加偏置电场量子阱中的电光效应_英文_

1、量子光学学报14(1):9396,2008ActaSinicaQuantumOpticaArticleID:100726654(2008)0120093204Electro2opticalEffectsinElectricFieldBiasedQuantumWellsTANPeng,LIBin,CHENLI2bing(DepartmentofPhysics,FoShanUniversity,FoShan528000,China)Abstract:Byusingthecompactdensitymatrixapproachandtheiterativemethods,theelectro2opt

2、icaleffectsine2lectric2fieldbiasedquantumwellshavebeentheoreticallyinvestigated.Numericalresultshowsthattheelectro2opticaleffectsincreasewiththeenhancementoftheappliedelectricfieldFandthewellwidthdecrease.Alargeelectro2opti2caleffectcanbeobtainedbyadjustingthewellwidthLandtheappliedfieldF.Keywords:N

3、onlinearoptics;Quantumwells;DensitymatrixappoCLCnumber:O431Documentcode:A0IntroductionRecentlynonlinearopticalrquantumwellsystemareconsiderableinterestbecauseofstudyingpracticalappli2cationandasaprobefortheelectronicstructureofmicroscop2icmedia.Muchspecialattentionshavebeenpaidtothesec2ond2ordernonl

4、inearopticalproperties,suchasopticalrectifi2cation,second2harmonicgeneration,electro2opticaleffectandsoon,becausethesecond2ordernonlinearopticaleffectsarethesimplestandthelowest2ordernonlineareffectsandthemagnitudesofthesecondordernonlinearopticaleffectsareu2suallystrongerthanthoseofthehigher2ordern

5、onlineareffectsifthequantumsystemhavesignificantasymmetry13shownthatthesecond2orderopticalsusceptibili2tywas10to100timeslargerthaninbulkmaterials6.Kur2ginandYuhetalusedasymmetrycouplequantumwelltogetalargeopticalrectificationcoefficient7.Rosencheretal.suggestedthatthestepquantumwellcanbedesignedsoth

6、attheabsorptioncouldbedoubleresonant,theresultshowntheopticalrectificationcoefficientwas10timeslargerthanthatinbulkmaterials83.Theselargeopticalrectificationcoeffi2cientinAQWisduetosecond2orderopticalsusceptibilityhav2ingacubicdependencerelativetothetransitiondipolematrixelements,sothestrongsecond2o

7、rderopticalsusceptibilityisexpectedinAQW.ThesepropertiesoftheAQWhavethepo2tentialapplicationinfar2infraredlaseramplifies,photo2detec2tors,andhigh2speedelectro2opticalmodulators9,10.Inordertoobtainastrongsecond2orderopticalnonlinear,theinversionsymmetryofthequantumsystemshouldbebro2ken.Ingeneral,peop

8、legettheseasymmetricquantumtheotheristhroughtwoways,oneisbyusingadvancedmaterialgrowingtechnologytoobtainaasymmetricconfining,anasymmetricquantumsystemorderopticalsusceptibilities54.Inthispaper,electro2opticaleffectsinelectric2fieldbi2asedquantumwellsareinvestigated.Inthefirstpartthefor2mulaofelectr

9、o2opticaleffectisdeducedusingthecompactdensitymatrixapproachandtheiterativemethod;Inthesec2ondpart,thenumericalresultsarepresented.throughapplyinganelectricfieldtoasymmetricsystemtoget.Ithasbeenshownthatasymmetricquantumwell(AQW)displayverylargesecond2.Inthepioneeringwork,Gur21TheoryHere,weconsidera

10、ninfinitequantumwellwithawidthLnickandDeTemplefirstdiscussedtheMorsepotentialwellReceiveddate:2006204209Foundation:NaturalScienceFoundationofGuangdongProvinceunderGrant(No.Z06029431).Biography:TANPeng(19742),male,borninHunan.NowheisateacherinFoshanUniversity.Hiscurrentresearchinter2estsmainlyinclude

11、theopticalnonlinearitiesinlow2dimensionalsemiconductorsstructures.94量子光学学报14(1)2008dipoleoperatorMandthedensitymatrixas1-iP(t)=/e0()inthepresenceofaappliedelectricfieldFalongthepositivedirectionofthewellz.Intheindependentelectronapproxima2tion,thewavefunctionsfortheinitialstate1andthefinal8state2int

12、heconductionbandcanbewrittenas:t(2)+/e02(2)2ti2+(8)c.c+00/2,(1)(2)(2)wheremittivityofthefreespace,0istheper201(󰁤r)=SUc(󰁤r)exp(ik󰁤rt)<1(z)t󰁤|z|<arethelinear,second2harmonicgeneration,andopticalrecti2(1),ficationcoefficientrespectively.Theelectronicpolarizationoft

13、henthorderisgivenby:P(n)2(󰁤r)=SUr)exp(ik󰁤rt)<2(z)c(󰁤t󰁤|z|<(t)=STr(n)ez),(9),(2)whereSistheareaoftheinteraction.Finally,theelectro2opticaleffecteoeobtainedinthispa2(2)perisrelatedtotheopticalrectificationthrough0whereSisthecrosssectionareaofthewell,󰁤rtist

14、hepositionvectorinthexyplane,andUcandUodicfunc2caretheperitionsneartheconductionbandextreme.Intheeffectivemassapproximationtheenvelopefunction<1and<2satisfytheequa2tion(3)andaregivenbythelinearcombinationoftwoinde2pendentfunctionAi()andBi(),whereisdefinedbye2quation(4).-2eoe=(2)20.nr04(10)Byus

15、ingEquation(7)to(10),electro2opticaleffecteoecanbeobtained:432r0T2+2+1+12TT232m()+|e|Fz<(z)=E<(z)2<zdz|z|<=-wherem3,3(3(12-)E-|),(4)T2-+T2(12+)T2,(e󰂼F)(11)andedenotetheeffectivemassandchargeofthee28where|,12=12=|<1|z|<2-11|,s=(-)S(E-E)lectron.Asweknow,Equation(3)canbesolved

16、exactly.󰂼,12=|22Nexttheformulasofelectro2opticaleffectsinelectric2fieldbiasedquantumwellswillbededuced.Assumingthatamono2chromaticincidentfieldE(t)=/ethetime2dependentSchrodingeritisthesurfacedensityofelectronin+/3e-tisappliedtothequantumwells.Itisclearthattheproducto1212equalstthesystemandt

17、heevolutionofthedensitymatrixisgivenbyzeroforsymmetricquantumwell.When12,thepeakvauleoftheelectro2opticaleffectisgivenby(eoe)max322e=43(󰂼2)2.nr0H0-ezE(t),ij-ij(-0)ij,9ti󰂼(5)(12)where0istheunperturbeddensitymatrixandijistherelax2tionrate,forsimplicity,onlytwodifferentvaluesoftherelax2

18、tionrateareassumed:forthediagonalrelaxtionrate,ij=T12NumericalResultsandDiscussionsInthefollowing,thepeakvaluleoftheelectro2opticaleffectobtainedin(12)iscalculatednumericallyforvariousFandL.Theparametersareasfollows:m3andfortheoff2diagonalone,ij=T2.Equation(5)issolvedusingtheusualiterativemethod5,9,

19、10.(6)=0.067me,nr=3.2,(t)=with9t(n+1)n=0(n)(t)s=3×1024m-3,T2=T1=0.14psInFig.1,thegeometricalfactoroftheelectro2opticaleffectonofappliedfieldF.Itcanbe1212isplottedasafucti(n+1)H0,-iji󰂼(n)(n+1)ez,-ij.ijiji󰂼(7)seenfromFig.1thatwhenappliededfieldFiszero,thewellisasymmetricwellandthe

20、electro2opticaleffectequalstoze2ro;WhenwellwidthLisaconstantthepeakvauleoftheelec2tro2opticaleffectwillincreasewiththeinceraseofappliedfieldFbecausetheasymmetryofthequantumwellwillincreaseTheelectronicpolarizationP(t)andsusceptibility(t)causedbytheopticalfieldE(t)canbeexpressedthroughtheTANPengetal.

21、Electro2opticalEffectsinElectricFieldBiasedQuantumWellswiththeincreaseoftheappliedelectricfield.Hower,iftheappliedelectricfieldFistoostrong,thequantumwellswillbebreakdown495theappliedelectricfieldF,butdecreasewiththeincreaseingofthewellwidthL.Sowecanobtainalargeelectro2opticaleffectbyadjustingthewid

22、thLandappliedfieldF.andthismeansthereisasuperiorlimittoap2pliedfieldF.Fig.3electro2opversusthephotonen2Fig.1Thegeometricalfactoroftheelectro2optical2effect1212versustheappliedelectricfieldFfield.ergy󰂼electro2opticaleffectasafuctionofthefordifferentwellwidthL.fordifferentappliedfieldwhenthewe

23、ll󰂼widthis10nm.FromFig.3canbeseenthattheelectro2opti2caleffecthasapeakvaluewhen=21andtheresonantfre2quenciesofthephotonhavearedshiftswiththeincreasingoftheelectricfield.Averyimportantfeatureisthatthebiggertheappliedelectricfield,thesharperthepeakandthebiggerthepeakintensity.Astheappliedelect

24、ricfielddecrease,thepeakwillmovetotherightofthecurveandwilldisappeargradully.Itisshownthattheelectro2opticaleffectinelectric28fieldbiasedquantumwellsisover10timeslargerthanthatinbulkmaterials2Fig.2Thegeometricalfactor1212asafuctionof.Thesefeaturesmakeelectric2fieldbiasedquantumwellsmaterialsbecomeap

25、romisingcandidatefornonlinearopticalmaterials.thewellwidthwhentheappliedelectricfieldF=2×10V/m.73ConclusionInconclusion,byusingacompactdensitymatrixap2proach,theelectro2opticaleffectsinelectric2fieldbiasedquantumwellshavebeeninvestigated.Fromtheaboveresultscanbeseenthattheelectro2opticaleffecti

26、nelectric2fieldbi2asedquantumwellswilldecreasewiththeincreasingofthewellwidthL,butincreasingwiththeincreaseingoftheappliedfieldF.Byadjustingtheseparameterswecanobtainalargee2lectro2opticaleffectinelectric2fieldbiasedquantumwells.InFig.2thegeometricalfactoroftheelectro2optical72effectonofwellwidthLan

27、dtheap21212isplottedasafuctipliedelectricfieldF=2×.10V/m.ItcanbeseenfromFig2thatwhenappliedfieldFisaconstant,thepeakvauleoftheelectro2opticaleffectwilldecreasewiththeinceraseofthewellwidthL.FromtheresultinFig.1andFig.2,wecanseethat2thegeometricalfactor1212increasewiththeenhancementofReferences:

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