationsin thehydrodynamic regime,wecan useeither theBrillouin(light) scattering or ultrasonictechniques.Ultrasonic techniquescan only studyfluctuationsconfined to a regimeofverylowkand(,)whereas light scattering techniquesallowus to study flucruuticns over amuch wider rangeofkandw.ln Brillouin scattering.theinteractionbetween anincidentphotonandthefluctuations (phollOns)gives rise toa momentumtransferandaphotonof a different wavelength is scattered($1,.-':

AppendixC formore detail).Thewavelength of the momentumtransferis1- .\,/(2nsin

(en)).

wherei..., ;..and

e

specify the wavelengthclf hc fluctuations. wavelength ofincidcnt light andscattering angle respectively.The angular frequencyshinof the scancrcd Iiglu 'wouldbe ±w,

(I)

wherecisthe speed of the sound waves andn isthe refractiveindex.IfWucorrespondsto theangularfrequency oftheincident light ortheRayleighline .then w"+Wandtot-w wouldcom:spondto theupshil\edanddownshiftedBrillouin lines.TheBrillouinlineswould appearas satelliteson either side of theRayleighlinein lite spectrum.Sinceit is common practicetospecify theBrillouin shiftsinterm or frequency,

f ;.*

^{ratherthanitsangular}

frequency.weshall~fforour frequencyshiftsunlessstated otherwise.In the experiments reponed herein.we willbeusingBrillouin scatteringtechniques toprobe fornoncquilibrium effectsina dense gas with a forwardscatteringgeometry,thus probingforsound wavesin thehydrodynamicregime.

The abovementioned conceptofclastic(orsound)wavesin a continuous medium wasintroduced byDebyeinhistheoryofsolid statethermalcapacity.These elasticwaves

areessentially normal modes arising from the interaction ofvibrating particles ina solid crystallattice.The interactions betwee nlightand sound waves to producescatteredlight that possesse s two frequencyshiftedcomponentswereindependently predictedbyBriJlouin[1) in1922 and Mandelshtam[2}in1926.They were subsequentlyobserved by Gross[3] in1930 ina monocrystal of quartz.He latcr also observedthe frequencyshiftedBrillouin component in aliqu id. Even though there were attempts to observe Brillouinscattering in gaseous H2

•N~andO2as early as1942[4],thefirst successfulobse rvation ofthe Brillouincomponents in a gas did not come till 1965in a stimulated Brillouin scan eringexperiment(5).In the fo llow ing year, spontaneousBrillouin scattering was observed in Ar, Xe,Nz.COl andC~

(6].Even thoughparticles in a gas do not vibrate abouta welldefine location likein a crystallattice,sound waves canstill exist in agasaslong as thegas to be considered can be treated as acontinuous medium. ln this case,the wavelengthof the soundwaves probed have to bc muchlonger than the mea nfree path of'thcparticlesinthe gas[7]. Wehave

h i

(2)

wheredis the molecular diameter and p is thenumber ofmolec ules per unitvolume.Since pressure is directly relatedto density, observation of a Brillouin spectrawillget progre ssi ve ly moredifficult as the pressure of the gas getsloweruntilwereacha stage where),,-1,whenthe Brillou inlineswould notlonger exist.

Not onlycan Brillouinscattering techniques be usedto determine behaviours of variousthermodynamic propertiesin a systemin equilibriu m,given the rightconditions the se scattering techniquescan also beused to observe the behaviourofa systemnotin equ ilibr ium .AlthoughnonequiJibrium effectshavebeen observedinboth solid and liquid [8].I willconfinemydiscussion tojustthe effectsinanonequilibrium fluid;as mostofthe theo ries put forward sofar on lighlscattering in a nonequiJibriumsystem arcfor a

I(of

...0)

Figure1Brillouin intensityeffectsforfluidIndifferentnoncqullibrium conditions

nonequilibriumfluid.A nonequilibrium statein afluidmaybeachieved by severalmean.s, asfollows,

i)SubjCl:ting a fluidtoatemperaturegradient.

ii]Inducing amacroscopic velocitygradientinthe fluid.

iii) Inducinga differencebetweentherotationalandtranslationalgastem peraturesin!he fluid

Thenonequilibriumeffectsforthesedifferent conditions are shownin Figure I.Forafluid inanonequilibriumstatecreated throughconditionsii)andiii),anequal changein boththe upshiftedanddownshiftedBrillouin lines willbe observed19).Fora fluidsubjectedto a temperature gradient,theeffectonthe Brillouinlineswillbeanequal butoppositechange in theintensity of Brillouinlines,i.c there willbeanasymmetryaboutthe Rayleigh line. in theintensity betweenthe upshiftedanddownshifted Brillouinlines.In thiscase.the sound wavespropagate alongthedirectionofltlc temperaturegradient.1\noncqulibtiumeffectthat is similar to thatof a fluidexisting incondition ii)can alsobeseenin afluid witha temperaturegradient ifthesoundwaves that arc probedare propagating inadirection

perpendicular tothatprobed intheprevious scatteringgeometry[I0].

1.3Theory of lightscattering inanonequlibriumfluid

Therehavebeenseveraltheories,priorto [10], proposing to explainthe asymmetric BrillouinspectruminanonequHibrium fluidIJ^I~15].Thesetheoriesattemptto calculate thedynamic structuralfactor(which is relatedto the intensityoftheBrillouinlines) in a noncquilibriumfluid instationarystatesubjectedto a small steadyheatflux. By lookingat this system fora stateslightly perturbed from equilibrium.they were able to deduce an intensity differencebetweentheupshiftedanddownshifted Brillouinlines.correctedto the linearorderin thetemperature gradient.Theseare due to the so-calledmode-coupling effects.The Brillouinintensitycanbe separatedintotwoparts,a tocalequilibriumpartand amode-couplingpart:

(3)

lB.and lB.are the upshiftedanddownshifted Brillouin component,respectively.Any effectsfromthenonequilibriumfluidwouldcome fromthemodecouplingpart

I :; ,

^which

may causethe totalintegratedintensityofthe upshifted or downshiftedlinetobehigheror lower thanthetotalintegratedintensityatlocal equilibrium.

Theresults from thelinear theory were verifiedbyexperiments doneonwaterby I-I.Kiefte. M.J.Cloutcrand R.Penny[8}. These experimentswerecarriedOUIin conditions wherespatialinhomogeneitiesoverthe soundattenuationlength and"boundary effectscan beneglected.A similarolderexperiment performed byBeysens, GarrbosandZalezer[16]

whereconditions werenotas"ideal"yielddatathatcannotbeaccountedfor by the linear theory.Newer theories were later proposed10accountfor theresultsfrom boththese experiments.A theoryfromSanenand Ronis [17]incorporated boundaryconditionsinto the lineartheorywhileanotherfromKirkpatrickeral[18]uses anonlinear theorythattakesinto considerationthe spatial inhomogeneities in the nonequilibrium fluidbut neglectsboundary effects.Theresultsfromboththe experimentswereconsistentwith thesetwotheories, to withina large uncertaintyinthe data.Thus, eventhough the theorieswereable to account forthe results.they were notabletopoint to the actualeffect that explainstheresultsofthe

experiments.Tbeunderlyingmechanism that causesthedeviationof'rcsuusfromthe1,....r1l...'T lineartheorymaybenonlinearor boundarybynature.or itmaybea combinationof both cf'these effects.

A generaltheoryproposedbySchmitzand Cohen110). inte ndstoresolvethi~

ambiguity by incorporatingboth theboundary andnonlinear effects intotheirtheoryfor nonequilibriumfluid.Itwashopedthatthroughthis theory.differentdegreesofboundary andnonlineareffectscanbeadjustedto explainthe experimentalresults.Thenonlincl.lrity ofthistheoryrequiresthatthennar~undwaves producedfromspontaneou snuctu.1tions do notpropagate in a straightlinepath as wasinthe linear theory.butratherbecause ofsp.1tinl inhomogeneity. thesoundwaves nowpropagate alongcurvepaths.i.cthesoundmrs,Ire nowbent.Sincethelinear theoryandthe nonlineartheorynrcjustlimiting ca.sc'Sorlhis generaltheory.probing thesoundwavesfromdifferentscanoringgeometryinthe nonequilibrium fluid.as predictedfrom this theory.wouldallowus10probefor nonequilibriumeffectsfromone regimeto another.By probingsoundwaves withvectors intheverticaldirection(alongthe directionof

vn.

we can look fornonequilibriumeffec ts inthelinear regimewithoutboundaryeffects whereasprobingsoundwaves with vectors in the horizontaldirectior.(perpendiculartothedirectionofVT)would allow us to investigate nonlineareffects,likesoundbending.inthenoncquilibriumfluid.

These nonlineareffects ontheBrillouin lines intensityare investigated in this experimentin thehopeto validatethis generaltheory for ronequilibrium fluid.Brieny.the theory of sound bendingand~e_results for Brillouinlineintensity as calculatedforthe horizontalscatteringgeometrywill bediscussedin the followingsection.

1.3.1Sound bending

When the nonlineareffectsare consideredinthe general theoryof nonequilibrium fluid proposed by SchmitzandCohen. spatial inhomogeneitiesarenotignored.thus affecting thesoundspeedasitpropagatesthrough thenonequilibriumfluid.111eauthorhave throughthe application of WKBtechniques totheequationsof fluctuatinghydrodynamics.

foundthatthermalsoundwavesproducedfrom spontaneousfluctuationsnolonger propagate along straightraypaths,theraypathsare nowbent to curves,as shownin Figure2.This is similarto soundpropagationin a stratifiedmedium. Aray canbe uniquelycharacterizeif

'. '

'"

Figure 2SImplesoundbending

its waveveelorkand its scatteringpositionRare known.Anypositionalongthe ray pathis characterized by its tangentialvectorij(F)asfollows.

(4)

Since, thehorizontal componentofk.k,is conservedalongthe ray path,wecan write Snell'slawin termsofthemagnitudeofthe vectors.

c(z)q(f;R,k)=c(R:)k , (5)

wherec(z)isthespeed ofthe soundwave along the raypathat positionzand"(R,)isthe speedofthe soundwaveatzpositionof vector

ii.

Thesoundwaveswouldalsoexperience thetotal internalreflectioneffectifthe followingcriterionis met:

(6)

TIle authorsrefer to!valuescharacterizedby(6) as a "forbidden region".Iftheforbidden

,

~

;

, "

Figure3Totalbending, soundwavesonglllOlungfrom hea t sourcereturn to theheat source.

region is empty, thenraysaremonotonically bent asshown in Figure2.Butifitisnor empty,thenrays aredeviatedto theoppositeZdirect ionat thepointwhereIheytouch the forbiddenregioninthefluid, andpropagate backtothe plate'wheretheyorighuncd.;IS showninFigure 3.Theauthors refer to this phenome non as "totulsoundbending" .

Otherthan theneedforthesound beodingeffcci.tbcgl.'OCrall hcory alsorequirestill:

mod ificat ion of the concept of constantsound attenuatio nlength.Sincethe speed is not constant,thesound damping coefficient r.{z) wouldnolongerbeconstant100,thusthe attenuation lengthl,which is

I(R)). 2,(R,) •

, r,(R,)k' ⁽⁷⁾

needs to be subsequently modified100.For1«I.v,where'-"isthe length over whichIhe macroscopicpropertiesort he fluid change,nonlineareffectsmaybeignored.

'FromFigure2, "plate"hererefers10 eitherthe heat sourceor heatsink.

(8)

whereu(f)stands for thethcnno dynamic or transport coefficient that dependsmost sensitively on temperature. In our case, a can be the speedof soundc(z(f)).Sincethe temperaturegradientand the magnitudeofthesoundspeedgradientincreaserapidlyasz gets close to thebottom ofthe cell,we can expectLl'lodecrease rapidlyat that point 100.

Ina verticalscatteringgeometry,the soundwavesprobedhavevectorswith1k:1=I, they propagateina straightline alongthe vertical direction. In verticalscattering,onecan probefor ncnequilibriumeffectsinthe linearregime.as was doneintheprevious experimentsIS].For ahorizontal scatteringgeometry,we haveIk,1⁼0,andone can probe for nonlineareffects like totalsound bending at theposition wheretherayjust touchesthe forbidden region.The authors havefoundthe mode-coupling contributionsto the Brillouin line intensityus follows,

(9)

wheresgn~isthe signof~.Equation(9)may be evaluatedexplicitlyto thelowestorder in the temperature gradienttogive thefollowingresult,

whereJ,,(R)isthe localequilibrium Brillouinline intensity,andC(k)is thefinite size correction given inPO].Themode-coupling contribution in this case is the sameforboth theupshifted and the downshiftedline. The nonequilibriumeffect in this case wouldbea

change inthe totalintensityof boththeBrillouinlines whenthefluid is movedfroman equilibriumstatetoa nonequilibriumone.FromtheresultsinEquations(9) and(10). al3f\\c temperature gradient :Eor alargechange insoundspeedalong

=

,~.togetherwithsoued waveswith smullkwould producea largenonlinear effect in the Brillouinlineintensities.

tothisexperiment,we wouldattemptto createalargenonlineareffect inthe noncquilibrium fluidbyinducinga large~.For sound propagationinsulphurhexafluoridegas.the speed of soundwavesis relatedtothedensityas follows{19J.

,'. TJ<Jj,.2P

_Ml

8

m]

0.146' ^(II)

whereR is thegasconstant,Misthe molecular weight, p is thedensity, T istheratiooflhe specificheatscpandc.,and8(l)isthesecondvirlulcoefflclentofthevirialexpansionof theequationofstate. Equation (II)is valid fordensities up to100kgm·^landtemperatures from230 Kto1200K.From Equation(I I),we can seethatnlargc density gradientalong :rwouldinducea largechange inlhe soundspeedalongz,The largedensitygradientcanbe createdby workingwithtemperaturesthaiare close10thevapourpressurecurveortnegas.

This isdone in ourexperimentbycreatinga temperaturegradientsuchthaithe towcsr temperaturein the gradientis vel)'closedtothe vapour pressure pointofthegasheldata particularpressure. Acomputersimulationof the soundspeed fordifTcrcnt z alongtheheight ofthe cellis showninFigure4.ln thissimulationEquation (II)uses data fromthe temperatureanddensitygradient simulationfrom Chapter3.Becauseofthe approximations employed.the behaviour ofc(z)nearthe origininFigure 4isnot expectedtobeaccurate.

Wehopethaibycouplingamoderatetemperature gradientwith a largesoundspeed gradientin additiontolookingat scatteringat small anglcs.,wewouldbeable to observethe nonlineareffectsas requiredbythe generaltheoryfora noncquilibriumfluid.

1.4Scanering geometry

Due to theinherent geometryofthisexperimentalsetup,theusc of conventional optical techniques (i.eapertures,lensesand mirrorsmountedon opticaltracks)tocollect scatteredlight wouldbedifficult.One of thesedifficultiesstems fromthespacerestrictions arisingfromtheneedto lookatforward scattering alongthedirectionof the densitygradient.

10

0.04 0.05 0.06 0.07 0.011 z alon hetht⁰cell m Figure4Computersimulationofsoundspeed along height of cell according 10 theapproximations of Chapter 3.

The densitygradient is createdin a gas scatteringcell,soinordertolookatforward sceucringalongthegradient,....e wouldneed10 positionthecollection optiesbeneaththegas cell. Anotherdifficultyrelates to theneedto lookat scattering fromvariousscattering angles.Becauseoflh is,we wouldneedan opticalsetupthat wouldallowus toeasilyrealign the optic axisofthecollectionoptics along thedifferentscattering angles. To use conventional opticaltcchniquesunderthesecircumstances wouldbedifficult,Thereforethe uscofanimaging fibre opticprobe was investigatedasa meansofco llectingscattered light fromourexperimentalsetup.The imaging fibre optic probeismade upofanaperture, an opticalfil:ifeandasctofimagingopticsthatfocussesthe scatteredlightfrom the cellinto theoptical fibre.

Theuseofopticalfibres forscattered light collectionhasitsroots in DynamicLight Scattering (DLS).DLSisthescatteringof lightfromanensemble ofmacromolecules or paniclesthat moveunder Brownian motion. Under thisrandommotion,the intensity of scatteredlightfromtheseparticles fluctuateswith tirne.Iefonnation aboutthe particles'size andsizedistributioncanbeobtainedfrom thetimescaleoftheintensityfluctuations.The

11

usc of opticalfibretechniquesinOLS wasfirstdemonstratedbyTanakaandBcm:dckin 1975[20) and laterdeveloped further byDyctt in 1978121). There arevariousdesigns for the fibre optic probe used in fibre optic basedDLS experiments.they rangefrom simple lens/fibrebundletogradedindex (GRIN)lcns/singlemodefibre(22]combinations.The designofafibreopticprobeessentially consists of animaging lens systcrnthatfocusses scatteredlightintotheopticalfibretowithinthesolid anglespecifiedby itsacceptancecone.

Apenuresandspatial fillersmaybe incorporated inlOthe designto reducenoiseandangular uncertainty inthe scattered lightcollected.

The useofopticalfibretechniques as ameans ofscattered lightcollection and delivery forRaman andBrillouinscattering was discussed byBrownin1987 [23].Theusc ofoptical fibre inRamanspectroscopywas initialedbyEckbrethin1979[24). Sincethere are noangular dependenceofthe fTequencyshifts in Raman spectroscopy,therange of scattering anglescollectedbyoptical fibre techniquesmaybeaslarge asthatdefinedbyjhc acceptanceconeof thefibre.Forthisreason, apertures andlenses maynotberequiredfor someRaman scatteringexperiments[25]whereasBrillouinscattering experimentswould mostdefinitelyrequirethe use ofthese components.Thisisbecauseofthedependenceof its frequencyshifts onthescattering angles, awiderangeof scaucring angles wouldrocun alargeIinewidthintheBrillouin spectrum.

Although opticalfibre tcchniquessimilar to thoseinDLSexperiments, tomy knowledge,havenot been appliedin Brillouinspectroscopy before,there are manyBrillouin scattering experiments that havebeen performedon theopticalfibre itself.In thiscasethe opticalfibreis usedboth asthesampletobestudied(for 90^Dand180^Dscattering) and<IS

ameans ofchannelingscattered lightfrominsidethe fibretothcdetection optics(180·

scallering),and no fibreoptic probeisusedfor scatteredlightcollection.~~ofthese experimentswasdonein1972 withsimulatedBrillouin scatteringinasingle mode gla.'>S fiberbyIppenand Stolen[26].Theywe~^{able to}measurea backscatter frequencyshin of 32.2GHzwith aFabry-Perot interferometer. Anothersimilarexpcnmcnt,that usesthe Brillouin gain method ofmeasuring thefrequency shill, was done by Azuma et al(271in 1988.TheywereabletomeasurethebackscatterBrillouin shifts of the fibresdown1010.4 GHz and Brillouinlincwidthsdown10101MHz.A SpontaneousBrillouinscattering

12

experimentwithsingle modefibrewas donein1983by StoneandChraplyvy [28].They measuredthebackscatterBrillouin shifttobe12.7 GHzusinga Fabry-Perotinterferometer.

Olherexperiments wac doneto measurethe shiftsat 90-scaueringangle,butasmentioned befon;thefibreisusedonlyas a sample(29].Heterodynedetection techniquehas alsobeen usedto observedspontaneousbackwardBrillouin scatteringin an opticalfibre[30J.

'"'Inthisthesis,I wouldpresenta methodofscatteredlightcollectionanddeliverythat

is applicabletobothforwardand backwardBrillouin scanering.Scatteredlightiscollected bytheimagingfibreoptic probe!and deliveredtoa singlepassFabry-Perot interferometer forspectralanalysis,using a mullimodeopticalfibre.Thecompactness ofthe imagingfibre opticprobeandtheflexibility ofthe optical fibre wouldallowus to easily alignthe optic axisof the probe todifferent positions andscatteringangles.We wereabletomeasure the spontaneousBrillouinshifts of gaseoussulphur hexafluoridedown to about 98.5MHz and thewidthof theRayleighlinetoabout50.5 MHz.

2Refersto thefibreopticprobe usedinour experimentalsetup.

13

Cha pter 2

Experimental Method

2.1Introduction

Asinmost lightscatteringexperiments. our experimentalsetupconsistscsscmluhy of opticsto

i)directthelaserlightfroma sourceto a sampleand ii)collectscatteredlightfromthe sampleforspectralanalysis.

Wehavealsoaddedanexirasciof opticsfordirectingIIreferencebcnmthroughthesample and into thecollec tionoptics so as10activel yoptimizetheFabry-PerotinterferometerIC.1f spectralanalysis.Altogether.wehave 3 setsofoptics. one to directthelaserliBhlIIIthe sample.calledtheInputOptics. another10coll ec tend analyze the scauercdlighr. cattedInc Collection Opcicsandfinallyone fordirectingand controllinglhereferencebeamcalled the RefercnceOptics.

2.2Input Oplits

FIgure 5CavitymodesInIIlasmg medium linewidth.

The laserlight usedin ourlightscattering experiment is generated fromaCoherent lnnova90 Argonionlaser. The laseris set uptooperateatthe greenargonline of51 4.5 nm usingthe model934WavelengthSelector.The lasingmedium linewidth is about10 GH7.

/ r-.

l

[);,,,,,,~(,,,,,,) Ololallco(mm)

Figure6The honzontal(left)andvertical(nght)amplitudeprofileof thelaserbeam at a distanceof about 2 metresaway fromthe outputcoupler. Both the profilesare fitted to gaussian functions.

(8.83 x10')nm).Thislaser lineis,however,modulatedbythe resonantcavityin such way thatcavitymodesof muchsmallerline widthsare present.Thisisshowninthe Figure5.For a resonantcavityofrefractiveindexIand alengthof aboutI metre,wehave cavity modes thatarespaced about150MHzapan.Toselectonly one of these modes for laseroutput, we usca solid fusedquartzetalonplaced in the laser(resonant)cavity. This etalonacts as a filter to selectonlyonemodefor single frequency(singlelongitudinalmode) operation in the laser. Since the etalon maximum transmission frequency is temperature dcpendcnt(5.2GHzrC), it ishoused in a temperaturecontrolledopticmountforminimum frequency drift.The transversemodeof ourlaserlight istheTEMoomode,an amplitude prolilcof thislaserbeammode atadistance ofabout 2 metresaway from the output coupler isshownin Figure6.The powerofthe laser light used in ourexperiment rangesfrom about 140 mW toabout160 mW. Some of theo;E~.~:l'f~perties^ofthelaserlight are shownin Figure ?

The optics used fordirecting thelaserlight from the laserto the gas scatteringcell is shown in Figure8.The half-waveplate thatis positionedjust afterthelaser is used to orientate the polarizationof thelaserbeam in such a way that thepolarizationof the

15

ArgonIonLaserLightProperties

l.l""""lIe' ""inl<

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FlgUR 7Argon Ionlaserlight properties

scatteredlight emerging'fromthe cellisperpendiculartothedirection ofthe opticaxis of the imagingfibreoptic probe.After leaving thehalf-waveplate,thelaser beam is subsequentlydirected intoabiconvex lens thaifocusesthe laserbeaminto aregionatthe lower part of thecell,ina locationwherewe wantthe observedscatteringto take place.

Afterleavingthe biconvexlens, the laserbeamis directed intothecellthrough2 adjustable minors"onetodirectit alonglheyaxis towardsthegascell and anothertodirectit downthe:

gas cell. To align thelaserbeamtogo throughthegascellina direction that is perpendiculartoboththetopandbottom windows,weusc aplanemirror.The beam is first alignedwith the mirrorplaced onthe top of the cell.thenaligned again withthemirror placed belowthe gas cell. Inbothinstances,the path ofthereflectedbeam isndjustctlt o coincide with thepathof theincident beam. Thebeamsplitterthatispositionedafterthe biconvexlenstaps offasecondary (reference) beamoflightand directsit intotheReference Optics,asshown in Figure8.

2.3 ReferenceOptics

Afterthereferencebeam leavesthemainlaserbeam.it isattenuatedby an etalon 16

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Figure 8Input.Reference andInputEndof Collectionoptics 17

filter(for 514.5ronwavelength).Bypositioningthe filterat differentanglesto thereference beam,the referencebeam canbe attenuated todifferent degrees.Least attenuationoccurs whenthefilteris perpendicular tothereferencebeam.butattenuation increases as\VI:tiltthe filter positionawayfromtheperpendicu11rposition.Attenuationis required foethereferenc e beambecausetheintensityof an unattenuatedbeamwouldoverwhelm the photomultiplier tube withphotons.makingit impossibletodetect andoptimizeon theRayleighline.

A prismis usedtodirectthereference beam through1Icomputercontrolled shutter ontoanadjustablemirror.The computercontrolled sbuueris opened foraperiodthaIisof order1/16ththe10taltimespentin one scan ofthe spectrum.1bcreferencebeamis shutoIT for therestof the scan SO lhat the referencebeamwouldnotoverwhclmtheBrillouin lines.

Theadjustablemirror after the shutterwould then direct thereference beam through tho.=g;IS

cell andintotheimagingfibre opticprobe. Again, a plane mirror isused to align the referencebeamintothe gas cell.Thereferencebeamisalso used to fairlyaccurately determine the scatteringangle for thecollection optics.This isdone byfirstremovingthe imagingbeamprobe fromtheimagingfibreoptic probe,leaving behind only the aperture.

Inthis case, an aperture25.4mminlength and \.59mmindiameter isused.TIle aperture positionis thenadjusted eitherby usingthexyzaxisrnicroposhioncrand/orrotatingthe aperture about itsaxisinthe imagingfibre optic probemount.Thepositionis lldjuSlcdso thata maximumamountoflight from thereferencebeamgets through.We record thex and z micrometer position in the micropositioner.Next, we move theapertureto anotherxand zposition that wouldagain allowthemaximum amountof lightthroughandrecord its positionagain.Sinceweare essentially movingalongthe referencebeampath, knowingthe coordinatesof thispathat twodifferent positionwouldallow usto easily calculatethe angle betweenthe referenceand the mainbeaminthe cell.This calculatedangle also gives usthe angle of the scattered lightcollected.The referencebeamshould also notbeattenuated in thiscase. because we wantthebeam spot to be seenas clearlyas possibleaflcr passing throughtheaperture.

2.4Collection Optics

The collectionoptics is comprisedofa setof input optics which collects scattered lightinto an opticalfibreand a setofoutput optics which directs the scattered lightthrough

"

Figur e9Guidinglightthroughtheopticalfibre

the Fabry-Perotinterferometerforspectraanalysis.Theoretically,theycan beasfaraway asneeded ,provided'Wehave an opticalfibrelong enoughto link themtogether.

2.5InputEnd

Theimagingfibre opticprobeisthe centralcomponent oftheinput end ofthe collectionoptics.Itcollectsthe scattered light fromthecell and channels itto theoutputend foranalysis.In the followingsection,Iwill discussin detail, the design and workingsofthe imagingfibre opticprobe.

2.5.1Imaging Fibre Optic Probe

The imagingfibre opticprobe is made up ofan imagingbeam probe from Oriel,a muhimcdesingleopticalfibreandan apertureattachment, with or withoutthepolarizerfilm.

This isshown in Figure10.Becausethe opticalfibreservesasaconduitforscatteredlight from theimagingfibreoptic probetothe Fabry-Perotinterferometer,itisimportant for us to knowhowthe optical fibre would modify the scatteredlightas itenters and propagates throughthe fibre.Therefore,Iwillstan off this sectionwith a shortdiscussionofsome of thc basic principlesofopticalfibreoperations.

Lightisguidedthroughan opticalfibre bytotal internalreflection.The opticalfibre is madeup of a core thatissurroundedby a cladding,asshown in Figure9.In orderfor total internal reflectionto take place,therefractive indexofthecoremust be greaterthan that of the cladding.Angleaisthe incidentangle at which a light ray entering thefibre wouldproduce a refractedray that wouldbeincidenton the claddingand coreinterfaceat criticalangle. Anyincident anglethatislarger thana wouldproduce a refractedraythatis

19

llmm ferrulesfor terminated fibre /

Imagingbeam probe . \ \

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T erminationfor optic fibre

Figure 10TheImagingFibreOpticProbe

20

~ ⁷ 5mm plano convex lens

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incidentonthe interface atlessthancritical angle.Only rays within theacceptancecone defined byawouldbeguided throughthefibrebyrepeated reflectionsattheinterface.A popularmeasure ofthesolidangle oftheacceptanceconeais calledtheNumerical Aperfure(NA).it is definedas follows:

NA"'sina "'~ . ⁽¹²⁾

The relativedifferenceintherefractiveindicesbetweenthecore andthecladdingdetermines the acceptanceconeangle.Aslight propagatesthrough thefibre.it willexperiencelosses initsintensity. theselossesare duetoabsorption andscattering from the corematerial.

Lossesare experiencedevenaslightenters andexitsthefibre. since reflections occurat thesesurfaces.Theselossesaremeasuredbythe transmittanceof theoptical fibre, whichis dependenton the wavelength.length offibre.material used inthe core ofthe fibre and the reflectivity oftheendsurfaces. The higherthe transmittance. thelowerare thelosses. The transmittance-length relationshipforconstantwavelengthis approximately as follows,

(13) whereP isthepackingfraction(1forsinglefibresandliquid lightguides).R is thereflection loss.lZis the absorptioncoefficientandListhelengthcf'the averagelight paththroughthe fibre[31].Figure 11 showsaplotofthetransmittanceversus the wavelengthoflightfor the singleopticalfibreusedinourexperiment,asreproducedfromtheOriel Corporationcatalog vol.ILpage4-6.The transmittancecurveshowsthat theuansminanceat 514.5 om is about 95%.

The characteristicoftheemergent coneoflight fromthe fibredependsbothon the propeniesof lheopticalfibreandthelaunching conditionsofthe entryconeof light intothe fibre.Fora longfibre(greaterthanImetre).thefibre properties dominate the characteristics of the emergent cone.Thisappliestothecharacteristic ofthe emergentcone ofour optical fibre too.Forashort fibre (shorterthan Imetre),thelaunching conditionsdominatethe

21

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Figure11Thetransmittancecurve for a10mlongfused silicasingle fibre.

emergentconeproperties.Another characteristic ofthcemergentconepertainstotheoogle at whichtheemergentcone exits the fibre,itwouldexititattheanglespecifiedbytheNA.

regardlessof theangle at whichthecone of lightenters thefibre.Thisisduepnmarllyto thefactthat thecoherent propertiesofthe optical field in the entryconecannotbe related tothecoherence propertiesoftheopticalfield intheemergentcone,i.c optical fibresare incoherent(32).

Even thoughlightmayente r theopticalfibrewithits intensity evenlydistributed aboutitscone,thelightconethatexitsthefibre veryoften doesnothaveaneven distribution cf'intensity.Wecan lookat tbe intensitydistributionin theemergent cone by simplyplacing a piece of cardboardabout 20 emfromtheoutputend of the fibre.Ratherthanseeingan evenly distributed circleoflight,we wouldsee symmetrical lightpatternslikethoseshown in AppendixB.These aremanifestationsof the socalled'propagative modes'of optical fibre.Thismeansthat although light enters thefibre ata continuous distributionof angles, itcanonly propagatethrough the fibreatcertainangles.This is becauseof interference effectsarisingfrom the coherentnature of laser light.Thesepropagativemodeswillbe discussedin detail in Appendix B.Thesingleoptical fibrethatweusedinourexperiment isasinglemultimodefibrefromOriel.it has acorediameterof J000urn.OpticalfibresthaI

22

©

Figu re12Some of the modes seen fromour optica lfibre.

ellcwcnty one mode to existinthe fibrearecalled singlemode (monomode)fibres.Their corediametersrangefrom51010IlID,theyaregenerally usedror communication purposes. Thenumberandthetypes of modespresentinan opticalfibredependsnot justonthe dimension ofthe fibre.hut also onfactorslikelaunchingconditions,stress in thefibreand bendingof the fibre.Launchingconditionsinclude factors liketheangleof the entry cone oflight(preferable 10haveitat the focal pointortheimagedistanceof theinputlenses) and the amount of core surface itoccupies on entryintothefibre.The above conditionsthat affect the mode distributions willhave tobecarefully optimizedifadesirableoutput from thefibreisto beachieved.Someof themodes seen fromourfibre are showninFigure 12.

An unoplimizedfibremayproducemodesthathavemostoftheir lightdistributedto thering oflhc modepatternwhereasanoptimizedfibre woulddistribucemost of thelight evenlyat the centralcircle.producing only a very faint ring aroundit. Thisisdesirableas the diaphragmin the collectionoptics collects onlylight fromthecentralpartoftheemergent cone. Someoftheother modecharacteristicsofanunoptimizedfibremay show upas time dependentintensityfluctuation,streaksof lines acrossthemode patternora combinationof theabove mentionedcharacteristics.

Thesolid angle of the cone oflightthatenterstheopticalfibre isdetermined bythe SCi of complexlens andthe apertureattachmentin the imaging fibre opticprobe.The apertureattachments2..-~solidcylindricalbrasspieces thatare15.7mm in diameterand 12.7 mm inlength witha holeboredaxially intothem.The hole maybeof6.35 mmor1.59nun in diameter. Theapertureattachmentsitspartially and freelyin theimaging fibre optic probe holderwiththe imagingbeamprobe.Choosing different holesizeswould allowscattering ofdifferentangularranges be collected. From now onwards,Ishallreferto the holeinthe cylindricalbrasspiece as the"collectingaperture"andthecylindricalbrass pieceasthe

23

Figure13Distancesofimagesfonnbythe FIgure14MagnificatIOn ofImagesfor imagingbeamprobefor objectsat various variousobjectdistances.

distances..

"aperture attachment".Asthesolidangleofthelightconeenteringthe probeislimitedby the aperture,lightthatis scatteredorreflectedfromother surfacesin the^g.1Sceltthatis outsidethis conewould notbecollected,thus reducingnoise.Sincetheangleof amythat enters the optical fibreis detennined bytheangleat whichthisraythat enterslheimaging fibreopticprobe,wecanmatchtheinpulconeinto theopticalfibretoits numericalaperture bychoosinganappropriateaperture size.Wehave alsoan aperture thutis25.4nuninlength and 1.59mmin diameter.This asmentioned earlierinthischapter,isused for determining the angle ofscatteredlight thatiscollectedbytheprobe.

If the directionofpolarizationof the scattered lightneedsto beknown,aperture attachmentswithpolarizerfilmare used.Thepolarizer filmisattached tothe frontend of theaperture attachmentasshowninFigure10.Sincetheapertureisfreetomoveinthe imagingfibre optic probeholder,rotatingthis polarizer aperture would allowusto varythe intensity ofthe scattered light collectedand10subsequentlydetermine its polarization direction.

Thecomplexlens systemin theimagingfibreoptic probe wouldimagea segment ofthemainlaser beamin thecell ontotheoptical fibre input surface.Theimagewillbe real anddiminished.Figure 13shows aplot ofthe imagedistanceforvariousobjectdistances cak:ulated&omthethin lensequationappliedtotheserieslensarrangementshowninFigun:

10.Figure 14shows the magnification or the images fordifferenlobjCCl distances.The

24

Figure15Couplingof lightrays at maximumefficiency

lensesarc 6.35 mm apan.In orderthat all the light froma sourceiscoupledto the optical fibreat maximumefficiency,we mustensurethat allraysfromthesourceenter the fibreat angles equal to orless thanthe anglespecifiedbythe numericalaperture[33]. In order to achievethis,a lensoran image-forming system,that focusesthe imageof the sourceonto theinput end of the fibre willbeneeded as the coupler.An approximatemethodof dctenniningthe focallengthoftheimaging system and the source size for maximum couplingto a fibreofa particulardiameteris showninFigure 15.Themagnificationof the imaging lensislIIe,if thesizeofthesourcecisequaltode/a ,where2d isthe core diameter, allthclightfromthesourcewillbecoupledtothe fibre.Therefore,fora givenmagnification lIIe,anysourcewithsizeless thanc=de/awouldhave all its rayscoupledinto a fibreof radiusd.Hlhesizeofthesourceislarger thanc,we wouldneedtoreducethe magnification so asto completelyimagethesource into the fibrecore.Reducingthe magnificationwould requiredecreasing the imagedistanceand increasingthe object distance.Butindoingso, we would increasetheangles at whichraysenterthe fibre,thuslosing raysthatenterthe fibre at angleslargerthan thosespecifybythe numericalaperture.

The imaging fibreoptic probe is mountedonthe fibreoptic probe mountvia an imagingfibreoptic probeholder,asshowninFigure8.Since theholderis held tothe fibre opticsmount byathumbscrew,it can freelyrotate about itsaxiswhenthethumbscrew is loosened. The fibreopticsprobemount is attachedto a EdmundScientificx-y-zlow profile micropositionerwitha metricmicrometerdrive.The imagingfibreoptics probecan therefore be linearlypositionedalong thexy.;axisand angularly positioned inthexz

25

• \ _t~

",.~

X

"V {\~.

/ \

\

plane. Thescatteredlightischanneledtothe output sectionofthe collectionoptics by means ofan opticalfibre.Theopticalfibreisa1000urndiametersinglefibre!from Oriel.Oneend of thisoptical fibre is attachedto theimaging beamprobe and the otherendleads to an opticalfibre holder inthe outputsection of the collectionoptics.Thiscompletes our discussionofthe inputend ofthe collectionoptics.

2.5.2 OutputEnd

The setup for thissectionis shown in Figure 16.The opticalfibre is attachedtothe opticalfibre holderby means of an adapter,and the holdermountson to axz mtcropcsntoner.The opticalfibre holderitself allows limited6y(pitch)and 6. (yaw) adjustmentso ihat,togetherwith themlcropositicner,theoutputend oftheoptical fibrecan bc positionedbothlinearlyin thex,zaxis and a, gularlyin the 6_yand 6. direction.

Scattered lightleavesthe optical fibre at a positionthat islocated at the focal point ofa collimatingconvex lens.The functionof thislens is to producea beam of collimated light whose direction of propagationis perpendicularto the planemirrors insidethe Fabry- Perot interferometer.The focal length of this convexlens is 50 em. The variablesize diaphragmafterthecollimating lens serves to controlthe amount of light and the size of light beam goingintothe Fabry-Perotinterferometer.By doing so,it limits only raysfrom the paraxial region into theFabry-Perotinterferometer. Also,moving the diaphragmin the y,zdirectionwouldallow usto choose a paththroughtheFabry-Perot at the flattestpossible regionsof themirrors.Sincemirrors. in generalare not equallyflat throughouttheir surfaces.

itisimportant thaI the lightbeam select the flattest parts ofthe mirrors so thatthey can maintainas higha parallelismas possiblewith each other.Thiswouldallow us to optimize thefigure (variationinthe surfaceflatness)finesseof the interferometer.Ifdis the mirror (plate)separationand!:J.d isthe variationof tile plateseparationdue to variationsin surface flatnessgiven by!:J.d;~,thenthe figurefinesseis givenbyF,;~.

To analyzethe spectrum ofscattered light,weuse aBurleigh piezo-electrically scannedFabry-Perotinterferometer.The Fabry-Perotinterferometer is essentiallymadeup of2 highly parallelflat mirror plates facingeachother and separatedby a distanced.lfan

'Not to be confusedwith singlemode fibre.This singlefibre is a multimode fibre.

27

extendedsource (i.e source with diameters ofatleasta fewrom)is used to sendanincident beamoflig htintothe Fabry-Perot interferometer.a concentricringpaucmwillbeseen »r theoutputoftileinterferometer.Bright circularfringes~~~nifyconstructiveinterferenceand darkfringes signify destructiveinterference.As we chancethedistance oftheplate separationd.theopticalpath lengths of theinterferingrays change nndraysthath..-xJ interferedconstructivelybefore maynow interferedestructively.Where we hadseenbright fringesbefore.we maynowsee dark fringes andvice versa.IfwemoveIheplates continuouslyandgradually closer together,we willsec theconcentricring panemeoll:lpsing intothemiddle.Forabeamoflight fromavery smallsource (less thanIromin diameter], ratherthanseeing concentric ring patterncollapsing,we wouldsec a sinJ,;lespotofliJ,;ht blinkingastheplateseparationiscontinuouslychanged.This spotofliJ;:htdoesnut disappearinstantaneously,itshrinks beforedisappearing andthenreappearsagain.

Ifourextendedsource consists ofnotjust onefrequency oflightbut a rangeof frequencies,we wouldinadditiontoseeing bright concentric rings (forslrongcst frequencies)also sec weaker intensityconcentric rings(fromthe weaker frequencies) between thebrightones.This is becausethedifferent frequencies requiredifferentoptical path lengthsforconstructiveand destructiveinterference.Foraverysmallsource. wewould see weakerspots appearing inbetweentheappearancesof the brighterones as theplate separationischanged.Fromthis,we can see that the Fabry-Perotinterferometercanbeused as a highlydiscriminatingopticalfilter.Selectingdifferentplmeseparationswouldallowus to selectivelychange thefrequencyoflightthatgetsthrough the interferometer.

InourFabry-Perotinterferometersetup.a verysmallextendedsource(output from optiefibre) isusedand asetcfpiezoelectric driverschangestheplate separationas the Data Acquisition System(DAS) scans lIlescatteredlightspectrum.Thetotaldistance thatthe piezoelectricdrivers moveinone scanis separatedinto640 steps, Each of these steps correspondstoone channelin theDAS.After eachstep.thepiezoelectricdrivers will stop for a specifiedamountoftime to allowthe DAS toacquire data. Thisis called thechannel dwelltime(specified in~sec).Alargcrdwelltime maybeneededifthe signals arc weakand a shorterone maybechosenifthcsignals are strong.Since eachchannelis associatedwith adifferent platesqwation,they can thereforebecalibratedtothefrequency(orwavelength)

"

of light that getsthroughthe Fabry-Perotinterferometer.Calibrationis done by first calculatingthe free spectralrange (FSR)of the Fabry-Perotfromthe plateseparationusing the formulaFSR"~,for air n is1 andcis thespeed of light. Dividingthe FSR by the numberof channelsin one FSRwouldgiveus thefrequencyshift foronechannel, e.g a plate separationof 110 mm wouldgive a FSR of 1J6 GHz.For256 channels per FSR, one channelwould thereforebe equivalent to5.31 MHz.

Optimizationof theFabry-Perotinterferometer is done throughthe drift andfinesse controls in theDAS.The drift control in the DAS automaticallylockson to thefrequency of the referencebeam'and corrects for any axialdrift of the interferometercavity or frequencydrift fromthe laser.The finessecontrol optimizesthe figurefinesseofthe Fabry- Perotinterferometer by actively tilting the piezoelectricmirror mountso astomaintain minimumvariation inplateseparations across the beam diameter.A variation in the plate separationacross the beamdiametergivesrisetoa phase variationin thetransmitted rays, resulting in a lossof the figure finesse,just asin the variationofthe mirror's surface flatness. The optimizationis initiated whenthe DAS registers an intensitydropin the referencebeam.This isdonebycomparing the intensity inthecurrentscanfrom the previousscan.If the intensitydrop islargerthan aspecified value,the piezoelectric drivers mountedmirrorwouldbe tiltedthroughvariousanglesto attemptto regainthe intensityloss.

Once the intensityrises again, the optimizationprocesswill stop.Thefinessecontrolalso helpsin compensatingfor any loss in thefigurefinesseduetominutevariations in the solid anglecrure emergentcone.These angularvariationsin the emergentcone are generallydue to thermal ormechanical(vibrations)effectsin the collection optics.Sincethe reference beam follows the same propagationpathasthe scatteredlight,optimizingon the reference beam would consequentlyyield optimization forthe scatteredlight. The mirrors and piezoelectricdriversare mountedon a Super-Inverframework.Becauseofits zerothermal coefficientof expansion ncarroom temperature,the Super-Invarmaterial in the framework wouldhelp minimizefrequencydrift in theFabry-Perot interferometer.A temperature controllerfor the Fabry-Perotinterferometerisavailable if temperaturefluctuation in the

"The Rayleighlinefromthescatteredlight is too weakto be used for this purpose.

29

environment surrounding theinterferometer affectsits operations.

A 45 cm cameralensfocusesthecollimatedbeamof lightfromthe Fabry-Perotto a 200J.\m pinholebefore itreachesthe PhotomultiplierTube(PM1) . 111epinholeisplaced atthefocalpointof the cameralens.Thepurposeof the pinholeistolimittheangularmnse of theraysfromthe Fabry-PerottothePMT.whichhelps to improve00thewavelen gth resolutionof the Fabry-Perot. Ameasure ofthi!!effect ls calledthe pinhole finessedefined asF, • (4'-op)l(Q2d) ,wherefisthefocallength ofthc: cameralens.A..is the liGilt wavelengthandathe diameterofthepinhole [34}. Thenetfinesseof theFabry-Perot interferometer is thereforea combinationof thereflectivityfinesseF,.thefigurefinesse

I:;

and thepinholefinesseF,.The net(instrument)finesseF,is given as follows:

Otherthanthe singlefusedsilica fibreusedfor scatteredlight ccllccucn,I have also foundittobeusefultousealargerdiameter liquid)lightguide10performcoarsealignment to theFabry-Perotinterferometer.Thelight guide is3 mm in diameterand has anumerical aperture of0.47( 28"), italso possessesgoodtransmittance forwavelengths from 250 nm to700run.Becauseofthesccharacteristics,it can transmital:U'ge quantityoflightfromthe laserto theposition wheretheoutputend ofthe singlefibresits.This is donebyremoving the adapter(Figure 16) withsingle fibre from the optical fibreholderand replacing itwith an identicaladapterwithaliquid lightguide.Aligningtothis extendedsourcewouldnarrow downconsiderablytherangeofadjustments requiredfor the alignmentofthe single fibre's outputUsing this bright 514.5nmwavelengthextendedsource, we are ableto align the Fabry-Perotinterferometermanually by lookingattl1ebehaviouroflhe lightbeamcoming out of theinterferometer, while itis beingscanned.Whenproperlyaligned', we shouldbe able10seean imageof distinct collapsing rings atthe backpinhole position.Afierthisis

'Essentially a optical fibre with a largecorefilled with a non-toxicanaerobic liquid.

"lbe plates arestillnotparalleltoeachotherat thisstage,buttheyare parallelenough10 createaninterferencepatterncentredat the pinhole.

30

done,thesingle fibre witlt its adapterwillbe put back intothe opticalfibre holder and finer adjustments can be madethereafter to theinterferometerand itsoptics.These fine adjustments are usually made whilethe DAS acquiresanddisplays a spectrum ofthe reference beam. This methodofcoarseadjustmentfollowedby finer adjustmentis especiallyuseful when theplate separation in the interferometer is changed.This often resultsin a gross misalignmentof the interferometer.

TheDASusedin ourexperimentis a microcomputerbaseddata acquisitionsystem, design and developedbyOrlando Vazquezinthislaboratory.The software that controls this systemcan beeasilymodifiedor upgradediftheneed arises. The microcomputerused in this system isanIBM compatible80386DXPC, it collectsdata from thePMT throughadata acquisitioncardand controlsthepower amplifiertothe piezoelectricelements in the Fabry- PerotthroughDigitalto Analog Converters on anInput/Output Card. ThePMTis water cooledto maintainlow darkcounts. Electrical pulses generated from photoelectriceffect in thePMT arcsentthroughanamplifier/discriminatoranda pulseinverter before they reach the data acquisitioncardinthemicrocomputer.This concludes our discussionoftheoptical setup in our experiment.

2.6The GIISScatteringCell

Thegas scattering cell is thecentralcomponent of ourexperimentalsetup. Itis the placewherethe gas tobestudiedis housed, where the gas canbesubjected to a temperature gradie ntand where light scatteringoccurs.The gas scattering cell is designed and constructed by Dr.MJ.Clouterandassembledby me.

The designand thedimensionsofthegas cellare shownin Figure 17.ftis essentially madeup of a cylindrical stainlesssteel tubular bodywith copper plate covers at the top and bottom.TIlegoodthermalconductivityof the copperplate makesit easy for heatto flow into and outofthecell.Thebottom copperplateacts asagoodheat sink,it is cooledby running water throughcopper tubings attachedtoit. The water is cooled by runningitthrough a Lnuda constant temperaturebath and refrigeratedcirculator, model K-2/R.The top copper plate acts asIIhcat source for the temperaturegradient,the heatinghere is providedby a simplebeaterribbon. There is no temperature controlfor the heat sourceand temperature adjustmentsis madebyinput voltageadjustmentsthrougha Variac. Temperaturegradients

31

Solder jllinl

·S\a;nlasaa: 1 O.t5O"by.O. lOO"

...

...illl _ _

..-

r-

O.SOO"·

,

e.•

SO{ •

.- ",-;'.-

~ :~:~f- + ~f~ ~,:: -~~~

'---~, .~;ht~ ,,?wi~}'I~f:

^.",1

3·~

' 1

""I(

I

Ftgurc17Gasscatteringcelldimensions.ThegascellhasIront and back Mylarwindow'S.

createdbytheheat sourceandsinkcanbe maintained for aperiodofupto 3:0 5 hours.

Since stainlesssteel haslowthermalconductivityandhigh;;lcchan:cllistrength,it allowsferthe constructionofacellwith thinwalls(1.6mmor0.063inch)amiyet withthe abilitytowithstand highpressures.Thecellwalls.beingofJowthermalconductivity,allow ustoreducethennalconductionalongthestainlesssteel tubelengthto alow levelso asto pennitmaintenanceoftherequiredtemperaturegradientswith modestpowerdissipationin the topheater. To minimize walleffects,we wantthe walls10befar awayfrom the centre of thecell.But this requires aiarger volumeand thusthickerwalls tomaintainmechanical stability.The presentdesignofthe gas cellwallsseeksacompromisebetweenthe needfur lowthermalconductionalongthelengthofthe celland theneed10minimiz.c walleffects while at the same timekeepingthe celltoa reasonablesize.Theb~"01Tll:1J'yofthecell

)2

provides a cylindrically symmetric volume of gasthatis 76.2 mm (3.00 inch)in diameter and 76.2mm(3.00inch)inheight. This is(0ensure that minimum wall effects are present utthe centre cfthecell.wherelight scatteringis to take place.The gasis channeledinto the cellthrougha1.6mm(O.063inch) diameter stainlesssteel capillary tube. The sulphur hexafluoridegas usedin thisexperimentis suppliedby MathesonGas Productsanditis 99.8

%pure.

Allthe cell windows are made from0.1 mm (0.005 inch) thickMylar.Its transparency and strengthmake Mylara good choice as materialforthe windowsand inthe present arrangement, easilywithstoodpressures of upto1.96 MPa (270psig)'.Sinceit is verythin,the top and bottomMylarwindowsallowgood heat transfer from the heat source to thegas and fromthe gasto theheatsink.In orderto look at scatteringclose to the bcnom oftilecell,we need to block off scatteringfromthe bottomwindow by insertingamask into tileslotatthe bottomcopper plate. The side windowsallow us 10look at thepathof themain beam endthe amountof reflectionsandscattering that occur inside thecell.Significant amounts of reflections and scatteringof the main beam do occur at the bottomwindow.

especiallyifthe mainbeamisnot incidentonto it perpendicularly.These stray light rays may be deflectedfrom thewallsoftheeell and into the imaging fibreoptic probe.eventhough thewallsarc paintedblack.

~14.7 psia= 14.7 +0.0psig-O.lOIMPa,1MPa"" lxI~Pa.

33

Chapter 3

Simulatio n Of Scatt ered Ray Path s In SF, Gas With A Density Gra dient

a.t

tntrcdceuc n

Inanylightscatteringexperiment. observationofscaucrcdligjuoriginatingfromII pointsourceat one scatteringangleis oftenhighlydesirablebut inpractice not llltliinablc.

Inany ptactieallight scatteringexperiment.scatteredlightfromarangeof scatteringangles originatingfromII.regionof scatteringsitesis observedthroughlhecollectionoptics in order to attain an accceptablesignallevel.Inthe present experiment.the scatteredlight experiencesmanychanges in refractive indexasitpropagates throughandout oftbc g.as cell. The coneof scatteredlighllhat wouldhavebeenobservediftheprop.1gationpathefthc lightrayshadnot experienced any refractiveindex changebeforeitentersthe probe.would consequentlybemodifiedinourcase.Tofindout the rangeof scatteringanglesurulsitesth.u arebeing observed, a computersimulation of the ray pathspropagatingthroughthedensity gradient10 theopticalfibre wouldhavetobeused.Theanglesatwhichthescatteredmrs enter the optical fibre can also be found fromthis simulation.andthis wouldallowusto determine ifo ur scaueredlightemry concinto thefibreis withinthe acceptanceconeofthc opticalfibre.

Inorder to perform this computersimulation,wewouldfirstTM.'Cdto simulatethe steadystatedistributionofsome of the thermodynamic variablesalongtheheightof the cell, thisincludes temperamre,thclTl'lOCOOduetivityand density.Fromthese simulation.wewould alsobeableobtainanestimateofthetemperatureandsound velocitygradientsatdifTcn:nt heightsinthecell.Fromthe densitydistribution,wewouldbeableto findthe refractive index distributionatsteadystate.These distributionsarc obtainedfroma simple 2

34

0 0 0 0

Z40

n o

^• t.ocaljollwh~",

eIr~timenl lOOk

zoo

₀₀ ^place

,.0

o~

0

10 15

zo

Z5 30

Tern lurc (dc«:cCelsills) Figure18VapourPressure curveof SF.

dimensionalnon-convectiveheat flow model ofSF,gas subjected(0atemperature gradient in thecell.After!.herefractive indexdistributionis obtained.wecanperformaray tracing ofell tbepossiblescattered raypathsfromallpossible scatteringanglesandsites.Fromall

---

these mypaths.wewouldchoose only thoseraysthat....'ere abletopassthrough the collcctingapertureforfurtheranalysis.

To beginourdiscussion onthe computer simulationofthermodynamic:variable distributionsinthecell.wewillfirstlookat somecf thethermodynamic propertiesofSf, andtheequationsthat areusedtodescribethem.

3.2The Sulphur HcxaOuoridcGas

Most of the physicalpropertiesof SF,(jS] areshown in AppendixA.Thevapour pressurecurve ofSf,from·50·C1045.6"Ccan befitted10the followingequation[3SJ,

35

log1~41.:::P,.,.. "0.87652594-816.~99S +0.029287342T-0.40107S49x lO-~T2

+0.7142667(31 9.~2 -TJIOg(319.802-T)^• (15)

whereTisin Kelvins.This vapourpressurecurveis showninFil\urc18. Theregionswhere someof our experimentstookplace,withrespect to thevapour pressure curve.arc;tlSIl shownin Figure18.

The equationof statefora nonidealgasmayberepresented byvirialcoefficientsas follo....'5[36J.

(16)

whereZ is thecompressibilityfactorandthe secondvinalcoefficientor SF.is given as Iollc....'5[19].

Bcn=B-~-~

_CRT

r '

⁽¹⁷⁾

where~"'I.064xlQ'4(mlmol·'rMPa,Bois2xIO-lm'mot'andc '"1.24x10'(mKymol:^l• Ifonlythe secondvirialcoefficientisusedinequation(16).itis accuratetowithin1%for densitieslessthan100kgm-l(19].

Therelationsbetweenthermal conductivityand temperatureforgaseousSF. can be expressed asfollows[19J.

K=4.84 >cl O·sTc"uO+3.3Se-r)

'.

36

(10)

whereT,is the triple pointtemperat ure.Equa tion(18) is onlyvalid to within 5% in the temperature rangeof 230Kto 1000K.Itshouldbe noted from equation (18),thatthe thermal condu ctivity doesnet dependon density.

Themolecularweight ofSF₆is 146.07g mol",itis one of the heaviest gasesknown.

Itis colorless,odoorlcss.tasteless.Sinceallthe valenceelectrons of the sulphuratom are sharedwith those ofthe fluorin e atom, SF6posses seshigh chemical stability.SF6is also a substance of excelle nt electrical characteris tics:its high dielectric strength has made it one the mos tcomm onlyused electrica l insula tors,especia lly in the liquidstate.

Thc computersimulatio nofathermo dynamic model of our experiment,tobe presented inthe followingsection,will bebased on the preceding equationsdiscussed and docsnot claimto accurately represent theexperimentalconditions.This modelshouldbe treatedas thc simplestnon-ideal gasapproximationto the actualconditions.Itexhibitssome of the qual itativefeatures thatare expected ofthe experimentand should be regarded only as an initial approachto theproblem .

37