Analytical Calculation of Stimulated Brillouin Scattering in Magnetic Fields Applied to n-I

phys.stat.sol.(b)209,485(1998)Subjectclassification:78.35.+c;S7.13

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AnalyticalCalculationofStimulatedBrillouinScatteringinMagneticFieldsAppliedton-InSb1󰂆

K.L.Jat

DepartmentofPhysics,GovernmentDegreeCollege,Manasa-458110(M.P.),India(ReceivedJuly3,1998)

Forthestudyofparametricexcitation,wehaveconsideredthattheoriginofStimulatedBrillouinScattering(SBS)nonlinearinteractionliesinthethird-orderopticalsusceptibilityinacentrosym-metric,dopedsemiconductorwhichissubjectedtotransversemagneticfield.Thethird-orderopti-calpolarizationinaSBSsystemarisesduetononlinearcurrentdensityandacousto-opticalstrainofthemedium.ThedisplacementoflatticemotionandthresholdexpressionsaredeterminedandconditionsfortheonsetoftheSBSareobtained.Theinducedacousto-opticalpolarizationandeffectiveBrillouinpolarizationaredeterminedusingacoupledmodescheme.UsingtheeffectiveBrillouinpolarizationsoachieved,thetransmittedintensityandefficiencyoftheBrillouincellhavealsobeencalculated.Theeffectofwavenumber,electricfield,dopingandmagneticfieldondiffer-entparametersisalsostudiedandnumericalestimationsaremadeforn-InSbat77Kdulyshinedbyapulsed10.6mmCO2laser.Thelatticedisplacementissignificantlyenhancedbywavevector,electricfieldandtransversemagnetostaticfield.Itisobservedthattheacousto-opticalpolarizationincreaseswithmagneticfieldwhilethenonlinearinducedpolarizationdecreases.TheeffectiveBril-louinpolarizationincreaseswithwavenumber,electricfieldamplitudeandmagneticfieldwhichisrequiredtoachieveanoptical-phase-conjugationprocess.

1.Introduction

Nonlinearopticsdevelopedintoasignificantsubfieldofphysics.Itwasopenedupbytheadventoflaserwithhighpeakpowers.Theavailabilityoftunabledyelasershasmadedetailednonlinearspectroscopicstudiespossiblethroughoutthevisibleregionofthespectrumfrom0.35to0.9nm.Conversely,nonlineartechniqueshaveextendedtherangeoftunablecoherentradiationharmonicgeneration,parametricdownconversionandstimulatedBrillouinandRamanscatteringindifferentorders.Nonlinearopticalprocessesareessentialinmanyapplications.Modulatorsanddemodulatorsareusedinopticalcommunicationsystems.Saturationandgain(orexcitationofparameters)playanessentialroleinobtainingultrashortpulses.Thedomainoftime-resolvedmeasure-mentsmaybeextendedtothefemtoseconddomain.Thisopensupnewpossibilitiesinmaterialscienceandchemicalkinetics.Thefieldofnonlinearspectroscopyhasmaturedrapidlybutstillhasmuchpotentialforfurtherexplorationandexploitation.Theappli-cationsinchemistry,biology,medicine,materialstechnologyandspeciallyinthefieldofcommunicationsandinformationprocessingarenumerous,seee.g.[1].

ThestudyofStimulatedBrillouinScattering(SBS)insolidshasbeenanactiveareaofresearchduetoitsmanifoldtechnologicalapplicationsinthefieldofquantumelec-󰂆WorkdoneundertheUGC(Bhopal)minorresearchprojectªNonlinearOpticalSusceptibilityCalculationsinSemiconductorPlasmaº.

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486K.L.Jat

tronicsandacousticspectroscopy.TheSBSmechanismshavebeenemployedinhighpowerlasersystemsforimprovementsinamplifiers,isolators,prepulsesuppression,en-ergyextraction,pulsecompressionetc.[2to5].SBSisalsoregardedasoneofthemosteffectivenonlinearopticalphenomenaresponsiblefortheoccurrenceofnonlinearopti-calphaseconjugation(NOPC),duetoitspurityandhighconversionefficiency[6].Recently,ithasbeenobservedthatinadopedcentrosymmetricsemiconductorcrystalthetransversemagneticfieldisfoundtoreducethethresholdpumpfieldrequiredfortheoccurrenceofSBSinhighlydopingregimes[7].

InaSBSsystemitisalsoobservedthatthegainissignificantlyenhancedunderhighpowerpulsedexcitationbelowthedamagethresholdandundertheinfluenceofatrans-versemagnetostaticfieldwhenthecyclotronfrequencyislessthantheacousticwavefrequency[8].

Asfarastoourknowledgenoattempthasyetbeenmadetostudythelatticedispla-cement,Brillouinpolarization,acousto-opticalpolarizationandBrillouincelldesigninatransverselymagnetized,dopedsemiconductor.Inthefieldofnonlinearoptics,itisprovedthatthescatteringoflaserbeamfromsoundinadopedmagnetizedsemicon-ductor,affordsaconvenientmeansofcontrollingthefrequency,intensityanddirection-alityofanopticalbeamaswellastheamplificationprocess[9].Recently,JatandGhosh[10]reportedanalyticallythestudyofSBSphenomenaandtheconsequentam-plificationprocess.

Inthepresentinvestigation,thehydrodynamicalmodelofplasmasandcoupledmodetheoryhavebeenusedtostudyanalyticallytheSBSofanelectromagneticmodepropa-gationinamagnetoactivesemiconductorplasma.Itisassumedthatinann-typehighlydopedcentrosymmetricsemiconductorcrystal,thethird-orderopticalsusceptibilityori-ginatesfromthefiniteinducedcurrentdensity(cd)anacousto-optical(ao)polarization.Thecrystalissubjectedtoatransversemagneticfield,andtheeffectofdopingiscon-sideredwiththeplasmafrequencywpcoveringtheentireinfraredspectrum.Usingthecoupledmodetheoryofplasmas,thethreshold󰂅E0th󰂆conditionfortheonsetoftheBrillouininstabilityandeffectiveBrillouinpolarization󰂅󰂅Peff󰂆B󰂆isdetermined.Thedis-placementoflatticemotion(u)andtheelectronfluidvelocitiesintheCBband(v0xmdv0y󰂆oftheBrillouincellhavealsobeenstudiedinthepresenceofpumpandmagneto-staticfields.Thetheoryisbasedontheparametricexcitationsorcouplingofthreefinitewavesandthetimevaryingfieldwhichgivesrisetoacousto-opticalstrain,whichinturncandrivetheacousticwavesinthemedia.

2.TheoreticalFormulation

ForstudyingtheparametricexcitationoflaserbyBrillouinmodeinamagnetizeddopedsemiconductor,arisingduetothenonlineareffectiveopticalpolarization(Peff󰂆,thehydro-dynamicmodelofhomogeneous,one-component(electrononly),semiconductorplasmaofinfiniteextentisconsidered(i.e.kl(1Ykbeingthewavenumberofacousticmodeandlthemeanfreepathoftheelectrons).Thetheoreticalformulationstartswiththecalculationofthedisplacementoflatticemotion󰂅u󰂆andthetotalcurrentdensity󰂅J󰂆fortheresonantStokescomponentarisesduetononlinearinteractionofthewaves,followedbystudyingtheeffectiveBrillouinpolarization󰂅Peff󰂆Bthroughnonlinearpolarization󰂅Pcd󰂆arisingduetononlinearinducedcurrentandacousto-opticalstrain󰂅Pao󰂆.Theentiretheoreticalanalysisisdividedintothefollowingthreesubsections.

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2.1Totalinducedcurrentdensity

Inordertocalculatethetotalinducedcurrentdensity󰂅J󰂆,weapplythepumpelectricfieldE0exp󰂉p󰂅k0xÀw0t󰂆paralleltotheacousticwavevectorka(alongthex-axis),andadcmagneticfieldB0,normaltok1alongthez-axis.Asthecrystalisassumedtobecentrosymetric,theeffectofanypseudo-potentialcanbeneglectedforanalyticalsimpli-city.Thenonlinearpolarizationarisingduetotheacousto-opticalstrainandthenon-linearinducedcurrentdensityisobtainedbyemployingthecoupledmodescheme.Thefollowingbasicequationsareemployedfortheanalysis:

d2uCd2udu

󰂈FsYÀ󰂇2Ga

dt2rdx2dtwhere

Fs󰂈

1d

e󰂅h2À1󰂆󰂅EeffÁE*1󰂆Y2rdx󰂅2󰂆󰂅3󰂆󰂅4󰂆󰂅5󰂆󰂅6󰂆󰂅1󰂆

dV0dV0e

EeffY󰂇V0󰂇nV0󰂈mdtdxdV1dV1e

󰂅E1󰂇V1ÂB0󰂆Y󰂇nV1󰂇V0󰂈mdtdxdn1dn1dV0dV1

󰂇V0󰂇n1󰂇n0󰂈0YdtdxdxdxPao󰂈Àe0󰂅h2À1󰂆ru*ÁEeffYdE1n1e󰂅h2À1󰂆

󰂇󰂈Eeffr2u*Yee1dxwhere

Eeff󰂈E0󰂇V0ÂB0X

Equation(1)representsthelatticemotioninthecrystal,risitsmassdensityandu

thelatticedisplacement,Gathephenomenologicaldampingparameteroftheacousticmode,Ctheelasticconstant,htherefractiveindexofthecrystal,ethedielectriccon-stantofthemediumandE1thespacechargeelectricfield.Equations(2)and(3)repre-sentthezerothandfirst-orderoscillatoryfluidvelocitiesofelectronswitheffectivemassmandchargee;nistheelectroncollisionfrequency.Ineq.(2),EeffrepresentstheeffectiveelectricfieldwhichincludestheLorentzforce󰂅V0ÂB0󰂆inthepresenceoftheexternalmagneticfieldB0.Equation(4)isthecontinuityequation,wheren0andn1aretheequilibriumandperturbedcarrierdensities,respectively.

Equation(5)showsthattheacousticwavegeneratedduetoacousto-opticalstrainmod-ulatesthedielectricconstantandgivesrisetoanonlinearinducedacousto-opticalpolari-zationPao.Ataveryhighfrequencyofthefieldafrequencywhichislargecomparedtothefrequenciesofmotionoftheelectronsinthemedium,thepolarizationofthemediumisconsideredneglectingtheinteractionofelectronswitheachotherandwiththeatomicnuclei.Equation(6)determinesthespacechargefieldE1,wheree1isthepermittivityofthecrystalathighfrequency.IntheaboveequationswehaveneglectedtheeffectduetoV0ÂB1byassumingthattheacousticwaveispropagatingalongthedirectionofthelong-itudinalelectricfield,inInSbifkistakenalong[011]andthelatticedisplacementalong[100].Theelectricfieldinducedbythewaveislongitudinal.

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Theacousto-opticforcegivesrisetoacarrierperturbationwithinthemediumwheretheBrillouinscatteringprocessisactive.Inadopedsemiconductor,thisdensitypertur-bationcanbeobtainedbyusingthestandardapproach[11].Differentiatingeq.(6)withrespecttotimeandusingeqs.(2)and(6),onegetsthefollowingsimplification:

d2n1dn1n0e222\"Y\"󰂇nnÀk󰂅hÀ1󰂆󰂅Eeff󰂆xu󰂈Àikn1E󰂇w1p

me1dt2dtwhere

2

\"2wp󰂈wp

󰂅7󰂆

󰀒

󰀓

w2

1À2c2Y

n󰂇wc

\"󰂈eE0󰂇wcV0y󰂈e󰂅Eeff󰂆xYE

mminwhich󰂅Eeff󰂆x󰂈E0󰂇󰂅V0󰂇B0󰂆x.Here,wc󰂅󰂈eB0am󰂆isthecyclotronfrequencyand

wp󰂉󰂈󰂅n0e2ame󰂆0X5󰂊istheelectronplasmafrequencyofthemedium.WehaveneglectedtheDopplershiftundertheassumptionthatw0)n)kv0.Wehaveconsideredthelowfrequencyperturbationstobeproportionaltoexp󰂉i󰂅kaxÀwat󰂆󰂊,󰂅waYka󰂆character-izingtheacousticwavepropagation,whileV0variesasexp󰂅Àiw0t󰂆.

Theperturbedelectronconcentrationn1willhavetwocomponentswhicharedistin-guishedasfast󰂅n1f󰂆andslow󰂅n1s󰂆component,suchthatn1󰂈n1f󰂇n1s.Theslowcom-ponentisassociatedwiththelowfrequencyacousticwave󰂅wa󰂆,whilethefastcompo-nentoscillatesatthehighfrequencyelectromagneticwave󰂅w0Æwa󰂆.TakingonlytheStokescomponentofthescatteredelectromagneticwaveintoaccount,w1󰂈w0Æwaandk1󰂈k0ÀkaX

Forspatiallyuniformlaserirradiationjk0j%0yieldsjk1j%jkaj%jkj(say).

Weobtainthefollowingcoupledequationsfrom(7)underrotatingwaveapproxima-tion(RWA):

d2n1sdn1sdn*1f2\"\"󰂇nn󰂈ÀE󰂇wp1s2dtdtdxand

d2n1fdn1fn0ek22dn*1s2\"*\"󰂇nnÀ󰂅hÀ1󰂆Eu󰂈ÀE󰂇wX1feffpdt2dtme1dx󰂅8b󰂆󰂅8a󰂆

Itcanbeinferredfromeqs.(8a)and(8b)thattheslowandfastcomponentsofthe

densityperturbationsarecoupledtoeachotherviathepumpelectricfield.Thus,itisobviousthatthepresenceofthepumpfieldisthefundamentalnecessityforSBStooccur.

Fromequation(1)weobtainthedisplacementvector(u)oflatticemotionas

*e󰂅h2À1󰂆kw20jE0jjE1jjuj󰂈Y2󰂆jR*j2r󰂅w2Àwc0

where

220X5222

jR*j󰂈󰂉󰂅w2XaÀkVa󰂆󰂇4Gawa󰂊

󰂅9󰂆

Usingequations(8)and(9)weget

n0e0󰂅h2À1󰂆2k2E*0ÁE1A*n1s󰂈Y

2rR*󰂅10󰂆

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where

A󰂈

4

2

󰂅d21Àiw1n󰂆󰂅d2󰂇iwan󰂆1À

\"j2k2jE

5À1

Y

20X5222\"󰂈󰂅eam󰂆E0w2a󰂅w2Àw2󰂆Yd2󰂈w\"2E1cpÀw1,d2󰂈wpÀwa,Va󰂉󰂈󰂅car󰂆󰂊istheacoustic00

velocityinthemedium.Fromtheaboveexpression,itisclearthatn1sdependsuponthemagnitudeofthepumpintensity󰂅Iin󰂆,whereIin󰂈󰂉0X5he0c0jE0j2󰂊withc0theveloc-ityoflight.Thedensityperturbationsthusproducedaffectthepropagationcharacteris-ticsofthegeneratedwaves.

TheresonantStokescomponentofthecurrentdensityduetofinitenonlinearin-ducedpolarizationcanbegivenby

J󰂅w1󰂆󰂈neeV1x󰂇n1seV0xY

fromtheaboveRWA,onegets

J󰂅w1󰂆󰂈

iew2pw1E1

2w21Àwc

2222

iw2pee0k󰂅hÀ1󰂆w0jE0jE1A󰂇X

2rR*󰂅w2Àw2󰂆c

0

󰂅11󰂆

󰂅12󰂆

Thefirsttermoftheaboveexpressionrepresentsthelinearcomponentofthein-ducedcurrentdensity.Thesecondtermrepresentsthenonlinearcouplingamongthe

threeinteractingwavesviathenonlinearcurrentdensity.Thecomponentsoftheoscil-latoryelectronfluidvelocityintheconductionbandofthecrystalinthepresenceofpumpandmagnetostaticfieldsareobtainedfromeq.(3)as

jV0xj󰂈

and

jV0yj󰂈

ewcjE0j

X2󰂆m󰂅w2Àwc0

󰂅13b󰂆

20X522m󰂅w20Àwc󰂆󰂅n󰂇w0󰂆

ew20jE0j

󰂅13a󰂆

2.2EffectiveBrillouinpolarization

Tobeginwith,letustreattheinducedpolarization󰂅Pcd󰂅w1󰂆󰂆asthetimeintegralofthe

currentdensityJ󰂅w1󰂆

󰂅

J

Pcd󰂈Jdt󰂈ÀX󰂅14󰂆

iw1Usingeq.(12)andtheapproachofNeogiandGhosh[7],weobtainPcdduetotheperturbedcurrentdensity,

Pcd

2322\"2e2pw0k󰂅hÀ1󰂆jE0jE10w

󰂈X22rjR*j󰂅w2Àw2󰂆w1c

0

󰂅15󰂆

Inobtainingeq.(15)wehaveomittedthefactorA,becausethevalueofitis

1󰂇10À19%1inouranalysis.

NowitiswellknownthattheoriginoftheSBSprocessliesinthatcomponentofPcdwhichdependsonjE0j2E1.Thecorrespondingthird-ordersusceptibilityisknownasthe

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Brillouinsusceptibility.FromtheaboverelationwecandeterminethenatureofthethresholdfortheonsetofSBSsettingPcd󰂅w1󰂆󰂈0,(i.e.A󰂈0).Thisconditionyields

2

m󰂅w2222221a40Àwc󰂆jE0thj󰂈󰂉󰂅d2X1󰂇w1n󰂆󰂅d2󰂇wan󰂆󰂊2ekw0

󰂅16󰂆

Therefore,theinteractionbetweenthepumpandthecentrosymmetriccrystalwillbe

dominatedbytheSBSphenomenaatapumppowerlevelwellabovethethresholdfieldE0th.

BesidestheBrillouinpolarizationPcd,thesystemshouldalsopossesanacousto-opti-calpolarization󰂅Pao󰂆,arisingduetotheinteractionofthepumpwavewiththeacousticwavegeneratedinthemedium.

Thisisduetothefactthatthescatteringoflightfromtheacousticmodeaffordsaconvenientmeansofcontrollingthefrequency,intensity,anddirectionofanopticalbeam.Thistypeofcontrolmakespossiblealargenumberofapplicationsinvolvingthetransmission,displayandprocessingofinformation.Theacousto-opticalpolarizationisobtainedfrom(5)and(9)as

24222

e20k󰂅hÀ1󰂆w0jE0jjE1jjPaoj󰂈X

2󰂆22rjR*j󰂅w2Àwc0

󰂅17󰂆

Fromeqs.(15)and(17)weobtaintheeffectiveBrillouinpolarizationbyusing

󰂅Peff󰂆B󰂈Pcd󰂇Paoas

23

2222222\"wekw0󰂅hÀ1󰂆jE0jjE1jp

X󰂅18󰂆󰂅Peff󰂆B󰂈01󰂇

2󰂆2ww2rjR*j󰂅w2Àw10c0

2.3EffectiveBrillouinsusceptibility,transmittedintensity

andefficiencyoftheBrillouincell

Inordertoinvestigatethethird-ordereffectiveBrillouinsusceptibility,weusethefol-lowingrelation:

󰂅ceff󰂆B󰂈

󰂅Peff󰂆B

X

e0jE0j2E1

󰂅19󰂆

Substitutingthevaluesof󰂅Peff󰂆Bfromeq.(18)ineq.(19),wecanobtain󰂅ceff󰂆B.

Usingtheexpressionof󰂅Peff󰂆Bdeducedforaninfinitemedium,onecancalculatetheelectricfieldamplitudeETinacrystalcelloflengthL[12],withtheassumptionthatthesamplelengthisabouttwoordersofmagnitudegreaterthanthepumpweave-length,

ET󰂈ÀikLaej󰂅Peff󰂆BjX

󰂅20󰂆

Noweq.(20)canbeemployedtodeterminethetransmittedintensity󰂅IT󰂆byusingtherelations

IT󰂈󰂅1a2he0c0󰂆jETj2

as

IT󰂈k2L2j󰂅Peff󰂆Bj2a2he0c0e2X

󰂅21󰂆

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491

TheefficiencyoftheBrillouincell󰂅b0󰂆isobtainbyb0󰂈ITaIias

b0󰂈󰂅Lae󰂆2󰂅k2ajE0j2󰂆j󰂅Peff󰂆Bj2X

󰂅22󰂆

Eqs.(18),(19),(21)and(22)maybeusedtostudytheeffectiveBrillouinsusceptibility,transmittedintensityandefficiencyoftheBrillouincellmadeofacentrosymmetriccrystal.

3.ResultsandDiscussion

Inthepresentanalyticalinvestigation,thedisplacementoflatticemotion,effectivepolarization,transmittedintensityandefficiencyoftheBrillouincellarededucedinaheavilydopedmagnetizedsemiconductorcrystalduetononlinearcurrentdensityandacousto-opticalpolarizationprocess.Fornumericalappreciationthisanalysisisappliedtoaspecificcaseofacentrosymmetriccrystal,whichisassumedtobeirradiatedbya10.6mmCO2laser.

Itisawellknownfactthattheimportantpropertyattachedtothesolidstateplasmaisthatitretainsitsownphysicalpropertiesandyetattainstheplasmastateduetothepresenceoffreecarriersinsidethemedium.Theelasticpropertieswhicharerelatedtothedensityofthemediumdeterminethepropertiesofpropagation.Thefirstexperi-mentalobservationsofsoundwaveandotherpropertiesaremadeinInSbbyLibcha-berandVeilex[13].Thetheoryisalsoappliedton-InSbcrystalforanalyticalinvestiga-tion,becauseInSbisasingle-valleysemiconductorhavingalargedensityofmobileparticlesintheplasmacomparedtoothers,whileGaAsandSibotharemany-valley

Fig.1.Variationoflatticedisplace-ment󰂅u󰂆andthresholdelectricfield󰂅E0th󰂆withwavenumber󰂅k󰂆atwc󰂈1X6Â1014sÀ1

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Fig.2.VariationofeffectiveBrillouinpolarization󰂅Peff󰂆B(inmksunits)withwavenum-ber󰂅k󰂆atE0󰂈107VmÀ1andwc󰂈1X6Â1014sÀ1

Fig.3.Variationofacousto-opticalpolarization󰂅Pao󰂆andinducedpolarization󰂅Pcd󰂆withwavenum-bers󰂅k󰂆atE0󰂈107VmÀ1andwc󰂈1X6Â1014sÀ1

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493

semiconductors.ThebandgapofInSbisalsomatchedtothepulsewavelength10.6mmofCO2laser.

Thematerialandsystemconstantsaretakenas[14]:m󰂈0X015m0,wherem0isthefreeelectronmass,h󰂈3X9,r󰂈5X8Â103kgmÀ3,Ga󰂈2Â1010sÀ1,n󰂈3Â1011sÀ1,Va󰂈4X8Â103msÀ1,w0󰂈1X78Â1014sÀ1,wa󰂈1012sÀ1,k0󰂈5X92Â105mÀ1,ka󰂈2X08Â108mÀ1,andne󰂈2X44Â1024mÀ3,L󰂈10À4m,e1󰂈15X8,e0󰂈8X85Â10À12FCÀ1.Wenowfocusourattentiononthefactorsthataffectthedisplacementoflatticemotion.Variationoflatticedisplacement,polarizationandthresholdelectricfieldwithwavenum-ber,magneticandelectricfieldwasfound.Itwasfoundthatthethresholdelectricfielddecreaseswiththewavenumber(Fig.1),andthisisquiteobviousasthelower(lessthan4Â105mÀ1)thevalueofk,thegreaterwillbethedisplacement.Fig.1alsoshowsthatlatticedisplacementincreaseslinearlywithwavenumber.ThedependenceofeffectiveBril-louinpolarizationwithwavenumberisshowninFig.2.Itisseenthatthepolarizationincreasesparabolicallywithincreasingk.Fig3showsthevariationoftheacousto-opticalandinducedpolarizationwithwavenumberoftheincidentwave.Itisclearfromthefigurethat,asthewavenumberincreases,bothpolarizationsincreaseinaparabolicalform.Buttheorderofacousto-opticalpolarizationisalwayslargerthantheinducedpolarization.

Fig.4.Variationoflatticedis-placement󰂅u󰂆andeffectivepolarization󰂅Peff󰂆Bwithelec-tricfield󰂅E0󰂆atk󰂈105mÀ1andwc󰂈1X6Â1014sÀ1

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Fig.5.Variationofacousto-opti-calpolarization󰂅Pao󰂆andin-ducedpolarization󰂅Pcd󰂆withelectricfield󰂅E0󰂆atk󰂈105mÀ1andwc󰂈1X6Â1014sÀ1

TheeffectofelectricfieldamplitudeonlatticedisplacementandeffectiveBrillouinpolarizationcanbeobservedfromFig.4.Thedisplacementandpolarizationbothin-creaselinearlywiththeamplitudeofelectricfield.Thus,wemayconcludethatahighervalueofthefieldismoresuitableforSBSandamplificationofthescatteredsignal.Fig.5displaysthedependenceofacousto-opticalpolarizationandinducedpolarizationonelectricfield.BothtypesofpolarizationsintheSBSsystemincreaselinearlywiththeamplitudeofelectricfield

Fig.6to8depicttheinfluenceofmagneticfieldonthelatticedisplacement,effec-tivepolarizationandthresholdelectricfield.Fig.6illustratesthevariationoflatticedisplacement󰂅u󰂆andthresholdelectricfield󰂅E0th󰂆withmagneticfieldintermsofcyclotronfrequencyatfixedwavenumber.Itisfoundthatuisindependentatlowervaluesofmagneticfield,butitincreasesrapidlyathighervalues(largerthan1014).Itcanbeseenfromthefigurethatthethresholdelectricfielddecreaseswithmagneticfield.

ItisobservedfromFig.7thattheacousto-opticalpolarization󰂅Pao󰂆increaseswithmagneticfield,whiletheinducedpolarization󰂅Pcd󰂆decreases.Paobecomesmaximumatwc󰂈1X6Â1014sÀ1,butPcdgoestominimumatthisvalue.Fig.8showsthattheeffectiveBrillouinpolarizationchangesparabolicallywithincreasingmagneticfield.Thus,thresholdelectricfielddecreasesandlatticedisplacementandeffectivepolariza-tionincrease,sothatahighermagneticfield󰂅wc w0󰂆issuitabletoobtaintheSBSprocessforamplificationphenomena.

StimulatedBrillouinScatteringinMagneticFieldsAppliedton-InSb

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Fig.6.Variationoflatticedisplacement󰂅u󰂆andthresholdelectricfield󰂅E0th󰂆withmagnetostaticfieldintermsofcyclotronfrequency󰂅wc󰂆atk󰂈105mÀ1andE0󰂈107VmÀ1

Acloselookateqs.(19),(21),(22)andFigs.2,4and8revealsthattheeffectiveBrillouinsusceptibility󰂅ceff󰂆Borgain,transmittedintensity󰂅IT󰂆andBrillouincelleffi-ciencyofacrystalincreasewithwavenumber,electricfieldamplitudeandmagneticfield,respectively.

TheabovediscussionsandanalysisrevealsthatlargeBrillouingain(orsuscept-ibilityorpolarizationorlatticedisplacement)andcellefficiencycanbeeasilyachievedinmagnetizedcentrosymmetriccrystalsbyselectingpropervaluesofdependingparameters.Thus,thepresenttheoreticalworkprovidesamodelmostappropriateforthefinitelaboratorysolidstateplasmaandfortheconstructionoftheBrillouincellanddiagnosticoflatticemotionandpolarizationofsemicon-ductors.

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Fig.7.Variationofacousto-opticalpolarization󰂅Pao󰂆andinducedpolarization󰂅Pcd󰂆withmagneticfieldintermsofcyclotronfrequency󰂅wc󰂆atk󰂈105mÀ1andE0󰂈107VmÀ1

Fig.8.VariationofeffectiveBrillouinpolarizationwithmagneticfieldintermscyclo-tronfrequency󰂅wc󰂆at

5À17À1

k󰂈10mandE0󰂈10Vm

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AcknowlegementTheauthoracknowledgesthefinancialsupportfromUGC,Bhopal(M.P.)underaminorresearchproject(1997).

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