CONTROLOFLASINGFROMAHIGHLYPHOTOEXCITEDSEMICONDUCTORMICROCAVITYByFeng-KuoHsuADISSERTATIONSubmittedtoMichiganStateUniversityinpartialoftherequirementsforthedegreeofPhysicsŒDoctorofPhilosophy2016ABSTRACTCONTROLOFLASINGFROMAHIGHLYPHOTOEXCITEDSEMICONDUCTORMICROCAVITYByFeng-KuoHsuTechnologicaladvancesinthefabricationofopticalcavitiesandcrystalgrowthhaveenabledthestudiesonmacroscopicquantumstatesandemergentnonequilibriumphenomenaoflight-matterhybridsincondensedmatter.Opticalexcitationsinasemiconductormicrocavitycanresultinacoupledelectron-hole-photon(e-h-g)system,inwhichvariousmany-bodyphysicscanbestudiedbyvaryingparticledensitiesandparticle-particleinteractions.RecentlytherehavebeenreportsofphenomenaanalogoustoBose-Einsteincondensatesorforexciton-polaritonsinamicrocavity.Anexciton-polaritonisaquasiparticleresultingfromstrongcouplingbetweenthecavitylightandtheexciton(e-hpair)transition,andtypicallyisonlystableatalowdensity(˘1011to1012cm2orless).Atahigherdensity,ithasbeentheoreticallypredictedthatpairingofelectronsandholescanresultinaBCS-likestateatcryogenictemperatures,whichcanproducecooperativeradiationknownassuperradiance.Inthiswork,weexplorecooperativephenomenacausedbye-hcorrelationandmany-bodyeffectinahighlyphotoexcitedmicrocavityatroomtemperature.High-densitye-hplasmasinaphotoexcitedmicrocavityarestudiedunderthefollowingcon-ditions:(1)thesampleisphotoexcitedGaAs-basedmicrocavitywithlargedetuningbetweenthebandgapEgofquantumwellandcavityresonancetopreventcarriersfromradiativeloss,(2)thedensityofe-hpairsishighenoughtobuildlong-rangecorrelationwiththeassistanceofcavitylightTheFermilevelofelectron-holepairsisabout80meVaboveEg,and(3)thee-hcorrelationisstabilizedthroughthermalmanagement,whichincludesmodulatingtheexcitationpulselasertem-porallyandspatiallytoreducetheheatingandcarrierdiffusioneffect.Wehaveobservedultrafast(sub-10picoseconds)spin-polarizedlasingwithsizableenergyshiftsandlinewidthbroadeningsaspumpisincreased.Withopticallyinducedmultiple-lasingmodeswereproduced,withsequentiallasingtimedependingonenergies.Thesephenomenaareattributedtothespin-dependentstimulatedemissionfromcorrelatede-hpairs.Wefurtherperformedanon-degeneratepump-probespectroscopytoinvestigatedynamiccarrierrelaxation.Wetransientresonanceswithchangesindifferentialvitythatcanlastmorethan1ns.Theresonanceexhibitsapolarization-dependentsplittinginabout1meVundercircularlypolarizedpumping.Alltheaforementionedphenomenacanbeexplainedbythecombinationeffectofcarrier-inducedrefractiveindexchangeandthelight-inducede-hcorrelation.Ourresearchenrichesthestudiesofcouplede-h-gsystemsatroomtemperatureandahigh-densityregime;however,furtherexperimentsandtheoreticalworksarerequiredtoclaimandclar-ifytheformationofsuchcorrelatede-hpairsinahighlyphotoexcitedmicrocavity.Nonetheless,wehavedemonstratedthatmany-bodyeffectscanbeharnessedtocontrollasingdynamicsandener-giesinhighlyphotoexcitedsemiconductormicrocavities.Weexpectanimprovedunderstandingofthemany-bodyeffectresultedfrome-hpairingtohelpthedevelopmentofpolarization-controlledandwavelength-tunablelasers.CopyrightbyFENG-KUOHSU2016ACKNOWLEDGEMENTSIwouldliketothankallthosewhocontributedtotheresearchpresentedinthisdissertation.Fistofall,Iwishtoexpressmydeepgratitudetomyadvisor,Chih-WeiLai,forcountlessguidance,encouragement,andsupport.DuringmyveyearsinPh.D.,Ihavelearnedinvaluableexperiencefromhimsuchasproblemsolvingaswellascommunicationskill.Inaddition,hissupporttomynextcareerstepcouldnotbeoverstated.Secondly,Iwouldliketoappreciatemysecondmentor,WeiXie.Hewaspatientonclearingmyconfusioninresearch,andwasenthusiasticaboutdiscussingphysicswithme,whichenrichedmyphysicsinsightofmyproject.HealsosupportedmewhenIwasdepressedbothinresearchanddailylife.Honestlyspeaking,thetimethatthethreeofusweretogetherwasprobablymyhappiestperiodinmyPh.D.life.TherearemanymembersatMichiganStateUniversityIwouldliketopubliclythankwithhelp-ingmeingraduateprogram.ProfessorBrageGoldingandJohnMcGuirejoineddiscussionsformyprojectswithusefuladviseonresearchdirection.Mycommitteemembersalwaysofferedmegreatguidanceandsuggestions,soIcoulddeliberatetheresearchplanandlearninghowtopresentworkbettertopeopleoutsidemyRezaLoloeegavesupportswithequipmentassistanceallthetimeaswellasthefaithonthemeaningofmywork.BarryTigner,RobBennett,TomHudson,andThomasPalazzoloprovidedgreathelpwithassistanceonelectronicdevicesormechanicaltools.Thesecretariesinthedepartment,DebbieBarratt,KimCrosslan,andCathyCordassistedmealotwithaffairsingraduatelife.Ourgraduatedirector,ScottPrate,waswillingtohelpuswithanyproblems.IwanttoparticularlythankZeynepAltinsel,whogavemelotsofsupportonimprovingmyEnglishspeakingandcommunication.Withoutthem,mygraduateprogramwouldnothaveprogressedsmoothly.IwouldliketoacknowledgeGregTaftfromKMLabscompanywhotaughtmealotaboutthemode-lockedmechanisminlasingandprovidedgreatconsultationontechnicalproblems.Hissupportboostedourprogressontwo-colorpump-probeproject,andthisexperienceinitiatedmyvinterestintheultrafastlaserIamfortunatetohavemanyfriendsduringmygraduateyears,whohavesupportedthroughtraveling,concernandparties.Amongmyfriends,IwanttoparticularlythankmycloseclassmatesfromNationalTaiwanUniversity,whoarealmostmysecondfamilyfortheirconcernandsupport.Morethansevenyearsaftergraduationfromuniversity,Istillfeelourfriendshipstronglyeventhroughweareseparatedinmorethantenplacesnow.Finally,thisdissertationcouldnotbepossiblewithoutthesupportfrommyfamily,especiallymyparents'permanentlove.Althoughweliveatbothendsoftheearth,theyneverstopstandingbehindme.Ithankthemfortheirbackinme,andIlovemyfamilyforever.viTABLEOFCONTENTSLISTOFTABLES.......................................ixLISTOFFIGURES.......................................xCHAPTER1INTRODUCTION...............................11.1Macroscopicquantumphenomena..........................11.2Phasediagraminelectron-holephysics........................21.3Motivationandapproach...............................41.4Outlineandresults..................................6CHAPTER2BACKGROUND(LITERATUREREVIEW).................82.1Quantumwellexcitons................................82.2Microcavityphotons.................................92.3Exciton-polaritons...................................102.4Polaritonlasingandcondensation...........................132.5Polaritonsinpotentiallandscapes...........................162.6Correlatedelectron-holepairsatlargedensity....................192.6.1Meantheoryforexcitons........................202.6.2Condensationofelectron-holepairsatbandgap...............232.6.3Reviewofsuperradiance...........................252.7Opticalorientationandspinrelaxationinsemiconductors..............292.8Transfermatrixmethod................................34CHAPTER3EXPERIMENTALMETHODS........................383.1Samplecharacteristics.................................383.1.1Samplestructureandfabrication.......................383.1.2Samplecharacteristics............................403.2Experimentalsetup..................................423.2.1Imagespectroscopysetup...........................433.2.2Thermalmanagement.............................443.2.3Opticalcontrolandbeamshaping......................453.2.4Polarizationcontrol..............................453.2.5Temporalmeasurementsetup.........................473.3Conclusion......................................49CHAPTER4SPIN-POLARIZEDLASINGINAHIGHLYPHOTOEXCITEDSEMI-CONDUCTORMICROCAVITY.......................504.1Spin-polarizedlasingatroomtemperature......................504.2Spectralcharacteristics................................534.3Emissionpolarizationproperties...........................55vii4.4Dynamicsandenergyrelaxationofluminescence..................584.5Theoreticalmodel...................................604.5.1Carrier-inducedstrongnonlinearity......................614.5.2Spin-dependentstimulatedprocess......................634.6Discussionandconclusion..............................65CHAPTER5TRANSIENTDUAL-ENERGYLASINGINASEMICONDUCTORMI-CROCAVITY.................................675.1Spectralcharacteristics................................675.2Dynamicsofdual-energylasing...........................695.3Polarizationofdual-energylasing..........................715.4Discussion.......................................72CHAPTER6MULTIPLE-PULSELASINGFROMANOPTICALLYINDUCEDHAR-MONICCONFINEMENT...........................746.1Visualizationofharmonicoscillatorsinopticaltrapping...............746.2Dynamicsofmultiple-pulselasing..........................776.3Harmonicoscillatorspropertieswithdensitydependence..............786.4Theoreticalmodel...................................816.4.1Opticallyinducedpotentialandrefractiveindexchanges..........816.4.2Phenomenologicalmodeling.........................826.5Conclusionanddiscussion..............................85CHAPTER7OPTICALLYINDUCEDRESONANCESINASEMICONDUCTORMI-CROCAVITY.................................877.1Resonanceinmicrocavity...............................897.2Polarization-dependentresonanceinmicrocavity..................917.3SimulationResult...................................937.3.1Drude-Lorentzmodel.............................937.3.2Transfer-matrixmethod............................977.4Theoriginofopticallyinducedresonance......................987.5ConclusionandDiscussion..............................100CHAPTER8DISCUSSIONANDFUTUREDIRECTION.................1028.1Summaryanddiscussion...............................1028.2Futuredirection....................................105APPENDICES.........................................107APPENDIXATYPICALVERTICAL-CAVITYSURFACE-EMITTINGLASERCHARACTERISTIC...........................108APPENDIXBREFERENCEOFTERMINOLOGYABBREVIATION........111BIBLIOGRAPHY........................................112viiiLISTOFTABLESTable2.1Parametercomparisonofbosonicquasipartilces..................13Table6.1Fittingparameters.................................84ixLISTOFFIGURESFigure1.1Phasediagramofpairedelectronsandholes....................2Figure1.2Macroscopicquantumstatesinelectron-holesystem...............4Figure2.1Planarsemiconductormicrocavity.........................10Figure2.2Dispersionofexciton-polariton...........................12Figure2.3Polaritonlasingvs.photonlasing.........................15Figure2.4Polaritoninnaturaltrap...............................17Figure2.5Polaritontrappedinnanowire...........................18Figure2.6Polaritontrappedinamesaofsemiconductormicrocavity.............18Figure2.7Schematicofe-hcondensationatbandgap....................24Figure2.8Schematicofsuperradiance.............................25Figure2.9Symbolicdynamicsofsuperradiance........................26Figure2.10SuperradianceinQWwithmagnetic....................27Figure2.11Interpretationofsuperradiancewithdynamicallyred-shiftingenergy......28Figure2.12OpticalOrientation.................................30Figure2.13SchematicofDyakonov-PerelSpinRelaxation..................32Figure2.14Schematicofmultilayerstructure..........................35Figure3.1Microcavitystructure................................39Figure3.2andlaserspectralcharacteristics....................40Figure3.3Microcavitysamplecharacterization........................41Figure3.4Time-dependentpolarizedPLinInGaAs/GaAsMQWs..............42Figure3.5Angle-resolvedimaging/spectroscopysetup....................44Figure3.6WholeExperimentalSet-up............................46xFigure3.7Pump-probesetup..................................48Figure4.1Spin-polarizedlasingatroomtemperature.....................51Figure4.2Nonlinearinput-output...............................52Figure4.3Evs.kkdispersion.................................54Figure4.4Luminescencecharacteristics............................54Figure4.5Emissionpolarizationvs.pump.......................56Figure4.6effect..............................57Figure4.7ExternalEfy.................................57Figure4.8Luminescencedynamics..............................58Figure4.9Spindynamicsofphotoexcitedcarriersatlasingthreshold............59Figure4.10Dynamicsandenergyrelaxation..........................60Figure4.11TransientlasingspectraatP=4Pth........................61Figure4.12Energylevelsofsample...............................62Figure4.13Simulatedcavityshiftingwithband....................63Figure4.14schematicsofspin-dependentstimulatedemission................64Figure4.15Spin-dependentstimulation.............................65Figure5.1Spectralcharacteristicofduallasing........................68Figure5.2Two-statelasinginamicrocavity..........................69Figure5.3Dynamicsofduallasing..............................70Figure5.4Polarizationpropertiesofduallasing........................71Figure6.1Visualizationofthemacroscopicharmonicstates.................75Figure6.2Quantizedstatesinopticallycontrolledpotentials............76Figure6.3Dynamicsofharmonicstates............................77Figure6.4K-spaceimagingspectra..............................78xiFigure6.5Harmonicoscillator:below-thresholddynamics..................79Figure6.6Densitydependenceofharmonicstates......................80Figure6.7resonanceenergyandpolarizedluminescencespectra..80Figure6.8Schematicdiagramsforthetheoreticalframework.................83Figure6.9Simulateddynamicsoftheharmonicstates....................84Figure6.10Simulatedrisetimesandtime-integratedoftheharmonicstates.......85Figure7.1Pumpingschemeofpump-probemeasurement..................88Figure7.2Differential..............................89Figure7.3Dynamicoftheresonance.............................90Figure7.4Angulardispersionoftheresonance........................92Figure7.5Polarization-dependentresonance.........................93Figure7.6Simulationof.............................95Figure7.7Timedependentdielectricconstant.........................96Figure7.8changefromabsorptioneffect.....................97Figure7.9Carriereffectonblankcavity............................99Figure7.10ComparisonofblankcavitywithandwithoutMQWs...............100Figure8.1Diagramofterahertzexperiment..........................105FigureA.1spectrumofVCSEL..........................108FigureA.2NonlinearincreaseandefyinVCSEL....................109FigureA.3Angle-resolvedspectroscopyinVCSEL......................110xiiCHAPTER1INTRODUCTION1.1MacroscopicquantumphenomenaOurworldismainlybytwolimits:themacroscopiclimitdescribedbyNewton'sLaw,andthemicroscopiclimitdescribedbyquantummechanics.Bridgingthesetwolimitsarefewexamplesof"quantummacroscopicstates,"inwhichacorrelationbetweenparticlesmakesthesystembehavelikeamacroscopicsinglestateinclassicalphysics.Themostcommonexampleisthelaser,wherealargenumberofphotonshavethesameenergyandmomentum.Othertypicalphenomena(correspondingtoconstitutedparticles)are(liquidhelium),super-conductivity(boundedelectronpairs,orCooperpairs),andBose-Einsteincondensation(atomicgases)[1,2].Theconstituentparticlesinthesemacroscopicphenomenaareallcompositebosons.Avarietyofquasi-particleswithbosoniccharactersarefoundinsolidstatephysics.Inpar-ticular,theexciton,whichisanelectron-hole(e-h)pairboundedthroughCoulombinteractioninsemiconductors,attractsmuchattentioninresearch.Indilutedensity,excitonsareregardedasbosonswithalighteffectivemass(0.1-1freeelectronmassm0)comparedtothatoftypicalatomicgases;therefore,excitonscouldformBose-Einsteincondensation(BEC)at˘1K[3,4].SincethetransitiontemperatureTcofBECisinverselyproportionaltoitseffectivemass,theTcofexcitons'BECisexpectedtobethreetosixorderofmagnitudegreaterthanthatofatomicgases'BEC.Thestrongcouplingofanexciton(inbulksemiconductorsorquasi-2Dquantumwells)andaphotonresultsinaquasiparticle,knownasanexciton-polariton[5].Likeanexciton,anexciton-polaritonisacompositebosonwithanevensmallereffectivemass(101104m0),andhasbeenconsideredasacandidateforroom-temperatureBEC[6].11.2Phasediagraminelectron-holephysicsFigure1.1Phasediagramofpairedelectronsandholes.Symbolicschematicofpairedelectronsandholes(e-h)phasediagramasafunctionoftemperatureanddensity.Ate-hdensitybelowMott-transitiondensityandT>Tc,whereTcisthecriticaltemperatureforthecondensateofe-hpairs,thesystemphasemightbediluteexcitongases(X),bi-exciton(XX)gases,andexcitonicscatteringprocess.TheMotttransitionisaregionseparatingthesystembetween"conductingstate"(brokene-hpairs)and"insulatingstate"(exciton,e-hpairsarechargeneutral).Atlowe-hdensityandT<Tc,excitongasundergoesatransitiontoexcitonBose-Einsteincondensation(BEC).Atlargee-hdensityandT<Tc,collectivepairedelectronsandholesformbyweakcoupling,resemblingCooperpairsinsuperconductors,andarenamedasBCS-state.Ate-haboveMotttransitiondensityandT>Tc,electronsandholesarealmostfreecarriersformingelectron-holeplasma(EHP).Theinteractionandquantumcorrelationbetweenexcitonsvarydependingontheelectron-holedensityandthetemperature;Fig.1.1illustratesthephasediagramoftheelectron-holesystem.Indilutedensityofelectronsandholes,theexcitonbehaveslikeabosonicparticle,andformsBECintemperaturesbelowtransitiontemperatureTcinwhichthequantumcorrelationamongexcitonsdominatesthesystem.Theexciton"condensate'hasbeenexperimentallyreportedinvariousstudies[7,8,9,10].Whentheelectron-holedensityincreases,theinteractionofe-hpairsbecomescomplicatedduetoscreeningandspineffectsinthee-handexcitonsystem.Atsufhighdensity,screeningofe-hCoulombattractioninhibitsthebindingofe-hpairing,in2whichexcitonsundergoaMotttransitiontoelectron-holeplasma(EHP)[11].However,correlatede-hpairscanstillformaBCS-likestates,neartothequasi-Fermi-levelofanEHP[11,12,13].SuchamacroscopicBCS-likestatewouldresultinacooperativeradiationknownassuperradiance.SuperradianceorsuggestingtheformationofsuchaBCS-likestate,hasbeenreportedinsemiconductorquantumwells(QWs)[14,15,16].Suchastatecouldexistatcryogenictemperaturesaslargethermalwoulddestroythebindingofe-hpairs.Atlargeelectron-holedensityandroomtemperature,theelectronsandholesareusuallyincoherent.Thecommonmacroscopicphenomenoninthisregionislaserthroughphotonstimulation.Theadvancedtechnologyofcavityfabricationenablesthestudyofcoupledphoton-electron-holesystems.Duetotheirbosoniccharacteristics,aswellasbeingacandidateforroomtempera-tureBEC,exciton-polaritons(hybridsoflightandexcitons)havebeenintensivelyinvestigatedinsemiconductormicrocavitysystemsbynumerousscientistsinthepastfewdecades.Theexciton-polaritonhasalifespan,anditisannihilatedintophotonradiationduetotherecombinationoftheelectronandthehole.Therefore,anexciton-polaritons'condensatecouldresultinalargecoherentradiationknownaspolaritonlasing.Sofar,polaritonlasinghasapparentlybeenfoundinGaAs-baseddevices[17,18,19],andCdTe-baseddevices[20].Besidesthe"condensate"study,thebosoniccharacteristicsofexciton-polaritonshavestimulatedotherresearchrelatingtomany-bodyphysicsinthereduceddimensionalsystem.Many-bodyphysicsincludestopicssuchasquantumvortices[21,22],Berezinskii-Kosterlitz-Thouless(BKT)phases(aboundstateofvor-texandanti-vortex)[23,24],Bogoliubovexcitation[6,25,26],and[27,28].Thequantuminterferencebetweenexciton-polaritonshasalsobeenstudiedinthesuchasnaturaldefectandpotential[29,30,31,32],nanofabrication[33,34,35,36,37,38],andopticalpotential[39,40,41,42].Mostexperimentsonexciton-polaritonsareperformedatcryogenictemperatures,duetothesmallbindingenergyofexcitonscomparedtothermaltion.Nevertheless,theroom-temperaturepolaritonlasinghasbeenreportedinGaN-baseddevices[43,44,45]andZnO-baseddevices[46,47,48],inwhichexcitonsarestableatroomtemperatureasaresultofalargebindingenergy(˘20-60meV).However,theaforementionedpolariton3lasingoccursatadensitymuchlowerthantheMott-density;thisisbecauseahighcarrierdensityenhancesthescreeningeffectandweakenstheformationofexcitons.1.3MotivationandapproachFigure1.2Macroscopicquantumstatesinelectron-holesystem.Simplephasediagramofmacroscopicquantumstatesine-hsystemasfunctionoftemperatureandthedensityofe-hpairs.Thecriticalcarrierdensityseparatedfromthelowandthehighe-hdensityisastheoneatMott-transition,whichistypicallyabout1018cm3.Fig.1.2showsasymbolicdiagramoftheaforementionedmacroscopicquantumstatesatvari-ouslevelsofe-hdensityandtemperature.Basedonthediagram,itisrarethatresearchconvinc-inglypresentsmany-bodyphysicsofparticlesathighdensityandroomtemperature,becausethethermalandscreeningeffectdestabilizethebounde-hpairs.However,theoreticalstud-iesclaimedthatthecondensationofe-hpairspotentiallyexistsnearabandgapofsemiconductorsindenseEHPatroomtemperature[49].Duetotheinsufnumberofexperimentalstudiesofmany-bodyphysicsine-hsystemsathighdensityandroomtemperature,weshoulddevoteoureffortstoexploringthecorrelatede-hpairsatthisregion.4Fromthetheoreticalview,thepresenceoflightwouldenhancethecorrelationbetweenelec-tronsandholes[50,13];therefore,wechosethesemiconductormicrocavityasoursample.Throughtheexaminationofthestudiesofcavitylasersandexciton-polaritonsinmicrocavitysystems,wecanproposeafewreasonswhytheformationofe-hcondensateswasinhibitedatroomtempera-ture.First,theclosedenergydifferencebetweencavityresonanceandthequantumwellbandgap(knownasdetuning)madeithardforthesystemtomaintainahighdensityofe-hpairs,becausetherecombinationofelectronsandholeslimitedtheheightoftheelectron-holegas'sFermi-edge.Second,thethermalheatingandcarrierdiffusionmaydestabilizetheformationofe-hboundpairs.Toaddresstheseissues,weappliedafewdifferentmethods:(1)thecavityresonancewasdetunedto80meVabovethequantumwellbandgap,toprotectdensee-hcarriersfromradiativedecay;(2)theexcitationlaserpulsewastemporallymodulatedbythreeordermagnitudesmallerthantheoriginalone,inordertosuppressthermalheating;(3)theexcitationwasspatiallymodulatedasabeaminordertoreducecarrierdiffusion.Besidesexploringcorrelatede-hpairs,wewouldliketoinvestigatespindynamics.Insemi-conductorlasers,thespinisexploitedtoenhancethelaserperformanceorappliedtospintronicdevices'integration.Thespin-controlledsemiconductorlasers,knownasspinlasers,areproventooperateatthelowerthreshold[51,52,53]andtoofferalargerpolarizationdegree[54,55,56,57,58].Ontheotherhand,excitons,aswellasexciton-polaritons,carryspin.Besidesbeinganewcandidateforspintronicdevices,thespin-dependentpolariton-polaritoninteractionenrichesthephysicsphenomena(seereview[6,59])suchastheopticalspinHalleffect[60,61]andpolar-izationchangeuponpolariton-polaritonscattering[62].However,suchspininteractionhasrarelybeendiscussedintermsoftheaforementionedBCS-likestateofe-hpairsathighdensity,aswellasinsuperradiance.Moststudiesofphotoexcitedquasiparticlesinsemiconductorshaveinvestigatedtheirlumines-cenceproperties;itisrarethattheyexploretheirstatebeforetheannihilationofquasiparticles.Theexcitationenergyisusuallyfarabovetheemissionlevelinordertopreventtheexcitationcoher-encefromimprintingontotheformingcorrelatedquasiparticles;however,exploringthedynamical5spectroscopyofcorrelatedstatesbecomeschallenging,becausepump-probeexperimentsrequiresynchronizedtwolaser-pulsesystems.Inthisdissertation,weaimtodemonstratetherealizationofsuchpump-probespectroscopymeasurement.1.4OutlineandresultsInthenextchapter,Ipresentanintroductiontotheknowledgerelevanttoourwork,includingquantumwellexcitons,microcavityphotonsandexciton-polaritons(abbreviatedaspolaritonsinthefollowingpart),andspinrelaxation.Ialsoreviewselectivearticlesthatarehighlyrelatedtoourwork.InChapter3,Iillustratethestructureanddesignofourmicrocavitysample,anddetailtheexperimentalapparatus.Chapter4to7presentstheexperimentalresultswiththeabstractforeachchapterillustratedinthefollowingparagraphs.InChapter4,room-temperaturespin-polarizedultrafast(˘10ps)lasingisdemonstratedinahighlyopticallyexcitedGaAsmicrocavity.ThismicrocavityisembeddedwithInGaAsmultiplequantumwellsinwhichthespinrelaxationtimeislessthan10ps.Thelaserradiationremainshighlycircularlypolarizedevenwhenexcitedbynonresonantellipticallypolarizedlight.Thelasingenergyisnotlockedtothebarecavityresonance,andshifts˘10meVasafunctionofthephotoexciteddensity.Suchspin-polarizedlasingisattributedtoaspin-dependentstimulatedprocessofcorrelatede-hpairs.ThesepairsareformedneartheFermiedgeinahigh-densityEHPcoupledtothecavitylightInChapter5,sequentiallasingattwowell-separatedenergiesisobservedinahighlyphotoex-citedplanarmicrocavityatroomtemperature.Twospatiallyoverlappedlasingstateswithdistinctpolarizationpropertiesappearatenergiesmorethan5meVapart.Underacircularlypolarizednonresonant2pspulseexcitation,asub-10-pstransientcircularlypolarizedhigh-energy(HE)stateemergeswithin10psafterthepulseexcitation.ThisHEstateisfollowedbyapulsedstatethatlastsfor20Œ50psatalowenergy(LE)state.TheHEstateishighlycircularlypolarizedasaresultofaspin-preservingstimulatedprocess,whiletheLEstateshowsasreduced6circularpolarizationbecauseofadiminishingspinimbalance.InChapter6,theobservationofmacroscopicharmonicstatesisreportedinanopticallyin-ducedinahighlyphotoexcitedsemiconductormicrocavityatroomtemperature.Thespatiallyphotomodulatedrefractiveindexchanges(Dn)enablethevisualizationofsequentialtran-sittransversemodes,correspondingtoharmonicstatesinamicrometer-scaleopticalpotentialatquantizedenergiesupto4meV.Wecharacterizethetimeevolutionoftheharmonicstatesdirectlyfromtheconsequentpulseradiationandidentifysequentialmultiple˘10pspulselasingwithdif-ferentemittingangles,energies,andpolarizations.Suchadynamicmultiple-pulselasingeffectisattributedtolight-inducedcorrelatede-hpairsinahigh-densityplasmaandtheireffectivecouplingtodiscretetransversemodesinthespatiallyphotomodulatedopticalInChapter7,therelaxationprocessofcarriersinahigh-densityEHPisstudiedinanIn-GaAs/GaAsquantum-wellbasedmicrocavityusingopticalpump-probespectroscopictechniques.Atransientoptically-inducedresonanceappearsnearthecavityresonance(Ec)within5psafter2pspulsedpumpexcitationwithnearly0.2eVexcessenergyaboveEc,andthende-cayslowlywithadecaytimeconstantover500ps.TheopticallyinduceddifferentialchangeDR=Rcanexceed50%,whichisthreetofourordersofmagnitudehigherthantypicalpho-tomodulatedmeasurementsinGaAs-basedquantumwellsorvertical-cavitysurface-emittinglasers.ThelargejDR=Rjisthecombinationeffectoftheenhancementofopticalnonlin-earityduetoe-hcorrelationandthecarrier-inducedrefractiveindexchangeinmicrocavitysample.Polarization-dependentpump-probespectrarevealedatransientspinsplittingupto˘1meVwithadecayconstantof30psunderanonresonantellipticalpolarizedpump.InChapter8,Isummarizetheessentialresearchresultsanddiscussthecorrelatede-hpairsissuewithfurtherperspectivesonthisproject.7CHAPTER2BACKGROUND(LITERATUREREVIEW)Inthischapter,Iintroduceafewimportantconceptsandreviewrelevantliteratureaboutthelight-matterinteractingsystems.Inthebeginning,theexcitonandmicrocavityphotonarepresented,andthenfollowedbytheintroductionofthehybridofexcitonandcavityphotonknownasexciton-polariton.Atlowdensityandcryogenictemperature,theexciton-polaritonsbehaveslikebosonicparticles,andarepredictedtobehavelikemacroscopicstateknownasthepolaritoncondensateinthermalequilibriumsystemorpolaritonlaserinnon-thermalequilibriumsystem.Insection4,theissuebetweenconventionallaser,polaritonlaserandpolaritoncondensatewillbediscussed.Insection5,theworkofthepolaritoncontrolinthedesignedisdemonstrated.Athighdensityandroomtemperature,thecorrelatede-hpairsarepredictedtoforminhigh-densityEHP,andmayresultinsuperradiance.Next,Ipresentedtwodistincttheoriesaboutcorrelatede-hpairsatroomtemperature,andreviewrecentexperimentalworkexploringthesuperradiance.Insection7,thespindynamicsofphotoexcitedcarriersinthesemiconductorsisintroduced,andthelightpolarizationisdeterminedbythelifetimeandthespinrelaxationtimeofphotoexcitedcarriers.Finally,Iillustratethetransfermatrixmethod,whichisusedinourtheoreticalsimulationtothemeasuredofmicrocavitysample.2.1QuantumwellexcitonsAsolidnormallyconsistsof1023atoms.Inordertodescribethe1023atomsstate,acommonwayistoregardthestablegroundstateofasystemasaquasivacuumandintroducequasiparticlesasunitsofelementaryexcitations,whichonlyweaklyinteractwitheachother.Thequasivacuumofasemiconductoristhestateofvalencebandandemptyconductingband.AnexcitonisaquasiparticleconsistingofanelectronandaholeboundbyCoulombinteractione2=er,wheree8isthedielectricconstantandristhedistanceofelectronandhole.ThewavefunctionofexcitoncanbeanalogoustoHydrogenatom.Duetothestrongdielectricscreeningandasmalleffectivemassratiooftheholetotheelectron,thebindingenergyofexcitonisabout10Œ100meV.ItsBohrradiusisabout10Œ100Å,thesizeofanexcitonextendsovertensofcellsinthesemiconductor.TheexcitoncanbeconsideredasbosonswhentheexcitoninterparticlespacingismuchlargerthanitsBohrradius.AsemiconductorQWisathinlayerofasemiconductorwithsmallthicknesssandwichedbetweentwobarrierlayerswithlargerbandgap.ThethicknessofthemiddlelayerindesignisnormallycomparabletoexcitonBohrradius.ThereduceddimensionresultinginquantumleadstoexcitonpropertieswithlargerbindingenergyandsmallerBohrradius.2.2MicrocavityphotonsTherearevariouswaysofcavitydesigntophotonsinalocalarea,andhereweintroduceoneparticularcavity:distributedBragg(DBR)basedsemiconductormicrocavity.ThestructureofthiskindofcavityisshownasFig.2.1,whichcontainscavitybarrierswithemittersuchasQWsandwichedbytwoDBRs.TheDBRiscomposedofalternativetwo-layermaterials,andeachthicknessoftheindividuallayerischosentomatchtheBraggconditiond=lc=4ni.Thelciscavityresonancewavelength;niistherefractiveindexofthatmaterialsatlc.Insuchdesign,theinterferenceoftransmittedandlightleadstoexcellenthighvityinaspectralwindowofwidthabout100nm,whichsymbolicspectrumisshowninFig.2.1(b).Theopticalmode(thedipofinFig.2.1(b))insuchFabry-Perotresonatorcanbedeterminedbytransfer-matrixmethod,whichthelightintensityisenhancedinsidecavitybarrierbutdecaysinsidetheDBRmirrors.Fromthecalculationandthedecayinreference[63],wecananeffectivecavitylengthas:Leff=Lc+lc2ncn1n2jn1n2j,whereLcisthephysicallengthofcavity,n1andn2arerefractiveindexoflayersinDBR,andncisrefractiveindexofthecavitylayer.9Figure2.1Planarsemiconductormicrocavity.(a),Schematicofplanarsemiconductormicrocavity,whichtypicallyconsistsofmultiplequantumwells(MQWs)sandwichedbytwodistributedBragg(DBRs).TheDBRismultiplepairsoftwolayermaterials,thethicknessofindividuallayerd=lc=ni,wherelcistheopticalmodeinthecavity.(b)SchematicoftypicalofaDBR-basedsemiconductormicrocavity.Thewidthofhighvityisstopband,whilethedipwithinstopbandisthecavityphotonmode.Themicrocavityisnormallynotperfect,sotheresonantphotonmayleakoffthecavity.ThequalityofcavitycanbequantitativelydescribedbyQ-factorviaQ=w=dw,wherewisthefre-quencyofopticalmode,anddwisthelinewidthofresonantopticalmode.ThisQ-factorrelatesthelifetimetofcavityphotonbyQ=wt.Sincethephotoncannotpropagatefreelyinsidethecavity,thedispersionofphotonisstronglyInaconditionofsmallin-planemomentumkk,thedispersionrelationisapproximatelydescribedbyaparabolicshapewithaneffectivephotonmassmc:E(k)ˇE0+¯h22mck2k(2.1)Theeffectivemassisas:mc=hnccLc,whichisontheorderof105offreeelectronmassm0.2.3Exciton-polaritonsForasemiconductormicrocavityimplementedbyQWwithhighoscillatorstrength,ifcavitypho-tonmodecancoupletoexcitonintheQWresonancewithcondition:theenergyexchange10ratebetweenexcitonandcavityphotonexceedstheexcitondecoherencerateandphotonleakage.TheresultgivestheRabioscillationinatimedomain,leadingtoanormalmodesplittingofpo-laritonbranches.Theenergy-momentum(kk)dispersionofpolaritonissimilartoresolvecouplingtwo-levelsystem,whichHamiltonianis[6]:‹Hpol=‹Hcav+‹Hexc+‹HI=åEcav(kk)‹aƒkk‹akk+Eexc(kk)‹bƒkk‹bkk+åg0(‹aƒkk‹bkk+‹akk‹bƒkk)(2.2)Hereaƒkkandbƒkkarecreationoperatorsofphotonandexciton,respectively.EcavandEexcareenergyofcavityphotonandQWexciton.g0istheexciton-photondipoleinteractionstrength.TheHamiltonian‹Hpolcanbediagonalizedwithtransformation:‹Pkk=Xkk‹bkk+Ckk‹akk‹Qkk=Ckk‹bkk+Xkk‹akk(2.3)TheXkkandCkkarecoefsatisfyingXkk2+Ckk2.The‹Hpolbecomes:‹Hpol=åELP(kk)‹Pƒkk‹Pkk+åEUP(kk)‹Qƒkk‹Qkk(2.4)Here(‹Pkk;‹Pƒkk)and(‹Qkk;‹Qƒkk)arethecreationandannihilationoperatorsofeigenstatesofthesystem.Theseeigenstatesarecalledlowerexciton-polaritonandupperexciton-polaritoncorre-spondingtotheirenergy:ELP;UP(kk)=12Eexc+Ecavq4g20+(EexcEcav)2(2.5)ThedispersionofcavityphotonEcav(kk)isparabolicshape,andtheEexc(kk)isnormallyinsmallkk,thusthedispersionoftypicalexciton-polaritoncanbereferredtoFig.2.2.InFig.2.2,thedispersionofpolaritonsareclosedtoparaboliccurvewithcurvature,thiscurvaturecorrespondstoaneffectivemassofthequasiparticle.Theeffectivemassofexciton-polaritonistypicallyinaorderof101Œ104m0.TheExciton-polaritonhaslifetimedue11Figure2.2Dispersionofexciton-polariton.Thedashedcurveswithlargeandsmallcurvaturearethedispersionofcavityphotonmodeandquantumwell(QW)exciton.AscavityphotonandQWexcitonareinthestrongcouplingregion,neweigenstatesofthesystemappearshownasredcurves,theyarelowerandupperexciton-polaritoncorrespondingtolowerandupperbranches.Theexciton-polaritonhasalifetimeandradiativelydecaytophotonduetotherecombinationofelectronandhole.Thephotoncarriesinformationofenergyandin-planemomentum,whichcanbedetectedintheexperiment.torecombinationofelectronandholefromtheexcitonicpart,whichthelifetimeistypicallyabout1Œ10psatthebottomofbranches.Thespectralpropertiesofexciton-polaritonlikeenergy-momentumdispersioncanbemea-suredbyangle-resolvedphotoluminescence.Intheexperiment,thesemiconductormicrocavityisopticallypumpedatahighenergytoproducelotsoffreee-hpairs.Thesee-hpairsarecoolinginenergythroughcarrier-phononscatteringandpopulateatthepolaritonstate.Thepolaritonscanrelaxenergybytwoways.Oneisthroughexciton-photoninteractionthroughemittingopticaloracousticphonon,anotherisviaCoulombinteractionswithotherpolaritonsorwithfreecarriersinthesystem.Thephotoluminescencedynamicsisdeterminedbyenergyrelaxationrateandsponta-neousemissionrate.Iftheenergyrelaxationrateisslowerthanthepolaritonemissionrate,thentherelaxationofpolaritonstotheloweststateissuppressed,andradiativedecayoccursathigherenergywithkk.Thisphenomenaisknownasrelaxationbottleneck.Theleakagephotonfrom12AlkaliGasExciton(X)X-polaritonm=m01030.1Œ1101104.Bohrradius(nm)0.11010103Spacingn1=3c(nm)˘10210102102103Tc1nK1mK1mKŒ1K1Œ300KThermalization1Œ10ms10Œ100ps1Œ10psLifetimes1Œ100s1Œ100ns1Œ10psTable2.1Parametercomparisonofbosonicquasipartilcestherecombinationofelectronsandholesrevealstheinformationofenergyandkkofthepolaritons.2.4PolaritonlasingandcondensationSimilartoexciton,theexciton-polaritoncanberegardedasabosoninalow-densitylimit.Duetolighteffectivemassoftheseparticles,theyarepredictedtoformbosoniccondensationwithelevatedtemperatureinthesemiconductors.Thetable2.1showsthecomparisonoffewimportantparametersinBose-EinsteincondensationforAlkaligases,excitons,andexciton-polariton.ThepotentialcandidateofBECatroomtemperatureleadsnumerousresearchinvolvingthistopic,butafewconsiderationsshouldbedeliberated:(1)Polaritonlifetimeinamicrocavityistyp-icallyshortas1Œ10ps,whichiscomparabletothermalizationtime.Therefore,thecondensationofexciton-polaritonisreferredtoasadynamicalopen-dissipativecondensation,ora"polariton-laser".Thereissomedebatewhetherthepolaritonachievesthethermalequilibriumtoformacondensate,andthecomprehensivediscussionbetweenthecondensateandthepolaritonlasercanbeseeninreference[64].(2)Athighdensity,thescreeningeffectofexcitonbecomesandattenuatetheoscillatorstrength,leadingthesystemtoplasmaphase.ThetransitiondensityisontheorderofMotttransitionabout10101011e-hpairspercm2.(3)Withincreasingtemper-ature,thethermalenergyexceedsthebindingenergyofexciton,leadingtoinstabilityofexcitoninthesystem.Theexciton-polaritoninaplanarsemiconductormicrocavityisequivalenttoatwo-dimensionalsystem.Anuniform2DsystemofbosonshaveBECtransitiononlyatzerotemperatureinthe13thermodynamiclimitbecauselong-wavelengthdestroythelong-rangeorder.However,suchsystemwithsizerestrainsthedensityandphaseallowingtheformationofcondensateattemperature.Thelong-rangespatialandtemporalcoherenceofpolaritoncondensateshasbeendemonstrated,revealingthesignatureofBEC[65,66].Generallyspeaking,thecoherencelengthofpolaritoncondensateisandrangesontheorderofopticalpumpingspotsize.Themacroscopicpopulationofcoherentpolaritoncouldgivecooperativeradiation,resultinginpolaritonlasing.Arisingquestionishowtomakepolaritonpopulateeffectivelyatonestatewiththekeybeingthestatestimulation".Thestimulationisadistinctfeatureofasystemwithidenticalbosonicparticles,whichdescribesthescatteringrateintoaparticularstateisproportionaltoN+1ifthereisN-particleaccumulateatthatstate.Inconventionallasers,suchstimulationofphotonsisessentialtothelasingmechanismbehind.Similarly,thestatestim-ulationenhancesthepolariton-polaritonscattering,givingpotentialaccumulationatthebottomofthelowestpolaritonbranches.Theearlyreportsonpolaritonlasingfromkkhavebeendemon-stratedonGaAs-baseddevice[17,19],CdTe-baseddevices[20]andGaN-based[43]devices.Thesepolaritonlaserssharefewcharacteristics:(1)Inaninput-outputrelationship(pumpintensityvs.emissionintensity),theemissionwithincreasingpumpshowsasharpsu-perlinearincreasearoundthethresholddensityPth.ThecorrespondinginjecteddensityinQWatPthisabouttwoordersofmagnitudethantheMottdensity.(2)Theenergy-momentumdispersionbelowPthismeasuredwithanagreementofLPdispersioninsteadofcavity-photondispersion.(3)WithincreasepumpingdensitystartingfromPth,butkeepingpolaritonsfrombeingdestroyed,thelasingexhibitsenergyblue-shiftaccompanywithlinewidthbroadening.[20,67,19,35,26]Thesephenomenaareattributedtopolariton-polaritoninteraction,whichmostlyresultsfromCoulombexchangeinteractionandisarepulsiveforce.Althoughphotonlaserandpolaritonlasersystemallinitiatelasingwiththestimu-lation,theirmechanismsarequitedifferentasillustratedinFig.2.3.Inphotonlasersystem,thelasingemissionresultsfromthestimulationemissionofthephotonintocavitymodeswithoccu-14pationnumberlargerthan1.Itrequireselectronsandholesstayingatmetastablestatestobuildelectronicpopulationinversionbeforestimulationemission.Inpolaritonlasersystem,thelasingistriggerbybosonicstimulationofpolaritons,andlasingenergyisnotrestrictedtocavitymodes.ThisalsoexplainswhytheenergyofpolaritonlasershiftsinsteadofaconstantwithincreasingpumpNormally,thethresholddensityisontheorderof˘1=l2T(lTisthede-Brogliewave-lengthofpolariton),andaboutthreetofourorderofmagnitudelowerthanthatofaconventionallaserthreshold.Figure2.3Polaritonlasingvs.photonlasing.Thediagramdemonstratestheoperationalprincipleofpolaritonlasing(left)andphotonlasing(right),andtheynormallyareoperatedatquitedifferentcarrierdensityregimes.Inpolaritonlasersystemwhiche-hdensityisabout10111013cm3,thegeneratedexciton-polaritonfallsontothelowerdispersionbranchatin-planemomentumkk,thenrelaxestolowestenergystatekk=0bystimulatedcoolingviamultiplephononemissionorpolariton-polaritonscattering.Amacroscopicpopulationofpolaritonatthebottomofdispersioncooperativedecaystoradiationthroughe-hrecombination.Therefore,thepolaritonlasingisnotlockedtocavityphotonmode.Inphotonlasersystemwhiche-hdensityisabout10161018cm3,theinjectedelectron-holepairsrelaxtothebottomofcavitydispersionthroughspontaneouscoolingandbuildupapopulationinversion.Oncethecavityphotontriggersthestimulatedemission,thebunchofe-hpairsrecombinetocoherentradiation.Thisisadaptedfrom[6]Thephotonlasingandpolaritonlasingsometimesareintoweakcouplingregionandstrongcouplingregion,respectively,andtheycanbemeasuredinthesamesamplestructure.Inreference[18],twolasingthresholdswithdistinctlasingenergyareobservedwithincreasingpumpTheyattributedtherstlasingispolaritonlaser.Asinjecteddensitycontinuouslyincreases,15thesaturationof2Dcarrierdensitydiminishesthepolariton,makingthesystemundergoatran-sitiontoweakcouplingandthengivephotonlasingradiation.Inreference[68],theyclaimedtoobservethecrossoverbetweenphotonandexciton-polaritonlasinginasemiconductormicrocav-ity.Inthisresearch,theynon-resonantlypumpedthemicrocavityandperformedenergy-,time-andangle-resolvedmeasurementtocharacterizethetransientcarrierdistributionandeffectivetem-perature.Underhighinjecteddensity,thelasingcommencesatthebottomofcavitydispersion,but50to100pslaterthemainlasingenergyredshifttowardthebottomoflowerpolaritonbranch.2.5PolaritonsinpotentiallandscapesTrappingisausefultoolbothinphysicsresearchandinindustrialapplication.Inphysics,ithelpswithobservingquantummany-bodyphysics,liketheearlyrealizationofBECinatomicgases.Inapplication,theinmicrocavityenhancethelasingefyandlasingthresholdreduction.Inpolaritonsystem,theisnotnecessarytoobservethein-planepolaritoncondensate,butengineeringpolaritoncanstudytheinteractionsandthetransportoftailoredpolaritonsinacomplexenvironment.Thestudyofpolaritonswiththeengineeringcanemulatemany-bodyphenomenainanothersystemsuchasthephysicsinhigh-temperaturesuperconductors,grapheneorfrustratedspin-lattices[69,70,71].Ontheotherhand,theengineeringpolaritontrappingenablestocontrolthewofpolariton,whichcanbeexploitedtooptoelectronicdeviceslikephotonicintegratedcircuitsandlogicelements[72,73].Theexciton-polaritonisconstitutedoflightandmatter,andbothpartscanbesubjectedtotheInthissection,wereviewfewarticlesofpolaritoninthepotentiallandscapes.Wewillhighlightafewcharacteristicofpolaritonlasingbehaviors.Thesimplewaytotrapthepolaritonistakingadvantageoftheubiquitousdefectsinsemicon-ductormicrocavities[30,31].Thesizeofthedefectisaroundfewtotensmicrometerssquare.Undernonresonantexcitation,asequentiallasingmodesmayappearwithanorderofenergies16Figure2.4Polaritoninnaturaltrap.Theexperiment[31]wascarriedoutinanAl0:15Ga0:85As/AlAsmicrocavity.Theexciton-polaritonsweregeneratedfromanon-resonantpumping,andthenformacondensateinanaturaltrapwithsizeof1to10mm2.Theimageshowsthespectral-andtime-resolvedluminescencewithincreasingpumppower.Sequentialmultiplelasingmodesappearathighpumppower,andmayhaveoscillationeffect.Thisisadaptedfrom[31]fromhightolowatpumpmuchabovethelasingthresholdshowninFig.2.4(cŒe).Athigherexcitationpower,thelasingmayappearasanoscillationinasuitablesizeofthedefectshowninFig.2.4.ThesequentiallasingmodeswithoscillationwereattributedtotheinterplaybetweenreservoirfeedingandBosestimulation.Namelywhenthepolaritonsformacondensatethroughbosonicstimulationanddecayswithcooperativeradiation,theexcitonsinthetraparedepleted.Lateron,theexcitonsinneighboringplacewillreplenishthetrap,helpingwiththebuildingofcriticaldensityagainforthenextlasingradiation.Onecommonwaytocreateaistakingtheadvantageofstructureorengineeringadesignedtrap.Inthereference[36],theyopticallypumpedananowireandcontrolledthetrappingsizebytranslatingthepositionofexcitationalongthenanowiredirectionshowninFig.2.5.Whenthedistancebetweentheexcitationandtheedgeofthenanowireisshortenough,quantizedlasingmodeswouldappearinrealspace.AnotherexampleoffabricatingtrappingistocreateamesainasemiconductormicrocavityshowninFig.2.6.Inthethemesahas9mmdiameterwith6nmheight.Aroundtheenergy1.480eV,discretelasingmodescommencebothintherealandthemomentumspace.Theselasingmodesdemonstratediscreteenergiesandthemode-numberchange17Figure2.5Polaritontrappedinnanowire.Intheexperiment[36],aGaAs-basedwiremicrocavity(graybar)wasopticallynon-resonantpumpatdifferentposition.Theedgeofwirecavityandpumpformsafortheformingexciton-polaritons,andthesizeofwascontrolledbythepositionofpumping.Thisisadaptedfrom[36]Figure2.6Polaritontrappedinamesaofsemiconductormicrocavity.ThesamplestructureisasemiconductormicrocavitywithsomemesaonthetopDBR.Alongthez-axis(perpendiculartocavitysurface)thepolaritonsforminterferenceinsuchshownasinrealspaceandmomentumspace.Thisisadaptedfrom[36]dependingonthesizeofthemesa.Inthesetwoexamples,thepolaritons'spatialdistributioninthecabbededucedbysolvingtheSchrodingerequationofquantumharmonicoscillators.However,thedrawbackofthesetwocasesisthatthecannotbecontrolledsincethesamplestructureisedafterthemanufacture.Theopticalpotentialhasbeenpopularforthestudyofparticlesinapotentialbecausethesizeandtheshapeofthecanbexiblycontrolledbylasers.Withtheadvancetechniqueofspatiallightmodulator,theopticalpotentialdesignstimulatesextensiveinvestigationsintheexciton-polariton[39,40,41,42].Inthesereports,multiplepolaritonspotsarecreated18bynon-resonantopticalpumpingwithadesignedshape,andthesepolaritoncondensatesinthemicrocavityareusedtovisualizetheformationofspontaneouslyoscillatingquantumThequantumformsdifferentinterferencepatternsbothintherealandthemomentumspace.Thesepatternsaredeterminedbytheinteractionofquasiparticlesintheanditsshapeandthesizearechangeddependingonthepumppoweraswellastheshape.Inchapter6,wewilldemonstratethemacroscopicharmonicstateinanopticallyinducedcon-atroomtemperature.Thepreviousinvestigationaforementionedhaveintensivelyex-ploredtheimageintherealandthemomentumspace,butthelasingbehaviorinspectral-andtime-resolvedanalysishavebeenrarelystudied.Inourproject,wewillpresentmorecomprehen-sivestudynotonlyonthespectroscopyintherealandthemomentumspace,butalsotheissueofthedynamicsandpolarizationofluminescencefromthesample.2.6Correlatedelectron-holepairsatlargedensityTheprevioussectionsillustratepossibleformationofquasiparticlecondensateatcryogenictem-perature.Withincreasinge-hdensity,exchangeeffectsandthescreeningoftheCoulombinterac-tionine-hpairsdestabilizetheexcitonandanEHPforms.However,sometheoristsusemeantheorytopredictthatthepairedelectronsandholesmayformBCS-likestateneartheFermi-edge.Thesee-hpairsarequitesimilartotheCooperpairsinasuperconductoratcryogenictemperature[13].Thecorrelationofe-hpairsmightbeenhancedbyapresenceoflight[50].Recently,therewasanotherreportarguingthatanenergylevelofbounde-hpairsatthebandgapofthesemiconductorsexistsinthelargedensityEHP[49].Intheexperiment,thebuild-upofmacroscopicelectricdipoleunderincoherentlyexcitationcanresultincooperativedecay,givingknownasorsuperradiance.Thissuperradi-ancecanevenhappenatlargee-hdensity.Althoughsuperradianceiscoherentemissionresemblingphotonlasing,thedynamicsofsuperradianceisquitedifferentfromthatofconventionallasers.Inthissection,Iwillillustratethemeantheoryofexcitons,whichdeducestheBCS-like19stateneartheFermiedge.Next,Iintroducethesecondtheorythatcorrelatede-hpairsformatthebandgapofthesemiconductors.Finally,Ipresentthecharacteristicsofsuperradianceandafewremarksoftherelevantwork.2.6.1MeantheoryforexcitonsInthissubsection,Iwillpresentthemeantheoryabouthowe-hpairsformneartheFermi-edgeofEHP.Inthebeginning,WetheHamiltonianine-hsystem:H=H0+HC(2.6)whereH0=åk[eckaƒc;kac;k+evkaƒv;kav;k](2.7)HC=12åq[Veeqreqreq+Vhhqrhqrhq2Vehqreqrhq](2.8)aƒc;kandaƒv;karecreationoperatorsforelectronsintheconductingandvalenceband,respec-tively.reqandreharedensityoperatorswiththeforms:req=åkaƒc;k+qac;kandrhq=åkaƒv;k+qav;k.ViqisCoulombinteractionandforhomogeneousthree-dimensionsystemVeeq=Vhhq=Vehq=4p=eq.Forparabolicbands,ec(k)=¯h2k2=2meandev(k)=Eg¯h2k2=2mh.Themeantheorystartsfromthefollowingansatzfortheground-stateoftheinteractingelectronandholes:jYMFi=Õk[uk+vkaƒe;kav;k]j0i(2.9)Herej0iisvacuumstateofthesystem,whichtheconductingbandsareemptybutvalencebandsarefull.ukandvkarecomplexcoefwithrelationjukj2+jvkj2=1,andthejvkj2isequivalenttooccupationnumberofe-hpairsinmomentumk.ThedeterminationofukandvkistominimizetheexpectationvalueofCoulombinteractiontermHCinequation2.6.Nextwewilldeterminetheequationsoftheseparameterswhenthesystemisatequilibrium.Supposethee-hdensityishniwiththecorrespondingchemicalpotentialm,thefreeenergyofthe20systemis:F=hH0+HCimhni(2.10)Theequilibriumofthesystemoccurswhenthefreeenergyisminimal,thatis¶F=¶vk=0.Con-sideringonlys-wavepairingisdominateinthesystem,asetofself-consistentequationscanbeobtainedinthefollowing:xk=ekm2åk0Veekk0nk0=ekmåk0Veekk0(1xk0=Ek0)(2.11)Dk=2åk0Vehkk0haƒc;kav;ki=åk0Vehkk0Dk0=Ek0(2.12)E2k=x2k+D2k(2.13)v2k=121xkEku2k=121+xkEkukvk=Dk2Ek(2.14)Heretheequation2.11describestherenormalizedsingle-particleenergyxkperpairmeasuredfromthechemicalpotential,whereek=¯h2k22me+¯h2k22mh.Equation2.12illustratesthe"gapequation",whichissimilartotheoneinBCStheoryinsuperconductors.Dkrepresentsthegapfunctionandisalsoknownastheorderparameter.TheorderparameterDexistsonlywhenbothukandvkarenon-zeroforsomeoverlappingrangeofmomentak,anditalsosymbolizestheoveralldegreeofphasecoherence.Inequation2.13,Ekisthepair-breakingexcitationspectrum,whichcanbeviewedastheenergycostofbreakingonee-hpairinthecondensationandplacingitinanavailablestateofmomentumk.Equation2.14describesthecoefofvkandukasthefunctionofEkandDk.InthefollowingIwilldiscussthestateofsystemwithdifferentregionofe-hpairdensityhni:1.Thedensityhniisthatmeanstheisolatedexcitonsoverlapverylittle.Hencetheparametersofoccupationarevk˝1andukˇ1.Inthislimit,thechemicalpotentialm(measuredfromthebottomofthecombinedelectronandholebands)isnegativeanditsmagnitudeapproaches21to1Ryd,whereRydisthebindingenergyofe-hpair.Thelowestexcitationoccursatk=0,whichcorrespondstoionizationofexcitonintothefreeelectronandhole.2.Asthee-hdensityhniapproachesto,thekineticenergyofelectronandholedomi-natestheinteractionenergy,andmostofthek-statesareoccupied.Weexpectvkisastepfunctionlikevk=Q(jkjkF),wherekFistheFermimomentum.Thewavefunctionwillapproximatelybe:jFMFin!¥!Õjkj<kFaƒc;kav;kjoi(2.15)HerethechemicalpotentialisclosetotheFermienergy.Intheextremelimitthatn!¥,theorderparameterdoesn'texist.3.ThedensityhniisthemodelcanbeelaboratedasFermisurfaceinstabilitywithmoredescriptioninthefollowing.TheelectronsandholesnearthebottomoftheFermiseaarealmostedduetothelargedensityandPauliexclusion.However,thestateclosedtotheFermisurfacecansufferCoulombinteractionandproducesasmallfractionoftheoccupationnumberabovetheFermienergy.TheelectronsandholesneartheFermienergyhavemorefreedomforthedensityofstateandmayforme-hpairs.ThebindingenergyofthepairingisequivalenttotheorderparameterDk,whichisquitesmallcomparedtomorFermienergy.TheDkisalsotheminimalexcitationenergytobreakthee-hpairs.Althoughabovemodelisbasedonathree-dimensionalsystem,quiteafewtheoriespredictthattheBCS-likestatecouldrealizeinatwo-dimensionalsystemsuchasintheQWs[13,12].Oneclaimedthat"Thequantumenhancesthee-hcorrelationbothintheatomicexcitonlimitandintheweak-couplingplasmalimit"[13].Theabsorptionandgainspectra,whicharecalculatedbasedonsolvingtheBethe-Salpeterequationofthee-hpairpropagator,deviatesignif-icantlyfromthecorrespondingspectrainthefree-particlesystem.Thesedeviationisenhancednearthequasichemicalpotentialmandredshiftsinenergyduetotherenormalizationofthesingleparticleenergy[12].AremarkispointedoutbyGuseinovandKeldyshthattheBCS-stateinanequilibriumsys-22tembehavesnodifferencefromanormaldielectricorcharge-densitywavesystem.However,inanon-equilibriumsituation,wheretheelectronandholepopulationsaremaintainedwithtwodif-ferentquasi-chemicalpotentials,therecombinationwillrequirenotonlytunnelingbutalsotheemissionofaphoton.Thedecayprocessduetotherecombinationwillbreakthecoherenceofe-hpairs,leadingtoacooperativeradiationknownassuperradiancephenomenon.Iwillintroducethesuperradianceinthelastsubsection.2.6.2Condensationofelectron-holepairsatbandgapNormallythemanybodyeffectarecommonlyusedinmanytheoriestoexplainthoseexperimentalresultsinlarge-densityEHPsystemthatcannotbeexplainedbyfreecarrierscalculationorcon-ventionallaserstheory.OnepopulartheoryaforementionedpredictstheformationoftheBCS-likestateneartheFermisurfaceatcryogenictemperature.Butthismodelishardlyappliedonthesys-tematroomtemperaturebecausethebindingenergyorthecorrelatede-hpairs1Œ2meVismuchsmallercomparedtothethermalatroomtemperature(˘25meV).HereIintroduceanothertheory[49]predictingtheexistenceofbounde-hpairsinalarge-densitysemiconductorEHPatroomtemperature.Theenergylevelofsuchbounde-hpairsisatthebandgapofthesemiconductorsinsteadofneartheFermi-surfaceinaforementionedtheory.Inthefollowing,Iwillintroducethemechanismofthe"condensate",andpresenthowthesebounde-hpairsstablyexistatroomtemperature.HereIpresenttheconceptualmechanismofcondensation,whichthecorrelatede-hpairsformatthebottomofthesemiconductorbandgapEg.Inthemodel,itassumesthatanelectronandholeareattractedbytheCoulombforceandmoveinameanofotherparticlesandlattices.Spinstatesareneglected.TheCoulombinteractionisscreenedwiththeThomas-FermiwavenumberkTF.Fig.2.7isthebandstructurediagramofasemiconductorwithdegeneratelarge-densityEHP.Insuchasystem,moststatesbelowFermi-surfaceareupduetolargedensityandPauliexclusion.NowifalightisresonantwithEg,suchresonantelectromagneticcanenhancethecorrelationofelectronsandholes.Occasionallythecorrelatedboundstatesaregeneratedfrom23Figure2.7Schematicofe-hcondensationatbandgap.Acondensateofe-hpairsformnearthebandgapwithanassistanceoflight.Theinitialvacancyforformationofe-hpairwillbereplenishedquicklyfromelectronsandholesatupperband.ThebindingenergyDisnormallysmallerthanthethermalenergykTatroomtemperature,andkTismuchsmallerThisisadaptedfrom[49]afractionofelectronsandholesnearEg,theenergyofboundstateisslightlylowerthanEgduetobindingenergyD.Aftertheformationofboundstates,thevacancyoftheirinitialstatewillbereplenishedbyhigherenergystatequickly.Thebindingenergyofcorrelatede-hpairsistoolargetobedestroyedbythermalenergy.TheenergyrequiredtobreakthepairingofcorrelatedboundstatesisequivalenttotheexcitationenergyfromtheboundstatenearEgtothefreeelectronsandholesabovetheFermi-surface.Theexcitationenergyistypicallymorethan30meV,sotheinternalsuchasthermalenergyhardlydestroysthebounde-hpairs.ThecriticaltemperatureTCoftransitionistypicallyasthethermalenergydiminishingthepairing,sointhismodeltheTCisdeterminedbythechemicalpotentialmratherthanrelatedtoorderparameterDdevelopinginBCStheoryforsuperconductors.Inthereference[49],theyfurtherdeterminetheprobabilityoftransitionfordestructinge-hpairing.Thedestructionofe-hpairsoccursduetocollisionswithopticalphononswithsimul-taneoustransitionsofelectronsandholestostatewithlargerenergies.TheauthorsusedGaAsmaterialtogiveanquantitativeexample.TheenergyofopticalphononinGaAsis¯hWˇ36meV,24andisalmostconstantforallphononshavingwavenumberaboutkF˘107cm1.Amongthedensity261018cm3atroomtemperature,thedestructionprobabilityislessthan0.3.Thisresultimpliesconsiderabledensityofcorrelatede-hpairsmightstayforawhileuntiltheyundergocooperativedecaytocoherentradiation.2.6.3ReviewofsuperradianceInquantumoptics,superradianceisaphenomenonofacooperativeradiationproducedfromagroupofNemitters(suchasexcitedatoms)couplingwitheachotherbymeansofphotonexchange.Theconditionisfulwhenthewavelengthofthelightismuchgreaterthantheseparationoftheemitters.TheoriginalideawasproposedbyDickein1954.However,theconceptofsuperradiancehasnotonlybeenextensivelystudiedinthequantumopticsbutalsoappliedinavarietyofsystemincludingthequantumphasetransition.ThesystemdiscussedinthefollowingisfocusedonanopticallycreatedEHPinasemiconduc-tors.Inrecentresearch[14,15,16],theultradenseEHPcreatedbyfemtosecondlaserpulsewouldgiveanultrashortburstofcoherentradiationuponacertaintimedelayafterexcitation,andsuchemissionhasamuchhigherintensitythanthespontaneousemissionofthesamenumberofe-hpairs.Intheseexperiments,thegiantpulsesoflightisgeneratedbyamacroscopicdipoleemittersdevelopedfromannon-resonantopticalexcitationandabruptenergyrelaxationofe-hpairs.Figure2.8Schematicofsuperradiance.Thephotoexcitedelectricdipolesareincoherentinthebeginning,butwillselforganizetoformacollectivestate,resultinginsuperradianceburst.Thisisadaptedfrom[14]Theuniquecharacteristicsofsuperradiancedistinguishedfromanothercoherentlightemis-25sionprocessaretheexistenceofself-organizationstagetospontaneouslybuildupamacroscopiccoherence(seeFig.2.8).Theself-organizationcoherenceinphasemanifestsitselfphysicallyasadelaybetweentheexcitationandemissionpulses.Itispurequantummechanicsdrivenbythequantuminthesystem.Fig.2.9illustratesthetypicaldynamicsofsuperradiance.Be-lowthecriticale-hpairdensityNc,theemissionrisesuptothepeakproportionaltoN,thenumberoftheexciteddipoleintheensemble,thenexponentiallydecayswithatimeconstantT1.AsthedensityexceedsNc,agiantburstcommenceswithatimedelayafterexcitation.ItsintensitypeakinthetimedomainisproportionaltoN2withpulsewidthinverselyproportionaltoN.Aftertheburst,asecondpulseemissionmayoccasionallycommencedependingonthedensity.Figure2.9Symbolicdynamicsofsuperradiance.Ahanddrawingdescribingthetypicaldynamicsofsuperradiance.AsdipolenumberNbelowNc,theemissionisaexponentiallylongdecaywithatimeconstantT1.ThepeakofintensityisproportionaltoN.AsNexceedsNc,agiantburstpulsecommenceswithatimedelayafterexcitation.ThepeakintensityisproportionaltoN2butthepulsewidthisinverselyproportionaltoN.Asecondpulsemayappearafterpulsesdependingonthedensity.Thisisadaptedfrom[14]Thesampleintheseriesstudies[14,15,16]wasastackofundopedQWsconsistingof8nmIn0:2Ga0:8Aswellsand15nmGaAsbarriers.Thequantumleadstoquantizedsubbandsforelectronsinconductingbandandholesinvalencebands.Thestrainintheirsampleresultedinalargesplittingoftheheavyholeandlightholestates,butonlytheheavy-holestatesarerelevanttothestudy.Theopticalexcitationenergyischosenas1.55eVabovethebandgapoftheGaAsbarriers.Boththeelectronsandholesexperiencemanyscatteringbeforerelaxinginto26QWstoformtwo-dimensionalexcitons.AsagiantpulsecommencesatpumplargerthanPc(correspondingtocriticaldipolenum-berNcinFig.2.9),theemissioncharacterizedinspectral-andtime-resolvedmeasurementdemon-stratesthesuperradiancedecayswithenergyrelaxationintimedomainatcryogenictemperature(˘20K)(seeFig.2.10).Theenergyshiftisabout13meV,andtheemissionappears50psafterex-citationandlastsmorethan150ps.Theradiationintensityisenhancedwithincreasingpumpbutdecreaseswithincreasingtemperature.Theemissionalmostfadesoutattemperatureabove150K.Figure2.10SuperradianceinQWwiththemagneticTheimagedemonstratessuperradiancefromsemiconductorquantumwellsintheconditionofwithoutandwiththemagneticWithoutthedynamicalspectroscopyofluminescenceislong-tailintime-andspectral-resolvedimage.Withluminescenceimagetransformsintodiscretemodeswithenvelopelikealongtail.Thisisadaptedfrom[16]WiththepresenceofmagneticalongthedirectionofQW,theemis-sionimageonenergy-timediagramtransformsfromacontinuouslongtailtomultiplelasingmodesandeachmodecarriesatail(seeFig.2.10).Thenumberoflasingmodesdecreaseswithanaug-mentingbuttheoverallintensityofindividualmodeenhances,andthemaximumintensityofmodewillshiftfromhightolowenergy.Again,theselasingwilldisappearastemperaturerisingabove150KatB=10T.Thephenomenaofemissionburstwithdynamicalred-shiftinenergyareattributedtoFermi-edgefromaquantumdegeneratee-hgas.Thediagramofinterpretationisshown27Figure2.11Interpretationofsuperradiancewithdynamicallyred-shiftingenergy28inFig.2.11.Thephotoexcitedelectronsandholesuptheconductingandvalencebands.How-ever,theCoulombinteractionenhancesthecorrelationofe-hpairsnearFermibandedge.Thesee-hpairscollectivelyformamacroscopicdipolewithself-organizationasmentionedbefore.Asthecooperativespontaneousrecombinationofelectronsandholesoccurs,thesuperradiancecom-mencesandtheFermienergyleveldropsduetoconsumptionofe-hdensity.Butthee-hpairsnearnewFermi-edgeagainbuildupthemacroscopicdipoleandresultinagiantburstpulsewithlowerenergy.Byrepeatingthissteps,thesuperradiancewithenergyred-shiftisobservedintheexperiment.WhenapplyingthetheenergylevelsarequantizedintoLandaulevels.Thee-hpairsatthehighestoccupiedLandaulevelrecombineagainduetothemany-bodyenhancementofgain,thentheycontributetosequentialburstofsuperradiancefromhighenergytolowenergy.WithincreasingthemagnitudeofthedensityofLandaulevelschanges,causingtovaryingemissionintensitywith2.7OpticalorientationandspinrelaxationinsemiconductorsInmydissertationproject,Iexploredthespindynamicsofe-hpairsthroughmeasuringthepolar-izationsofemission.Thereforeinthissection,Iintroducethesemiconductoropticsandafewspinrelaxationmechanismsinthefollowingparagraphs.IfocusthecaseoftheGaAs-basedQWandGaAsmaterialbecauseGaAsconstitutesthemostpartofoursampleinthisresearch.ThebandstructureofbulkGaAsisshowninFig.2.12(a),hereIonlyshowthelowestcon-ductingband(s-wave)andvalenceband(p-wave),whichmostlydeterminestheopticalpropertiesinsemiconductors.ThebandgapofGaAsisaboutEg=1:5eV.Duetothespin-orbitcoupling,thejh=3=2andjh=1=2bandsareseparatedbyD=0:3eV,wherejhistheangularmomentumquantumnumberofholeinvalenceband.Thejh=3=2bandhastwodegeneratebandscorre-spondingtoheavyhole(mh=3=2)andlighthole(mh=1=2).Heremharemagneticquantumnumbersofholestate.29Figure2.12OpticalOrientation.(a),bandstructureofbulkGaAswithlowestconductingandvalencebands.ThebandgapEgˇ1:5eV,whilethespin-orbitcouplingsplittingDisabout0.3eV.Thejh=3=2containstwodegeneratebandscorrespondingtoheavyhole(mh=3=2)andlighthole(mh=1=2).(b)SchematicofopticaltransitionofGaAsbulkmaterialswithcircularlypolarizedlight.Accordingtoangularmomentumconservation,thetransitionobeysselectionruleDm=1.wheremisthemagneticquantumnumberofe-hdipolestate.Thenumberattachedwithtransitionarrowistheprobabilityratiooftransitionpath.(c)Duetothequantumeffect,thevalancebandsoflightholesandheavyholesaresplitintotwonon-degeneratedispersions.Undercircularlypolarizedpumping,theopticaltransitionofelectronbetweenconductingandvalencebandneedstoobeyselectionruleaccordingtoangularmomentumconservation.Assumingthepumpingenergyislargerthanalldifferenceofconductingandvalencebandsdiscussedhere,inFig.2.12(b)itshowspossibletransitionpathswithrelativeprobabilityratioattachedoneachpath.ThetransitionruleillustratesthatthequantumnumberchangeDm=memhisthesameasmagneticquantumnumberofpumpphotonmg=1,whichisalsocalledselectionrule.IntheGaAs-basedQW,thebandsoftheheavyholeandlightholearenon-degenerateduetoquantumshownintheFig.2.12(c).Sinceinmostexperimentalstudies,thepumpingenergyissmallerthanEg+D,soIfocusonthetransitionbetweenje=1=2andjh=3=2.WithpumpingenergyEg<¯hw<Eg+D,theaverageelectronspinis1234+1214=14,whiletheav-erageholespinis54.Theirsumis1andequalstotheangularmomentumoftheexcitedphoton.Thephoto-excitedelectronseventuallyrecombinethemajorityofholestoemitphotons,andthesystemgoesbacktothegroundstate.Thetransitionofrecombinationisrequiredtosatisfythese-lectionrule.Insemiconductors,thesephoto-excitedcarriersmayredistributetheirspinpopulation30bycarrier-carrierscattering,thustheemittedphotonmaynotbetotallyrightcircularlypolarizedunderrightcircularlypolarizedexcitation.Normallythenon-equilibriumspinpolarizationtendstoredistributeequalpopulationoftwooppositespins,thisphenomenaiscalledspin-relaxation.Ingeneral,wecouldstudythecarrierspindynamicsthroughmeasuringemissionpolarizationfromthesemiconductors.Theemissionpolarizationfromanopticallypumpedsemiconductorisdeterminedbythelife-timeofexcitationdipoleandspinrelaxationtime.Duetotheangularmomentumconservation,theemissionpolarizationisthesameasthepolarizationofradiativedipoleinthesystem.Thepolarizationofe-hdipolecanbeasthefollowingequationandrelatestodipolelifetimetandspinrelaxationtimetsas:P=n+nn++n=P01+t=ts(2.16)Therearetwolimitstoquicklygetaninsightfromthisequation.(1)Underthelimitt˝ts,thespinrelaxationisnegligiblecomparedtotheelectrons'andholes'lifetime.Inthiscondition,theensembleofoptical-inducede-hdipoleisalmostnotchangedafterexcitationandgivetheemissionwiththesamepolarizationasthatofpump,orPˇP0.(2)Underthelimitt˛ts,thecarrierspinre-arrangesquicklybeforee-hrecombinationwithequalcarrierpopulationofspinupandspindown.ThusweobtainunpolarizedemissionwithPˇ0.FromDyakonov'ssaying:"SpinrelaxationcanbegenerallyunderstoodasaresultoftheactionofngintimemagneticInmostcases,thereisnorealmagneticbutwecouldimagineaneffectivemagneticexistinginthesystem.Generallyspeaking,theeffectivemagneticoriginatesfromspin-orbitcouplingorexchangeinteraction.Thespinrelaxationresemblesthephysicspicture:thespinmakesaprecessionaroundarandomdirectionofmagnetic(orB-withatypicalangularfrequencywandcorrelatedtimetc.Aftertimetc,thedirectionandtheamplitudeofeffectivechanges,andthespinprecessesaroundthenewAfteracertainnumberofsuchsteps,theinitialspindirectioniscompletelyforgotten.Ingeneral,anyorinhomogeneityofspininteractioncaninducespinrelaxation.31Thevariousoriginsleadtoseveralspinrelaxationmechanisms.InthespintronicsstudyofIIIŒVsemiconductors,thereareafewspin-relaxationmechanismsdominatesthantheothers.HereIintroduceselectivebutimportantmechanismsinthefollowingparagraphs,theyare(1)ElliottŒYafetmechanism(2)D'yakonovŒPerel'mechanism(3)BirŒAronovŒPikusmechanism.[74]ElliottŒYafetmechanism(EYmechanism)Inthepresenceofspin-orbitcoupling,theelectroniceigenstates(Blochstates)mixspin-upandspin-downstates.Thisleadstoaprobabilityofspinifthespatialpartofelectronwavefunctionsuffersatransitionthroughscattering,evenifthescatteringprocessisspin-independent.Inaddition,asthespin-orbitinteractionisinducedbytheperiodiclatticeions,thelatticevibration(orphonon)couldcoupletocarrierspinresultinginThespinrelaxationrate1=tsisinverselyproportionaltothecollisionstimetpandrelatestothescatteringgeometryf2.Wecouldusesimpleformtoillustratethisrelation:1ts˘<f2>1tp.DyakonovŒPerelmechanism(DPmechanism)Figure2.13SchematicofDyakonov-PerelSpinRelaxationInIIIŒVorIIŒVIsemiconductors,thebulkinversionasymmetryinlatticestructureresultsinspin-orbitcouplingintheconductingband.TheHamiltonianofthespin-dependenttermofelectronscanbedescribedby¯hW(p)S,whichisregardedasanenergyofaspininaneffectivemagnetic¯hW.Thiseffectivechangesitsdirectionduetotheelectron32collisions.Forconvenience,Iassumethecorrelationtimeistp,andthespinrelaxationtimeists.Toobtainasimplerelationbetweentsandtp,aspincanbeimaginedtogothrougharandomspinprocessduringtimetwithtotalsquareangleDj2,whichisequivalenttosquareofprecessionanglewithintptimesthenumberofsteps(seeFig.2.13).ThatisDj2=(Wtp)2(t=tp).Thespinrelaxationtimeisasj2(ts)˘1,thusweget:1ts˘W2tp(2.17)Thismechanismgivesacounter-intuitionthatmoreelectroncollisionscouldenhancethespinrelaxationtimeinthesystem.BirŒAronovŒPikusmechanism(BAPmechanism)Thismechanismismostlyseeninnon-equilibriumelectronsinpŒtypesemiconductorsduetotheexchangeinteractionbetweentheelectronandholespins.Therefore,thespinrelaxationrateisproportionaltothenumberofholes,meaningmechanismmightbeimportantinsomep-dopedsemiconductors.InaGaAs-basedsemiconductor,thespinrelaxationtimedependsonnumbersoffactors,liketemperature,momentumrelaxationtime,carrierdensityandcarriertypeslikeelectronorhole.Forexample,inundopedGaAs/AlGaAs(100)QWs,theDPmechanismdominatesathightemperature,whileBAPmechanismisenhancedatlowtemperatureorp-dopedQWs.Eveninthesamematerialofsemiconductors,differentcrystalorientationmighthavedistinctspinrelaxationtimes.ThefamousexampleisGaAs(110)QWsandGaAs(100)QWs[75].Thespinrelaxationtimeatroomtemperatureisabout2nsin(110)QWs,butisaround70psin(100)QWs.TheDPmechanismisthoughttobeimportantinthesesystems.TheeffectivethroughcalculationisperpendiculartoQWsplanein(110)QWscase,butliesinQWsplanein(100)QWs.Therefore,electronspinsprocessrelativestableeffectivein(110)QWs,resultinginmuchlongerspinrelaxationtime.332.8TransfermatrixmethodThetransfermatrixisausefulmethodtocalculatetheeffectiveandtransmissionoflayer-structurematerials.Inourproject,wealsoimplementittosimulatetheofthesemiconductormicrocavity.HereItakeasubsectiontooutlinethismethod.Inthestep,onecouldconsiderhowtoobtainandtransmissionofaparticularmedia,andthestructureofthemediais:n(z)=8>>>>>><>>>>>>:n1;z<0n2;0<z<dn3;d<z(2.18)Assumeanelectromagneticplanewavepropagatesatxz-plane,andtheelectrichastheform:E=E(z)exp[i(wtkxx)](2.19)wherewisangularfrequencyofwave,andkxisthex-componentofthewavevector.kxisaconstantforalllayertosatisfySnell'slawinallinterface,andwesetkxbforconvenience.Theelectricdcanbeeitherans-wave(withEky)orap-wave(withHky).ThemagneticHcanbeobtainedbyH=iwm5(E).Theincidencewavecanbedividedintoright-travelingandleft-traveling:E(z)=Reikzz+Leikzz=A(z)+B(z)(2.20)RandLareconstantsineachhomogeneouslayer.A(z)andB(z)representtheamplitudeofright-travelingandleft-travelingwave,respectively.kzzisthez-componentofthewavevec-tor.Inthei-thlayerthez-componentwavevectorkizcanberewrittenaskiz=q[(niwc)2b2]=(wc)nicosqi,whereqiistherayanglemeasuredfromthez-axis.Wewillneedthistermlater.Supposetheright-andleft-travelingwavesineachlayerhaveamplitudedistributionillustratedin34Figure2.14Schematicofmultilayerstructure.(a)Threelayersstructurewhichthethicknessofmiddlelayerisd.(b)MultilayerstructurewithNlayersinthemiddle.Thezihererepresentsthethicknessofi-thlayer.(a),thenweA1=A(0)B1=B(0)A02=A(0+)B02=B(0+)A2=A(d)B2=B(d)A03=A(d+)B03=B(d+)(2.21)where0(0+)representstheleft(right)sideoftheinterfaceatx=0,andtheissimilartod(d+).Nowboundaryconditionrequiresthatalltheelectromagneticanditsderivativearecontinuousateachinterface.Theserequirements,E(0)=E(0+),E0(0)=E0(0+),E(d)=E(d+),andE0(d)=E0(d+),givetherelationbetweenAiandBicoefIfthetwoamplitudeofE(z)arerepresentedascolumnvector,wecouldorganizetheserelations35as:A1B1=D11D2A02B02D12A02B02A02B02=P2A2B2=0B@eif200eif21CAA2B2A2B2=D12D3A03B03D23A03B03(2.22)ThematricesDidescribestheboundaryconditionateachinterface,itisalsocalleddynamicalmatricesinthebook[76].TheequationsofDiare:Di=8>>>>>>>>>><>>>>>>>>>>:0BB@11nicosqinicosqi1CCA;fors-wave0BB@cosqicosqinini1CCA;forp-wave(2.23)wherei=1;2;3isindexofeachlayer.TheP2isapropagatingmatrix,whichaccountsforthepropagationthroughthebulkofthelayer.Thephasef2is:f2=k2zd=n2wccosq2d(2.24)CombiningcoefinEq.2.22,weobtain:A1B1=D11D2P2D12D3A03B03(2.25)Thusthecolumnvectorsrepresentstheamplitudeofleftmostandrightmostsideofthreelayerstructureconnectedbytheproductof22matricesinsequence.EachsideofinterferenceisrepresentedbyaD-matrix,andthebulkofmaterialsisrepresentedbyaP-matrix.Wecouldextendthisformulaformultilayerstructureshownin(b),andobtain:A0B0=D10 NÕi=1DiPiD1i!Ds(2.26)36Assumingtheincidencewaveisright-travelingwave,andnoleft-travelingwaveappearsinsubstrate(B0s=0),wecanexpresstheRandtransmissionTwithcoefofA0,B0andA0sas:T=A0sA02;R=B0A02(2.27)Inmydissertationproject,thismethodcanbeappliedtosimulatetheofmicrocavitysampleandcomparedtotheexperimentalresult.Ialsousedthismethodtoseetheenergyshiftofcavityresonanceinmicrocavitysampleresultingfromtherefractiveindexchangeinmiddlematerials.37CHAPTER3EXPERIMENTALMETHODSOurgoalistoexplorethemany-bodyphysicsincoupledehgsystematlargedensityandroomtemperature.Inthischapter,Ipresentthesampledesigntoapproachtheissueinsemiconductormicrocavityaswellastheselectionofopticalexcitationtoavoidlasercoherenceimprintedonthesystem.Afterthat,theexperimentalsetupofimaging/spectroscopy,lightpolarizationcontrol,andbeamshapingofexcitationbeamismentioned.Thesemethodsareusedtoexploretheexcitationspatialintensityandpolarizationeffectonthesystem,andalsotocharacterizetheemissionproperties.Inaddition,thecarrierdynamicsinthesystemisinvestigatedbymeasuringtheluminescencedynamicsandabsorption/gainspectrumwiththecorrespondingsetupillustrated.3.1SamplecharacteristicsInordertomaintainhighdensitycarrierinsideamicrocavityandpreventcarriersfromradiativelossbeforelasing,onesolutionisdesigningcavityresonancefarabovequantumwells.Ontheotherhand,myco-workerandIareinterestedinexploringthecoherentstatesinhighEHPbutavoidopticalexcitationaffectingthecarriercorrelation.Thereforetheexcitationischosenatanenergymuchhigherthanemissionenergy,andsuchphotoexcitedcarriersnormallylosespincoher-enceafterlongrelaxation.Iwillintroducesamplecharacteristicsinmoredetailsinthefollowingparagraphs.3.1.1SamplestructureandfabricationThemicrocavitysamplewasdesignedbyDr.Chih-WeiLaiandwasmadebyourcollabora-torsYi-ShanLeeandSheng-DiLin.Thesamplewasgrownonasemi-insulating(100)-GaAssubstratebyusingamolecularbeamexpitaxymethod.Thestructureisentirelyundopedand38Figure3.1Microcavitystructure.(a),Structureofthemicrocavity:InGaAsmultiplequantumwells(MQWs)areembeddedwithinalGaAScavitybetweentwodistributedBragg(DBRs).ThethicknessofGaAsandAlAsinDBRsare61-nmand78-nm,whilethethicknessofInGaAsandGaAsinMQWare6-nmand12-nm,respectively.WeadjusttheantinodesofthecavitylighttotheMQWlayersbyaddingtwotransitionalAlAslayersandaGaAscaplayer.(b),Across-sectionalSEMimageshowingtheactiveregimeandadjacentlayersoftheDBRs.containsalGaAssandwichedbydistributedBragg(DBRs).Thetop(bottom)DBRconsistsof17(20)ofGaAs/AlAsl/4layers,andthecentralcavityconsistsofthreestacksofthreeIn0:15Ga0:85As/GaAsmultiplequantumwells(MQWs)each,positionedattheanti-nodeofthecavitylightd.(Fig.3.1)ThebarecavityresonanceisEcˇ1.405eV(lc=883nm)andtheQWbandgap(E0g˘1.33eVatroomtemperature)istunedthrougharapidthermalannealingprocess(at1010C-1090Cfor5-10ps),inwhichtheInGaAsQWbandgapblueshiftsbecauseofthediffusionofgalliumionsintoMQWlayers.39Figure3.2andlaserspectralcharacteristics.(a)spectrumatkk=0fromthefrontsurfaceofamicrocavitysamplewith1.405eVlasingenergyatthethreshold:measured(blacksolidline)andsimulated(orangesolidline).Thissampleisanas-grownsamplenotsubjecttoarapidthermalannealingprocess.Thesimulationisperformedviaatransfermatrixmethod,includingtheopticalabsorptionintheGaAslayers,butexcludingthecomplexdielectricconstantofexcitons(e-hpairs)inMQWs.Thecavityresonance(Ec)isabout1.41eV.(b)Opticalpumpingschemeintheexperiment.3.1.2SamplecharacteristicsHereIpresentourmicrocavitysamplepropertiesaswellastheenergyshiftinMQWsundernon-resonantpumping.Fig.3.2ismeasuredspectrumfromoneofoursamples.ThecavityresonanceEcisaround1.405eVwithnegligibleTEandTMenergyslittingatsmallemissiondirection(Fig3.3(a),therelationofin-planemomentumandemissionanglewillbeexplainedinthesection3.2.1).ThesmallTE-TMenergysplittingcontributestolaserpolarizationcontrolanddiminishesthecrystallineeffectonlightpolarization.Thepumpingenergyintheexperimentisabout1.58eV(lp=785nm),whichisalocalminimumofvity.Thechoiceofpump-ingenergyistopreventthecorrelationofcarriersatemissionlevelsfromthelasingcoherenceeffect,andinthemeantime,tokeepmaximumtransmittedaslargeaspossible.Thequan-tumwellbandgapisabout1.33eV.Atalowphotoexciteddensity,thechemicalpotentialmisfaroff-resonantwithrespecttoEc,andtheradiativerecombinationofe-hcarriersislargelysup-pressed.madvancestowardEcwithincreasingphotoexciteddensity,thenluminescenceefy40nonlinearlyenhancesandresultsinlaserradiationatthegainovercomesthecavityloss.Fig.3.3(b)demonstratesmattergainspectruminsidethemicrocavity.Figure3.3Microcavitysamplecharacterization.(a)Evs.kkdispersionsfortheTE(left)andTM(right)modesunderacircularlypolarizedpumpat1.579eVandP=0.6Pth.ThephotoexciteddensityatPthis˘231012cm2perquantumwellperpulse.ThesimulatedTEandTMdispersionsareshownasmagentaandblackcurves,respectively.TheTE-TMenergysplittingislessthan50meVatkk=0,allowingtheeffectivecontroloflasingpolarizationbyopticalpumping.(b)Todeterminethedensity-dependentspectralcharacteristicsofPLintheInGaAs/GaAsMQWs,wemeasurethetime-integratedandtime-resolvedPLinthesample,withthetopDBRmirrorlayersremoved,byselectivewetetching[77].PLspectraatP=0.2(blue),0.6(magenta),and1Pth(green)intheabsenceofthetopDBRmirrors.Here,PLisattributedtothespontaneousradiativerecombinationofphotoexcitedcarriersintheInGaAs/GaAsMQWs.ThedualPLspectralpeaksareattributedtotheandsecondquantizedenergylevelsintheMQWs,respectively.TheQWbandgap(E0g)correspondstothegroundstate,thetransitionbetweenthequantizedenergylevelsoftheelectronandtheheavy-hole(e1hh1).E0gcandecreasewiththeincreasingphotoexciteddensity(bandgaprenormalization).mcanbededucedfromPLfromtheexcitedstate(secondquantizedlevels,e2hh2transition).Withanincreasingdensity,E0gredshiftsslightlybecauseofbandgaprenormalization,whereasmblueshiftsconsiderably(˘10meV)asaresultofphasespace(Pauliblocking)atahighphotoexciteddensity(&1012cm2perQW).(c)NormalizedPLspectranear1.40eV,whichdisplaysaspectralblueshiftof15Œ20meVwiththeincreasingphotoexciteddensity(0.1to2Pth).TobetterunderstandhowthematterinInGaAs/GaAsMQWsaffectscavity,determiningthedensity-dependentspectralcharacteristicsofMQWsisnecessary.Timeintegratedphotolumines-cence(PL)inthesamplewithtopDBRmirrorslayersremovedisshowninFig.3.3(b).Themblueshiftsinenergybecauseofbandofelectronsandholes,anditapproachestoEcaspumpclosedtocriticalmagnitude(calledlasingthresholdPth,whichlasingeffectinitiatesinmicrocavity).Thespectralblueshiftscouldbeaslargeas15-20meVwithincreasingphotoex-41citeddensity(0.1-2Pth).ThePLandspindynamicsinMQWsareinvestigatedinFig.3.4.Undernon-resonantlycircularlypolarizedpumping(Episabout200meVaboveEg),unequalorthogo-nalcircularlypolarizedemissionsareobservedwithin10psafterexcitation,indicatingimbalancecarriersspinsexistsinMQWs.Thespinrelaxationofe-hcarrierscanbedeterminedbythede-cayofemissionintensitydifferencebetweentwoorthogonalcircularcomponents,whichdisplaysrelaxationtimelessthan10ps.Figure3.4Time-dependentpolarizedPLinInGaAs/GaAsMQWs.(a)Time-resolvedpolarizedPLI(t)(blacklines:I+(t),co-circulars+=s+component;redlines:I(t),cross-circulars+=s).Time-dependentDoCPrc(t)hasavalueof0.12whenPLintensityincreasestoitsmaximuminabout10ps,andthendecaysrapidlywithaspinrelaxationtimets<10ps.Ontheotherhand,thecarrierdecaytimeismuchlarger,tn˘1ns,asdeducedfromtheoveralldecayoftime-dependentPLintensityI(t)(inset).(b)EffectiveinitialstationaryDoCP,¯rc=Rt=10pst=0I+(t)I(t)I+(t)+I(t)dt,asafunctionofpumpWedetermine¯rctobealwayslessthan0.1inInGaAsMQWswithsimilarphotoexcitede-hcarrierdensities.ThephotoexciteddensityatPthis˘231012cm2perquantumwellperpulse.Thediminishing¯rcwithincreasingpumpabove2Pthsuggeststhatthespinrelaxationtimetsdecreasesfurtherascomparedtocarrierlifetimetnathighphotoexciteddensities,owingtoincreasinglydominantcarrier-carrierscatterings.3.2ExperimentalsetupInordertoanalyzetheradiationpropertiesfromourmicrocavitysample,webuiltacombinationoffewexperimentalsetupstomeasurethelightspectrum,polarizationanddynamics.Theimaging42spectroscopysetupdetectsangularandspectralpropertiesoflight.Acombinationofliquidcrystaldeviceshelpswithcontrolling/analyzingtheexcitation/luminescencepolarizations.Theheatingeffectandcarrierdiffusionarebothsuppressedinthermalmanagementsetup.TemporalimageobtainedfromStreakcamerareveallightdynamicsandprovidesinformationofradiativecarrierdynamicinmicrocavity.Ontheotherhand,theabsorption/gainspectrumismeasuredbytwo-colorpump-probesetuptoexplorewhetheragapopensunderintenseexcitationinmicrocavity.Wewillalsostudythetotalcarriers(includingnon-radiativecarriers)spectralandtemporaldynamicsaswellasthetransientcavityresonanceinthesystem.3.2.1ImagespectroscopysetupWemeasuretheangularandspectralpropertiesofluminescenceinthegeometry(seeFig.3.5).Inaplanarmicrocavity,carrierscoupledtothecavitylightarecharacterizedbyanin-planewavenumberkjj=ksin(q)becauseofthe2Dofbothphotonsandcarriers.Theleakagephotonscanbeusedtodirectlymeasuretheangulardistributionofopticallyactivecarriers.Angle-resolvedluminescenceimagingandspectraoftheseleakagephotonsaremeasuredthroughaFouriertransformopticalsystem.Aremovablef=200mmlens(lensL2inFig.3.5)enablestheprojectionofeithermomentum-space(k-space)orreal-space(r-space)luminescenceontotheentranceplaneoftheslitofthespectrometer.Luminescenceiscollectedthroughanobjectivelens,separatedfromthespecularorscatteredpumplaserlightwithanotch,andthendirectedtoanimagingspectrometer.Asinglecirculartransverselasingmodewithaspatialmodediameterˇ8mmisisolatedinmeasurementbyapinholepositionedattheconjugateimageplaneofthemicrocavitysamplesurface(referredtowholeexperimentalsetupinFig.3.6).Thespectralresolutionisˇ0:1nm(150meV),whichisdeterminedbythedispersionofthegrating(1200grooved/mm)andtheentranceslitwidth(˘200mm).Thespatial(angular)resolutionisˇ0:3mm(6mrad)perCCDpixel.43Figure3.5Angle-resolvedimaging/spectroscopysetup.Luminescencefromthemicrocavityiscollectedbyamicroscopeobjective.TheluminescencewithdistributionF(X;Y)isFouriertransformedintoafarimageinthebackfocalplaneoftheobjectivewithcoordinates(u;v).Thisplaneismappedintok-spacewith(kX;kY),wherekXorkYkk,thein-planemomentum.ThedistributioninthisplaneisrelayedtotheentranceplaneofthespectrometerusingapairoflensesL1andL3(bluelinepath).Tomeasurethereal-spaceimagingplane(r-space)onsample,theL2lensisinsertedtoformtwotelescopesandtheimageisprojectedontheentranceplaneoftheslit(redlinepath).3.2.2ThermalmanagementAtahighpumpthesteady-stateincidentpowertransmittedtothesampleatthe76MHzrepetitionrateofthelaserwillexceed50mWandresultinthermalheatingandcarrierdiffusion.Thetechniquesweusetocontrolthethermalheatinganddiffusionofthephotoexcitedcarriersare(1)temporallymodulatingthepumplaserintensitytosuppressthethermalcarrierheatingand(2)spatiallyshapingthepumpbeamtoenablelasinginasingletransversemode.Steady-statethermalheatingcaninhibitlaseractionandleadtospectrallybroadred-shiftluminescence.Tosuppresssteady-statethermalheating,wetemporallymodulatethe2-ps76MHzpumplaserpulsetrainwithadutycycle(on/offratio)<0.5%byusingadouble-passacousto-opticmodulator(AOM)system[78].Thetime-averagedpowerislimitedtobelow0.2mWforallexperiments.Multipletransversemodescansimultaneouslylasebecauseofthediffusionof44photoexcitedcarriersandcrystallinedisorder,whichleadtoinstabilityandcomplexlasingchar-acteristics.Tocontrolcarrierdiffusion,weholographicallygenerateapumpbeam(areaˇ300mm2)atthesamplesurfacewithaspatialbeamshaperconsistingofatwo-dimensional(2D)liquid-crystalspatiallightmodulator(SLM)[79].3.2.3OpticalcontrolandbeamshapingBesidescontrollingcarrierdiffusionthroughbeamSLMallowsustodesignothershapeofbeamtoaffectlasingbehaviors.Forexample,wecangeneratedouble-hump-shapedbeamservingasopticalandphotonsinsidethecouldformquantum-oscillator-likelasingmodes.TheseexperimentalresultswillbeexplicitlydescribedinChapter6.TheopticalexcitationsetupincludingSLMisshowninFig.3.6.Thefrontsurfaceofthemicrocavityispositionedatthefocalplaneofahigh-numerical-aperturemicroscopyobjectivelens(N.A.=0.42,50,effectivefocallength4mm).A3telescope,aFaradayrotator,apolarizingbeamsplitter,andtheobjectivelensformaFouriertransformimagingsystem.ThelightattheSLMandsamplesurfaceformaFouriertransformpair.The2DSLM(19201080pixels,pixelpitch=8mm)enablesustogeneratearbitrarypumpgeometrieswithaˇ2mmspatialresolutionatthesamplesurfaceusingcomputer-generatedphasepatterns.Asmallgoldmirrorinsertedinfrontofobjectivelensisusedtodirectlaserpumpingmicrocavitysamplewithasmallincidentangle,andispositionedtoblockluminescencelightpathassmallaspossiblebutmaintainpumpinthemeantime.Thepumpcanbevariedbymorethantwoordersofmagnitudeusingaliquid-crystalattenuator.3.2.4PolarizationcontrolThepolarizationstateofthepump/luminescenceiscontrolled/analyzedbyacombinationofliquidcrystaldevices,suchasvariableretarders,polarizationrotators,andGlan-Taylor/Glan-Thomsonpolarizerswithoutmechanicalmovingparts.Apolarizationcompensator(Berek'svariablewave45Figure3.6WholeExperimentalSet-up.Luminescencefromthemicrocavityiscollectedbyamicroscopeobjective(N.A.=0.42,effectivefocallengthf0=4mm).Thecollectionangleisuptoqˇ25inair.Themeasurementofimaging/spectroscopycanbereferredtoFig.3.5,withthelenslabeledwithfocallength(ex:L200meansf=200mm).Intheconjugatereal-spaceimagingplane(r-space),weplacea600-mmdiametercircularaperturetospatiallyisolateluminescenceandasingletransversemodewithinacircularˇ10-mmdiameterareaonthesample.TheimageattheentranceplanecanbedirectedtotheLN-CCDfortime-integratedimaging/spectroscopyortothestreakcamerasystemfortime-resolvedmeasurements.Inthiswemeasuretheangulardistributionofluminescenceask-spaceimages(k-images)orspectra(Evs.kkdispersions)usingrespectivelythe0-orderor1st-orderdiffractedlightfromthegrating.Byinsertingaremovable200mmfocal-lengthlens(L200),weprojectther-spaceluminescencetotheentranceplaneofthespectrometer.46plates)isusedtocompensateforthephaseretardanceinducedbythefromtheminiaturegoldmirrorsurface.Thecircularlypolarizedpumporluminescencewithangularmomentum+¯h(¯h)alongthepumplaserwavevector‹kk‹zisass+(s).Linearlypolarizedlightwithhorizontal(vertical)polarizationisassX(sY).ThepolarizationstateischaracterizedbytheStokesvectorfS0;S1;S2;S3g.S0istheandisdeterminedasS0=I++I=IX+IY=I45+I135.TheStokesvectorcanbenormalizedbyitsS0totheStokesthree-vectors=fs1;s2;s3g.s1=(IXIY)=(IX+IY),s2=(I45I135)=(I45+I135),ands3=(I+I)=(I++I).I+,I,IX,IY,I45,andI135aremeasuredtime-integratedortemporalintensitiesofthecircularorlinearpolarizedcomponents.Thepolarizationstateisrepresentedbyusingthefollowingthreequantities:thedegreeofcircularpolarization(DoCPrc=s3),degreeoflinearpolarization(DoLPrl=qs21+s22),anddegreeofpolarization(DoPr=qs21+s22+s23).Theaccuracyofthemeasuredpolarizationstateisˇ1-2%.3.2.5TemporalmeasurementsetupToknowcarrierenergyandspinrelaxationbetweenexcitationandradiativeemission,weper-formedtime-resolvedmeasurementonluminescenceintensity,transientspectraldistribution,andpolarization.Twowaysareutilizedintemporalmeasurement:(1)spectroscopydetectedthroughStreakcamera(2)absorptionofvespectrummeasuredthroughpump-probetechnique.OurStreakcameraenablestime-resolvedluminescencemeasurementinreal-andmomentumspaceaswellasspectrallytime-resolvedimagemeasurementwith5-pstimeresolutioninoverallsystemsetup.Thismethodprovidesquickinvestigationonradiativecarrierdynamicsinsidethesystem,butitcannotexplorenon-radiativecarrierdynamicsaswellasthefaste-hspinrelaxationifspin-relaxationtimeislessthan5ps.TocompensatetheshortageofStreakspectroscopymeasurementandtoinvestigatethepoten-tialexistenceofcarriercorrelationinthesystem(detailmotivationisintroducedinchapter7),weperformedtwo-colorpump-probeexperimentwithsetupshowninFig.3.7.Thepump-probesetupisbasedonprevioussetupwithfew(1)addprobelaserwithabout20fspulse47Figure3.7Pump-probesetup.ThesetupissimilartoFig.3.6,butthecompensatorisreplacedbychopperduetolimitedspace,andthegoldmirrorisswappedwithbeamsplitter(BS).Theprobepulselaserwithhorizontalpolarizationentersinsystemthroughtheothersideofpolarizedbeamsplitter(PBS),thenmergeswithpumpexcitationfromTi:sapphirelaser.Thusinpump-probesetupherethepolarizationsofpumpandprobepulseareorthogonal.Tosimplifythediagram,liquidcrystaldeviceandpinholealongopticalaxisthroughspectrometersarehidden.widthfromtheotherfaceofpolarizedbeamsplitter(PBS),andthelightpathofprobelasermergeswiththatofpumplaserafterPBS.Inthiscase,thepolarizationsofpumpandprobelaserpulsesafterobjectivelensarealwaysorthogonal;(2)removeAOMsetupinpumplightpath,andreplacecompensatorwithachopperduetolimitedspaceinoriginalsetup.The"on-and-off"ratiothroughchopperissetabout1:100;(3)swapgoldmirror(GM)withbeamsplitter(BS).Forsimplicity,fewopticalcomponentsarehiddeninFig.3.7.TheprobelaserhittingonthemicrocavitycanbetranslatedwithitspositionororienteditsincominganglewithrespecttothesamplesurfacebytuningtwomirrorssetbeforetheprobepassesthroughthePBS.Intheexperiment,thelaserspotsfrompumpandprobelaserareassuredtobespatiallyoverlappedforeachadjustmentoftheprobelaser.TheusageofBSallowustohavelargertuningangleofprobelaser,butitalsoaffectstheac-48curacyoflightpolarizationmeasurementbecausethetransmittanceofhorizontallyandverticallypolarizedlightarenotthesame.3.3ConclusionInsummary,thelargedetuningofcavityresonanceandQWbandgapprohibitsra-diativelossfromcavityandenhancestheaccumulationofphotoexcitede-hpairsinMQWs.ThenegligibleTE-TMsplittingresultsinastraightforwardimplementofspin-controllasers.Non-resonantlypumpingcanavoidlasercoherenceimprintoncarriercorrelation,whichhelpsustostudythephaseofe-h-gsystemathighdensity.Imagespectroscopysetupaccompaniedwithpo-larizationcontroldesignenabletomeasureangularandspectralcharacteristicsoflightaswellasitspolarization,andthesephysicalquantitiesrevealstheE-vs-kkdispersionandspinrelaxationofradiativecarriersinMQWs.TheStreakimageoffersafastinsightincarrierenergyandspindynamicsatthesametime.Ontheotherhand,absorption/gainspectrummeasuredbytwo-colorpump-probesetupuncovertheevolutionofcavityresonanceshiftinganditsdispersion.Allthesemeasurementsbringacomprehensiveunderstandingofphotoexcitedcarrierspinandenergydy-namicsinoursystem,andfurtherhelpwithanalyzingthelasingmechanisminsidethesystem.49CHAPTER4SPIN-POLARIZEDLASINGINAHIGHLYPHOTOEXCITEDSEMICONDUCTORMICROCAVITYInthischapter,Idemonstrateroom-temperaturespin-polarizedultrafastpulsedlasinginahighlyphotoexcitedplanarsemiconductormicrocavity.Theemissionabovecriticalthresholdexhibitsangularlynarrowpulsedlasingwiththepulsewidthabout20ps.TheradiationshowsenergyblueshiftandspectralbroadeningwithincreasingpumpInaddition,theemissionpolarizationcanbecontrolledbyexcitationintensityaswellaspolarizations.Theemissionpolarizationishighlycircularlypolarizedunderellipticallypolarizedpumpingandcanexceedtheinputcircularpolarizationdegree.Alltheseresultswillbepresentedinthefollowingsectionsfollowedbyatheoreticalexplanation.Toinvestigatethelaseractioninmicrocavitywithhigh-densityphotoexcitedcarriers,weop-ticallypumpthesamplenonresonantlybyusing2psTi:SapphirelaserpulsesatEp=1.579eV(lp=785nm)withsquarebeamThelaserpumpisvariedbytwoordersofmagnitude,whichthecreatedphotoexciteddensityrangesfromapproximately51011to1013cm2perQWperpulseandcorrespondstoa2Ddensityparameterrs=1=(a0ppnth)ˇ5.3Œ1.2fora0ˇ15nminInGaAsQWs[80].4.1Spin-polarizedlasingatroomtemperatureThelaserischaracterizedintermsoftheangulardistributionandenergyasfunctionsofthein-planemomentum[angle-resolved(k-space)imagesandEvs.kkdispersions](Fig.4.1).Atthethreshold,theemissionofthemicrocavityinvestigatedherebecomesangularlyandspectrallynar-rowfortheco-circulars+=s+component,wheres+=s+isthehelicityofthepump/emission,respectively.AnintenseradiationmodeemergeswithinanangularspreadDq<3,correspondingtoastandarddeviationDk=0:3mm1ink-space.Approximatingsuchapartiallycoherentbeam50Figure4.1Spin-polarizedlasingatroomtemperature.(a)Angle-resolved[k-space(kX;kY)]luminescenceimagesatthelasingthreshold(P=Pth)forco-circular(s+=s+,leftpanel)andcross-circular(s+=s,rightpanel)components.Here,s=srepresentsthepolarizationofpump/luminescence,respectively.Pthˇ2:5108photonsperpulse(overanareaof80mm2),resultinginaphotoexciteddensitynthˇ31012cm2perQWperpulseforanestimatedabsorptionof10%fornineQWs.Insetsarethecorrespondingrealspace(r-space)luminescenceimages.(b)Energy(E)vs.in-planemomentum(kk)dispersionsalongthekYaxis(kX=0;kY=kk).asaGaussianSchell-modelsource[81],wecandetermineaspatialcoherencelengthof4mm,whichisclosetothespatialdimensionofthelasingmode.Onthecontrary,nolasingactionoccursforthecross-circulars+=scomponent,whichexhibitsanangularlybroadintensitydistribution51andaparabolicEvs.kkdispersivespectrum.Accordingly,theradiationatthethresholdhasahighlycircularpolarization.Figure4.2Nonlinearinput-output.(a)Emissionintegratedoverkk.3mm1unders+(circularly)orsX(linearly)polarizedpump.(b)Radiativeemissionefyvs.pumpunderacircularly(s+)andlinearly(sX)polarizedpump.Next,Iwilldescribethenonlinearinput-outputandpolarizationcharacteristicswithvaryingpumpFig.4.2(a)showstheemission(output)vs.thepump(input)underacircu-larly(s+)polarizedexcitation.Thepumpisthephotonperpulsetransmittedintothemicrocavitywithinacircular10mmdiameterarea.Theoutputnonlinearlyincreasesbyoneorderofmagnitudeforanincreaseintheinputbylessthat20%nearthecriticalphotoexciteddensity.Theonsetofsuchanonlinearoutputfortheco-circularcomponent(s+=s+)isasthethresholdPth(indicatedbyanarrowintheForP&1:5Pth,thecross-circularlypolarizedcomponent(s+=s)alsolases.Underalinearlypolarizedpump(Fig.4.2(a),greendots),thelaseractioncommencesataslightlyhigherpump(P=1:05Pth).This5%thresholdreductionwiththeopticalinjectionofthespin-polarizedcarriersissmallbutcomparedwiththe<1%reductionpredictedforanInGaAs-MQW-basedconventionalspinlasers[82].Ingeneral,suchathresholdreductionislessthan5%inmostlocationsandsamplesstudiedinthiswork.Thetotalemissionunderacircularlypolarizedpumpisclosetothatunderalinearlypolarizedone(Fig.4.2(b)).Theoverallefy(theratiooftheemissionemanatingfromthefront52surface[output]tothepumptransmittedintothemicrocavity[input])reachesaplateauof˘10%atP&3Pth.Intheplateauregime,theoutputlinearlyincreaseswiththeinputandresemblesthecharacteristicsofaconventionalsemiconductorlaser.Themaximalefyrangesfrom3%to11%dependingonexcitedlocationsanddetuningoftheQWandcavityresonance.Anefygreaterthan10%canbeobtained.Absorptioninthenine6-nmthickIn0:15Ga0:85As/GaAsMQWsinthecavityis12%atlp=785nmatroomtemperature.Therefore,anefygreaterthan10%impliesthatessentiallyallofthecarriersphotoexcitedintheMQWscanrecombineradiativelyandcontributetolaseraction.Inanutshell,theradiationexhibitsangularlyandspectrallynarrowlasingatlasingthreshold.Thelaserradiationissimplyaresultofmattergainintheactiveregionofcavityexceedingtheradiativerecombinationloss.Theemissionnonlinearlyincreaseswithincrementpumpandthelasingthresholdsaredifferentfororthogonalcircularcomponents,s+=s,ofemissionsundercircularlypolarizedpumping.Suchdifferencecomesfromunequalspin-carrierinjectioninthereservoirofthesystem.Theefy10%indicatesallphotoexcitedcarriersinMQWscontributestolaserradiation.4.2SpectralcharacteristicsHereIpresentEvs.kkdispersionwithphotoexciteddensitydependenceandstudyspectralchar-acteristicsofemission.Fig.4.3displaysnormalizeddispersionspectraofco-circularemissionatselectivepumpFarbelowlasingthreshold,luminescencefromGaAslayersdominatesandformsanisotropicangulardistribution(notshown).Slightlybelowlasingthreshold,aparabolicEvs.kkappears,whichisequivalenttoeffectivecavityresonancebycarriersinInGaAsMQWs.Atthethreshold,theradiationbecomesspectrallynarrow.Faraboveathreshold,theen-ergyofradiationblueshiftswithincreasingspectrallinewidthwhiletheradiationremainshighlydirectionalwiththepumpInFig.4.4,Istudythespectralcharacteristics.WhenthepumpisincreasedfromP=0.553Figure4.3Evs.kkdispersion.Angle-resolvedspectroscopyatP=0.8,1and4Pth.Figure4.4Luminescencecharacteristics.(a)2Dfalse-colorimagesofmicrocavityluminescence/lasingspectravs.thepumpforco-circular(s+=s+,leftpanel)andcross-circular(s+=s,rightpanel)components.Spectraarenormalizedwithrespecttotheco-circularcomponent(s+=s+)foreachpumpNotethattheintensitiesofthes+=sspectrafor0.8Pth<P<1.3Pth(shadedarea)arescaledupbyafactorof10.(b)SpectrallinewidthsDE(FWHM)andpeakenergiesdeterminedfromtheemissionspectrain(a).Pthtowardthethreshold,luminescenceblueshiftsbyˇ5meV,whereasthelinewidthDEdecreasesfromabout10meVto0.3meV.Fig.4.4(b)showsthelinewidthDEandthepeakenergyoftheco-54andcross-circularlypolarizedspectraatkk=0underacircularlypolarized(s+)pump.Thelinewidthisasfullwidthathalfmaximum(FWHM)ofthespectraldistribution.Slightlyabovethethreshold(Pth<P<1:5Pth),spectrallynarrow(DEˇ0.3Œ1.0meV)radiationemergeswithanonlineargrowthinmagnitude,whereasthepeakenergyremainsconstant.Farabovethethreshold(P>1:5Pth),thespectrallinewidthincreasestomorethan2meV.Theoverallemissionenergyshiftswiththeincreasingpumparemorethan10meV,whichislargerthanthecorrespondingenergyshiftofthecavitystopband(<2meV).Thelargeenergyshiftoriginatesfromphoto-modulatedcavityresonanceshifting,whichwillbeexplicitlypresentedinSec.4.5.Thespectralbroadeningisattributedto(1)moreenergyregionreacheslasingcondition(thegainexceedsradiativelossintheactiveregionofthecavity)undermorephotoexcitedcarriersinjected;(2)time-integratedspectralshiftofemissionduetothetime-dependentcavityresonancechange.Itisnoticedthatinfarabovethethresholdregion,co-andcross-circularcomponentsbothlasewiththerisingpeakenergywhileretaininganenergysplittingofˇ1Œ2meV.Thesplittingisaresultofdifferenttime-integratedspectraldynamicsfors+ands,andIwillexplainitindetailattheendofSec.4.4withFig.4.11.4.3EmissionpolarizationpropertiesAsaforementionedintheprevioussection,aspontaneousbuildupofthecircularlypolarizedradia-tionoccursatacriticalphotoexciteddensity.HereIdiscusstheemissionpolarizationpropertiesasfunctionsofphotoexciteddensityaswellasexcitationpolarizationchange.ThepolarizationstatecanbecharacterizedbytheStokesthree-vectors=fs1;s2;s3g,whichisinSec.3.2.4.Fig.4.5demonstratesthedegreeofcircularpolarizationDoCP(s3componentinStokesthree-vector)withpumpdependence.Belowthethreshold,theradiationisunpolarized(¯s3ˇ0).Slightlyabovethethreshold(Pth<P<1:2Pth),theradiationishighlycircularlypolarized(¯s3>0.95).ForP>1:5Pth,theradiationbecomesellipticallypolarizedwithreduced¯s3asaresultofincreasingradiationwithanoppositehelicity.Whenthehelicityofthecircularlypolarized55Figure4.5Emissionpolarizationvs.pumpThedegreeofcircularpolarizationDoCP(¯rc),determinedfromtheluminescenceintegratednearkkˇ0(jkkj<0:3mm1)underas+orscircularlypolarizedpump.Thedashedlinesarethecalculatedemissionandthe¯rc,withaspin-dependentstimulatedprocessassumed(seeSection:TheoreticalModel)pumpisswitched,DoCPchangesinsignbutmaintainsthesamemagnitude,i.e.,thepolarizationstateissymmetricwithrespecttothehelicityofthepump.ThepumpDoCPisquantitativelyreproduced(dashedlinesinFig.4.5)byarate-equationmodelassumingaspin-anddensity-dependentstimulatedprocess,whichisfurtherdescribedinSec.4.5.2.Anothermanifestationofthespin-dependentprocessishighlycircularlypolarizedlasingevenunderanonresonantellipticallypolarizedopticalexcitation(Fig.4.6).Here,thepumptrans-mittedintothemicrocavitysampleiskeptconstantwithvaryingpumpcircularpolarization(sp3,representedbythepumpStokesvectortracingameridianatthePoincarésphereshowninFig.4.6(a)).Whentheinitialspin-dependentpopulationimbalanceiscontrolledbyvariationofsp3,theDoCPofthelasingradiation(¯s3)canexceedthatofthepumpfor1:0Pth<P<1:5Pth(Fig.4.6(b)).Suchaspinarisesfromthefigain"anisotropyinthepresenceoftwothresholdpumpesfortwohelicitiesoflaserradiation,typicallydenotedasJT1andJT2intheliteratureonspin-controlledVCSELs[83,84,85].Highlycircularlypolarizedlasing(¯s3>0.8)occursevenwhenthesp3isaslowas0.5(altitudef=30).Next,Iconsiderapolarization-dependentexternal56Figure4.6effect.(a)Representationofpolarizationstates(Stokesvectors)inaPoincarésphere.Thepumppolarizationisvariedalongthemeridianinthes1-s3(x-z)plane.(b)Thetime-integratedDoCPofthespin-polarizedlaserradiationasafunctionofpumpDoCP(rpc)(blueline)at0.8(blackdots),1.0(magentadots),and1.2Pth(reddots).Thepumpismaintainedataconstantwhenrpcisvaried.Foraf,onlythehexofthemajoritypolarizedemissioncomponentisshown(s+for0f<180andsfor180f<360).Figure4.7External.Externalquantumefy(hex)vs.pumpDoCP,representedbythealtitudef)at1.2,1.0,and0.8Pth.Foraf,onlythehexofthemajoritypolarizedemissioncomponentisshown(s+for0f<180andsfor180f<360).hexoftheminoritycomponentisnotshownbecauseofalowsignal-to-noiseratioforrpc˘1.Errorbarsrepresentthestandarddeviationofhexovervemeasurements.57efy(hex)(Fig.4.7),whichisastheratioofthepolarizedemissionemanatingfromthefrontsurface(output)tothepumptransmittedintothemicrocavityofthesamepo-larization(input).Theexternalefyhexofthemajoritypolarizedemissioncomponentislessthan103belowthethreshold,andincreasesbytwoordersofmagnitudeat1.2Pth.Inbothcases,hexisinsensitivetosp3.Atthethreshold,hexexceeds102forsp3ˇ1(f=90,270),whereasitremains˘103forsp3ˇ0(f=0,180).Thelowhexbelowthethresholdisduetolossthroughnonradiativerecombination,reabsorption,andemissionsintoothernonlasingmodes.Withtheincreasingpumpastimulatedprocessdominatesoverthelossandyieldsadramaticincreaseinhexabovethethreshold.Acompetitionbetweenlossandspin-dependentstimulationcanresultintheobserved"spin(¯s3>sp3)effectunderellipticallypolarizedpump-ing,whichisqualitativelyreproducedbytheaforementionedmodel.4.4DynamicsandenergyrelaxationofluminescenceFigure4.8Luminescencedynamics.Polarizedtime-dependentluminescenceatkk=0forselectivepowerP=0.8,1and4Pthunderacircularpolarized(s+)pump.Blue(red)curvesrepresenttheco-circularI+(t)[cross-circularI(t)]components.Notethatthecross-circularcomponentshownatP=Pthismultipliedbyafactorof100.Thetimezeroisdeterminedfromtheinstrumentresponse(blackdashedcurve),whichismeasuredviapumplaserpulsesoffthesamplesurface.Thetimetracesarespectrallyintegrated(temporalresolutionˇ5ps).Tounderstandthemechanismofthespin-polarizedlaseraction,studyingthepolarizationdy-namicsthroughtime-resolvedpolarimetryandspectroscopyisneeded.Fig.4.8showstheselected58time-resolvedco-andcross-circularlypolarizedluminescence[I(t)]underas+circularlypo-larizedpump.Belowthethreshold,thetime-dependents3(t)reaches˘0.1whentheluminescencereachesitspeak,andthenitdecayswithatimeconstantlessthan10ps,asdemonstratedbytheminimaltransientdifferencebetweenI+(t)andI(t)atP=0.8Pth(Fig.4.8(a)).Atthethreshold,theco-circularcomponentcommencesthepulsedlaseractionwithin30ps,whereasthecross-circularcomponentremainsnegligible[I+(t)=I(t)>100](Fig.4.8(b)),resultinginhighs3(t)within30ps.Thecross-circularlaserpulsecommencesatP>1:5Pth(Fig.4.8(c)).Figure4.9Spindynamicsofphotoexcitedcarriersatlasingthreshold.Polarizedtime-dependentluminescenceatkk=0forP=Pthundercircularly(f=90)andellipticallyf=40polarizedpump.ThecorrespondingDoCP(t)arerepresentedbygraylines.Fig.4.9illustratess3(t)ofemission(graylines)atcircularlyandellipticallypolarizedexcita-tionatlasingthreshold.Themaximumofs3(t)isclosedtounity,andspinrelaxationtimes(decaytimeofs3(t))undertwoexcitationcasesareabout70ps.Theseresultsareindicativeofaspin-dependentstimulatedprocessthroughwhichspinpolarizationis[56,57,86,87,88,89].Thetemporallyandspectrallyresolvedmeasurementsarefurtherconducted,asshowninFig.4.10.Atthethreshold,theradiationremainsspectrallynarrow,withapeakenergythatisnearlyconstantwithtime.Abovethethreshold,theradiationexpandsspectrallywhenthelaseractioncommences,anditgraduallyredshiftswithtime.Inaddition,polarimetricmeasurementsrevealacircularlypolarizedhigh-energycomponentduringtheinitial10Œ20pspulsedradiation,followedbyanunpolarizedlow-energyoneforP>1:5Pth.Fig.4.11presentscross-sectionaltransientspec-59Figure4.10Dynamicsandenergyrelaxation.Temporallyandspectrallyresolvedstreakspectralimagesoftheco-circularcomponentI+(dE;t)atP=1.0,2.0,and4.0Pth.They-axis(dE)isoffsetwithrespectto1:408eV,thelasingenergyatPth.Thetemporalresolutionisˇ30psbecauseofthegrating-induceddispersion.traat4Pthfors+=s+(red)ands+=s(blue)emissioncomponentsandrevealsaforementionedpolarizationproperties.Moreover,thetime-integratedtransientspectraresultsindifferentmeanenergiesforthesetwocomponents,givingenergysplittingshowninFig.4.4(b).4.5TheoreticalmodelTounderstandthespin-dependentpolarizationandspectralcharacteristics,weproposethatwhenthechemicalpotentialofEHPexceedsthebarecavityresonanceEc,afractionofe-hpairsneartheeffectiveEcformscorrelatede-hpairs.Fig.4.12showstheenergylevelsofQWsandEc.Underhigh-intensitypumping,thechemicalpotentialashighas80meVabovebandgapexceedsthesecondquantizedlevelofQWs.TheEcshiftsresultingfromeffectiverefractiveindexchangeinthesystemduetohigh-densityEHP.NeartheEcafractionofthereservoirofEHPconversetocorrelatede-hpairsn0,givingradiativedecay.Oncetheconversionovercomesthedecayandn0exceedscriticaldensity,astimulatedemissionprevailsandresultsinnonlinearlypopulationincreaseinn0andinlaserradiation.Inthefollowingsection,weintroducetheconnectionofexperimentalresultwithourtentativeexplanation.60Figure4.11TransientlasingspectraatP=4Pth.Cross-sectionaltransientspectraattimedelaysextractedfromthetemporallyandspectrallyresolvedstreakimagesofasample.Transientspectraareaveragedover5psandnormalizedtothemaximalpeakintensityoftheco-circularcomponent.Thespectraareequallyscaledbutoffsetverticallyby1.Redlinesrepresenttheco-circular(s+=s+)component,whilebluelinesrepresentthecross-circular(s+=s)one.Theenergyscaleismeasuredwithrespectto1.408eV,whichisthepeaklasingenergyatthethresholdPth.Ininitialtimedelayoffewpsafterpulseexcitation,theemissionisspectrallybroadandblueshiftsbyabout5meV.Fordelayslessthan20ps,theco-andcross-circularcomponentshavethesamespectralpeakenergy(verticaldashedlines),suggestingcarriersinteractionswithsamespinsandoppositespinsarecomparablemagnitudes.Thespectralpeakenergyisdeterminedbythetotalcarrierdensityinsteadofindividualspin-uporspin-downpopulation.Ontheotherhand,theintensityoftheco-circularcomponentishigherthanthecross-circularcomponentwithin20psafterpulseexcitationbecausetheineffectiveinreservoirresultsinimbalancespin-population.Theemissionspectrumreachesamaximumatabout10ps,andthengraduallydecreasesinoverallmagnitudeandredshiftswithtime.Thetemporalenergyredshiftinspectraisattributedtoadescendingchemicalpotentialmwithadecreasingcarrierdensity..4.5.1Carrier-inducedstrongnonlinearityTheobserveddensity-andtime-dependentlasingenergyshiftcanberegardedasaresultofindex-inducedcavityresonanceshift.Thecavityresonanceshift(dEc)isrelatedtothechangeintherefractiveindex(dnc)approximatelythroughdEc=Ec=dnc=nc,wherencistheeffectiverefrac-tiveindexaveragedoverthelongitudinalcavityphotonmode.Therefore,acavityresonanceshiftdE˘10meV(Fig.4.4)requiresasizablereductionoftherefractiveindex,i.e.,jdnc=ncj˘0.7%.SofarquiteafewpaperhavereportedDnchange(Dn˘0:1)inbulksemiconductorsor61Figure4.12Energylevelsofsample.Schematicofsimplebandstructureofquantumwellsink-space(left)andr-space(right).E0gandEflgrepresenttheandsecondquantizedlevelsofquantumwells,respectively.Intheexperimentstudiedhere,thechemicalpotentialmisabout80meVaboveE0gandisclosedtoEflgandbarecavityresonanceEc.ThemmaybebeneathorexceedEc,andnewcavityresonanceE0cpresencesasaresultofphoto-modulatedindexchange.Thecorrelatede-hpairsformnearE0candplayimportantrolesinstrongnonlinearityeffectobservedinresearch.QWs[90],butasfarasweknownonehavereportedonlargeDninmicrocavity.ToexaminethepossibilityofthelargedEcwithrisingchemicalpotentialm,IwouldliketoillustrateoursimulationresultbasedontransfermatrixcalculationandcarrierbandeffectinQWs.Thesimulationwasdevelopedbymyco-worker,WeiXie,andtheresultispresentedonFig.4.13.TheeffectiverefractiveindexchangedninQWs(Fig.4.13(a))canbechangedto0.1ascarrierdensityincreasesto2Pth,wherethePthcorrespondstoe-hdensityDeh=11018cm3.TheEcblueshiftsinenergyabout10meVduetotheaforementionedindexchangednasshowninspectrum(Fig.4.13(b)),whichtheiscalculatedbytransfermatrixmethod.Thesimplemodelwasperformedundertwoassumption(1)thedninMQWsmostlyresultsfrombandeffectduetomlocatednearthehigherquantizedlevelsofQWs;(2)therefractive62Figure4.13Simulatedcavityshiftingwithband.(a)EffectiverefractiveindexchangedninMQWs(solidline)withincreasingpumpThedashedlinerepresentstherefractiveindexofMQWswithoutexcitation.Eflgisthesecondquantizedlevelofquantumwell.(b)spectrumchangewithout(black)andwith(red)presenceofcarrierdensity.Theinsetexhibitsthecavityresonanceshiftwithincreasingphotoexciteddensity.DehisthephotoexciteddensityatthresholdunderexcitationPth.indexofGaAsvarieslittle,asmisbelowthebandgapofGaAs.Oncetakingintoaccounttheaforementionedassumptions,themodelpredictsthe10meVenergyblue-shiftwithdn=n˘0:3%,andtheresultindicatesthesizablecavityshiftispossiblewithhigh-densitycarriersaccumulatedinQWs.4.5.2Spin-dependentstimulatedprocessTomodelthespin-controlledlasingprocesses,weuseasetofrateequationswithspin-dependentstimulatedprocesses.Weconsidertwostatespopulatedwithspin-polarizedelectron-hole(eŒh)pairs:anonradiativeEHPreservoir(Meh)andradiativecorrelatedeŒhpairsatkkˇ0(n0).TheeŒhpairsnonresonantlyphotoexcitedbya2pspulsedpumplaserat1.58eVrelaxrapidly(<5ps)tothereservoirvia,forexample,aspin-preservedscatteringprocesswithLOopticalphonons.Therefore,weassumethatspin-polarizedeŒhpairsareopticallyinjectedintothereservoiratagenerationrateofGpP,wherePisthepumplaserofhelicity.ThespintimeoftheeŒhpairs,1=Wsf,islessthan10ps,asdemonstratedbythepolarizedtime-dependentPLbelowthethreshold(Fig.4.8)aswellasinasamplewithoutthetopDBRmirrorlayers(Fig.3.4).TheeŒhcarriersinthereservoircanalsodissipatethroughreabsorptionandnonradiativerecombi-nation(Gloss).WefurtherassumethatafractionofeŒhpairsneartheeffectiveEcopticallyinduce63Figure4.14schematicsofspin-dependentstimulatedemission:correlatedeŒhpairs(Neh=bMeh).TheconversionofcarriersfromNehtotheradiativen0stateisenabledbythefollowingprocesses:(a)Wk,aspontaneousconversionfromNeh,and(b)Wss,aspin-dependentstimulatedscatteringfromNeh.Then0statecontributestotheleakagephotonsmeasuredexperimentallyatarateassociatedwiththecavityphotondecayrateGc.Thelasingdynamicscanthenbedescribedbythefollowingsetofcoupledrateequations:dMeh(t)dt=Gp(t)PWsfhM+eh(t)Meh(t)iGlossMeh(t)Wss(n0)Neh(t)n0(t)WkNeh(t);dn0(t)dt=Wss(n0)Neh(t)n0(t)+WkNeh(t)Gcn0(t):Thegenerationrateofcarriers,Gp(t),froma2pspulsedlaserpumpisrepresentedbyaGaussiandistributionwithastandarddeviations=2ps.Thespin-dependentstimulationrateWss=W0(1n0=nsat)isphenomenologicallysettodecreasewithdensity,wherethesaturationdensitynsatisobtainedbyofthepumpstationaryDoCP(¯s3).Theparametersareasfollows:W0=1=10[ps1],Wsf=1=10[ps1],Wk=104[ps1],Gloss=1=1000[ps1],Gc=1[ps1],b=0.015,andnsat=200.Givenaspatialmodeareaof10Œ20mm2forthen0state,thecalculatedthresholddensityisabout510105mm2,64Figure4.15Spin-dependentstimulation.(a)CalculatedstationaryDoCP(¯rc)withvaryingpumppolarizationrpc(representedbythealtitude)forP=0.8,1.0and1.2Pth.(b-c)Calculatedpolarizedtime-dependentradiationintensityforco-circulars+=s+[I+(t)]andcross-circulars+=s+[I(t)]componentsunderas+pumpforP=1.0and2.0Pth.ThetheoreticalPthissettothepumpwhenthestationary¯rc=0.5underafullycircularlypolarizedpump(rpc=1).consistentwithexperimentallymeasuredcarrierdensityperQWatthethreshold.Thismodelreproducesthepolarizedlaseroutputes(I)andDoCP(¯s3)asafunctionofpumpP(Fig.4.5)andasafunctionofpumppolarizationsp3(Fig.4.6andFig.4.15(a)).Thepolarizedtime-dependentPLisalsoreproducedqualitatively(Fig.4.8andFig.4.15(bŒc)).4.6DiscussionandconclusionThespin-polarizedlaserstudiedherehasastructuresimilartovertical-cavitysurface-emittinglasers(VCSELs)[91]andmicrocavitiesusedforstudiesofexciton-polaritoncondensates[17,20,19,34,26,21].InVCSELs,thelasingenergyistypicallydeterminedbythebarecavityresonanceandhaslimitedenergyshifts[92,93]andlinewidthbroadening[94,95,96]withincreasingcarrierdensity(seealsotheAppendixA).ThepolarizationpropertiesofVCSELsaretypicallyaffectedbycrystallineanisotropies[97],butquiteafewspin-controlledlasersarereportedinthepasttenyears.[54,58,51,52,56,86,87,88].Incontrasttoconventionalspin-controlledlasers(spinlasers),thespin-polarizedlasingpre-sentedinthisstudydisplays(1)substantialenergyblueshiftofmorethan10meVwithincreasingphotoexciteddensity,(2)spin-dependentenergysplittingsintheabsenceofanexternalmagnetic(3)ultrafastsub-10-pspulsedlasing,and(4)ahighexternalquantumefyof˘10%,65whichmatchesthefractionofcarriersphotoexcitedintheMQWs.Weattributethespin-polarizedlasingtoaspin-dependentstimulatedprocessofcorrelatede-hpairsformedneareffectivecavityresonanceinahigh-densityEHP.66CHAPTER5TRANSIENTDUAL-ENERGYLASINGINASEMICONDUCTORMICROCAVITYAhomogeneousexcitationinaninhomogeneousstructuremaycauseexoticluminescenceunderhigh-photoexcitedinjection.Inthischapter,Idemonstratesequentiallasingattwowell-separatedenergiesinthemicrocavitywiththesamestructurepresentedinthelastchapter.Twospatiallyoverlappedlasingstateswithdistinctpolarizationpropertiesappearatenergiesmorethan5meVapart.Underacircularlypolarizednonresonantpumping,anultrafasttransientcircularlypolarizedhigh-energy(HE)stateemergesquicklyafterexcitation.ThisHEstateisfollowedbyapulsedstatewithamuchlongerlifetimeatalowenergy(LE)state.TheHEstateishighlycircularlypolarizedasaresultofaspin-preservingstimulatedprocesswhiletheLEstateshowsareducedcircularpolarizationbecauseofadiminishingspinimbalance.Inthefollowingsections,theseresultswillbepresentedindetails.5.1SpectralcharacteristicsFirst,Iwillintroducethedensity-dependentenergyshiftsandlinewidthsofemission.Fig.5.1(a)showstheco-circulars+=s+luminescencespectra[S+(E)]atkkˇ0asafunctionofpumpAbovethebifurcationpumpPb1:1Pth,radiationbifurcatesintoadoublet(two-statelasing)withadominantHEstate.InFig.5.1(b),theemissionoftheLEstatereachesaplateaunearabove1:5Pth,whereastheemissionoftheHEstatecontinuestoincreaselinearlywiththepumpSpectrally,theHEandLEstatesdisplaydistinctenergyshiftswithincreasingphotoexciteddensity.Fig.5.1(c)illustratesthepeakenergiesofthetwostateswithincreasingpumpBelowPb,theemissionissingle-peakedandblueshiftsby6meVwhenthepumpincreasesfrom0.5Pthto˘1:1Pth.Whenthepumpincreasesgraduallyfrom1.0Pthto3.5Pth,theHEstateblueshiftslinearlyby5meV,whereastheLEstateredshiftsbylessthan0.567Figure5.1Spectralcharacteristicofduallasing.(a)Normalizedtime-integratedspectraoftheco-circular(s+=s+)emissioncomponentforjkkj<3mm1.(b)EmissionoftheHEstate(solidredcircles),theLEstate(solidbluetriangles),andthesum(solidblacksquares).(c)Peakenergies(solidshapes)andlinewidths(errorbars)oftheHEstate(solidredcircles)andLEstate(solidbluetriangles).Thepeakenergiesbelowthethresholdarerepresentedbythesolidblacksquares.Theemissiones,peakenergies,andlinewidthsaredeterminedbyofthespectrawithmultiple-Gaussianfunctions.Thephotoexciteddensityatthethresholdpump(Pth)isncˇ21012cm2perquantumwellperpulse.meV.ThisresultindicatesthattheenergydifferencebetweentheHEandLEstatesenhanceswithincreasingphotoexciteddensity.AbovePb,thelinewidthoftheHEstateincreasesfrom˘0.3meVatPthto3meVat4Pth.Ontheotherhand,theLEstateremainsspectrallynarrowwithalinewidthof1meVorless.Next,Iillustratethespectralcharacteristicsink-spaceandr-space.Fig.5.2(a)showsthek-spaceimagingspectraoftheco-circularemissioncomponentforselectedpumpes.Anearlyparabolicenergyversusin-planemomentum(Evs.kk)dispersioncurveemergeslightlybelowthethreshold(Pˇ0:8Pth).Atthethreshold(pumpP=Pth),theradiationbecomesdirectional(angular-spreadDkk1mm1)andspectrallynarrow(linewidthDE0.3meV)(Fig.5.2(b)).Thetime-integratedemissionspectraappeartobifurcateintoadoubletwhenthepumpisincreasedabove2Pth.Thetwolasingstatesarespatiallyoverlappedin-plane,asevidencedinther-spaceimagingspectra(Fig.5.2(c)).68Figure5.2Two-statelasinginamicrocavity.(a)Angularlyresolved(k-space)imagingspectraoftheco-circular(s+=s+)emissioncomponentatP=0.8,1.0,2.0,and3.3Pth.(b)Time-integratedspectraat0.8(solidblackline),1.0(solidredline)and3.3Pth(solidblueline).(c)Real-space(r-space)imagingspectraat2.0Pth.Thek-spacespectrashownin(aŒb)aremeasuredthroughapinhole,asrepresentedbythegraybox.5.2Dynamicsofdual-energylasingThespectraldoubletsthatappearintime-integratedspectroscopymeasurementsaretemporallyseparated,asshowninthetime-dependentpolarizedluminescencespectraatkkˇ0(Fig.5.3).Whentwo-statelasingoccurs,luminescencefromtheHEstateappearswithin10psafterpulseexcitationanddecayswithatimeconstantt0d˘10ps.AftertheHEstatediminishes,theLEstateappearsandthendecayswithatimeconstantt00d˘30Œ50ps.HereIdiscussthedensityandtimedependenceofthepeakenergiesoftheHEandLEstates.Inthehighlyphotoexcitedmicrocavitystudiedhere,EHPofdensityˇ1to51012cm2perQWperpulseareformedfollowingnonresonant2pspulseexcitationasaresultofrapid(<10ps)energy69Figure5.3Dynamicsofduallasing.(aŒc)Time-dependentspectraoftheco-circularcomponentatkkˇ0underP=1.0,2.0,and3.3Pth.TheenergydEismeasuredwithrespectto1.415eV,thelasingenergyatthethreshold.(d)Polarizedtime-dependentluminescenceoftheHEstateatdE=5meV[HE0asindicatedin(c)](solidanddashedredlines)andtheLEstatedE=5meV[LE0asindicatedin(c)](solidanddashedbluelines)forP=3.3Pth.dissipationthroughopticalphonons.WhenthechemicalpotentialmoftheEHPapproachesEc,theaveragerefractiveindexnearEccanbeconsiderablytheresultisasizableblue-shiftoftheeffectivecavityresonance(E0c).ThepeakenergyoftheHEstateincreaseswiththepump(Fig.5.1),whichcanbeunderstoodasaresultofthelight-inducedrefractiveindexchangeandtheconsequenteffectivecavityresonanceshift[98].Furthermore,underpulseexcitation,theeffectivecavityresonanceE0cdecreasesovertimetowardthebarecavityresonanceEcowingtothetemporaldecayofthereservoircarriers(Fig.5.3).Slightlyabovethethreshold,theHEstateemergesasaburstofspectrallybroad˘10pspulsedradiation,spurredbythestimulationofthemajorityoftheopticallyactivecarriers.Thisrapiddepletionoftheopticallyactivee-hpairsinthereservoirprecipitatesadropinE0c.Afterwards,theLEstateensurestheradiationfromalocal70whichisreplenishedwithe-hcarriersviaspatialdiffusion(Fig.5.2and5.3).Theprolongedreplenishmentofe-hpairsfromthereservoircausesatemporalred-shiftoftheLEstateover&50ps(Fig.5.3).Theincreasingpumpresultsinanapparenttime-integratedspectralred-shift(Fig.5.1(c)and5.3(bŒc)).Atcryogenictemperatures,similarmultipleburstsofradiationhavealsobeenobservedinlocalizedexciton-polaritoncondensatesformedinaspatiallyinhomogeneousmicrocavity.Thesedynamicrelaxationoscillationsappearastheresultoftheinterplaybetweencarrierdiffusion(gain)andBosestimulation(depletion)[31].5.3Polarizationofdual-energylasingFigure5.4Polarizationpropertiesofduallasing.(a)Stationarydegreeofcircularpolarization(DoCP=¯rc)oftheHEstate(solidandopenredtriangles)andLEstate(solidandopenbluetriangles)undercircularlypolarizeds+pump(upperpart,solidtriangles)orspump(lowerpart,opentriangles).DoCP=¯rc=(A+A)=(A++A),whereAreferstotheareasofco-circular(A+)andcross-circular(A)componentsoftheHEandLEspectralpeaksandareobtainedbyofthetime-integratedspectra(Fig.5.2)withmultiple-Gaussianfunctions.The¯rcoftheHEstatesincreasesfromzerotonearunityforPth<P<1:2Pthanddecreasesgraduallyto0.25.The¯rcoftheLEstatesisrelativelyhigh(>0.8)initially,butitdecreaserapidlytolessthan0.1whenthepumpisincreasedabove2.0Pth.(b)Thetime-integratedpolarizedspectraS(E)oftheco-circular(s+=s+!S+(E),blackcurve)andthecross-circular(s+=s!S(E),redcurve)componentsatP=Pth.Theenergy-dependentDoCP(E)=¯rc(E)=[S+(E)S(E)]=[S+(E)+S(E)](bluecurve)showsamaximal¯rc(E)ˇ0.8,whichislargerthanthespectrallyaveraged¯rcshownin(a).InFig.5.4,Istudythepolarizationpropertiesofthetwolasingstates.Fig.5.4(a)showsthe71¯rcoftheHEandLEstatesasafunctionofpumpThe¯rcoftheHEstaterisesfromnearlyzerotounityatthreshold,remainsabove0.9forPth<P<1:2Pth,anddecreasesgraduallyto0.25at4Pth.TheLEstateappearswithasizable¯rcslightlyabove1.1Pth,andshowsrapidlydiminishing¯rcforP&1:7Pth.Moreover,anapparentspin-dependentenergysplittingof˘1meVbetweentheco-circularandcross-circularcomponentsoftheHEstateappears,asdemonstratedbytheselectedpolarizedemissionspectraat2.0PthshowninFig5.4(b)(seealsoRef.[99]).ThespectrallyresolvedDoCP(E)=¯rc(E)alsoshowstheenergy-dependent¯rc,inwhichtheHEstatereachesamaximal¯rc(E)ˇ0.8,evenatahighphotoexciteddensity.Suchahigh¯rc(E)occursdespitethesub-10-psspinrelaxationtimesofelectronsandholesinInGaAs/GaAsQWs,aresultthatisindicativeofsub-10-pscarriercoolingandspin-dependentstimulatedprocesses.Therapidcoolingresultsinasizablespinimbalanceinthecavity-inducedcorrelatede-hpairsformedneartheFermiedgeofthehigh-densityplasmas,whereasthespin-dependentstimulationofthesee-hpairssuchopticalspinpolarizationinthepresenceofnon-radiativeloss[99].Bycontrast,theLEstatehasavanishing¯rcbecauseofthelackofspinimbalanceatatimedelayof50psormoreaftertheopticalinjectionofthespin-polarizedcarriers.5.4DiscussionInthisstudy,theHEstateisdominatedbyamacroscopicpopulationoffihot"e-hpairsneartheFermedgeviathespin-dependentstimulation.TheLEstateformsinaareaofalateraldimensionof˘2Œ5mm,whichisbynaturalcrystallinein-planeinhomogeneities(Fig.5.2).Aftertheradiativerecombinationofthesefihot"e-hpairs,theremainingficold"e-hpairsformtheLEstatethatgivesspectrallynarrowanddirectionalradiation.Therefore,theformationoftheLEstatehingesonthepopulationoftheremainingficold"e-hpairs,whichtypicallybecomesinsamplesinwhichthechemicalpotentialmcanexceedthebarecavityresonance(i.e.,m˘E00g&Ec).Spectralfunctionsresemblingthetwo-statelasingspectrapresentedherehavebeencalculated72fore-hsystemsinthepresenceofacavitybyLittlewoodetal.[100]andOgawaetal.[101,102].Excitationsinexcitoncondensates[103,13,100,104]orBCS-likee-hstates[105,106,101,102,107,108]canleadtospectralmultiplets.Moreover,analogousfrequencyshiftsanddoublingsoftheopticalexcitationshavebeenreportedinBosegasses[109,110,111],inwhichcondensateandthermalcomponentscoexist.Ingeneral,thedoubletintheabsorptionspectrafornormalandcondensatecomponentsinacoldBosegasisfundamentallyrelatedtothetwmodelofsu-helium[112].Incontrasttotheaforementionedstatesofthermalequilibrium,thetransientdual-energylasingpresentedhereisanon-equilibriumphenomenon,inwhichcarrierinjectionbyphotoexcitation,energyrelaxation,spatialdiffusion,anddissipationbybothspontaneousandstim-ulatedprocessesshouldallbeconsidered.Ingeneral,acouplede-h-photonsystemliketheonedescribedherecanexhibitdiverseenergydistributionsandpolarizationproperties.Forexample,thecrossoverfromphoton(i.e.,weakcouplinglimit)toexciton-polariton(i.e.,strongcouplinglimit)lasingwithdecreasingphotoexciteddensityhasbeenstudiedintermsofthespectralandangulardistributions,dynamics,andpolarizationsofemissionsfromamicrocavityatcryogenictemperatures[107,113,67,68,114].Insemiconductorquantumwells,10Œ100psburstsofsuper-[115,116]havebeenobservedinhigh-densitymagneto-plasmaintheabsenceofacavitystructure[117,118,14,15].Toclarifythemechanismsofthetwo-statelasingeffectfoundinthesamplesstudiedhere,itisnecessarytoconductfurthertemporallyandspatiallyresolvedspectroscopiestocharacterizetheenergydistributionandrelaxationofnonradiativee-hcarriers.Forexample,onecoulduseapump-probespectroscopytoshowanytime-ordensity-dependentresonancesofthehigh-densityEHPthatiscoupledtothecavitylightEventually,itwillbecomepossibletodevelopmultiple-pulselasingwithenergiesandpolarizationsthatcanbecontrolledbyexternalopticalstimulus[99]andlateral[98].73CHAPTER6MULTIPLE-PULSELASINGFROMANOPTICALLYINDUCEDHARMONICCONFINEMENTOpticaltrappingcontributestothestudyofinter-particleinteractionsinquasiparticlecondensate,andcanbeexploitedtocreateoptoelectronicdevices.Duetotheadvanceofbeamshapingtech-nique,opticallyinducedwithcontrollablesizeandshapehasbecomepossible.Inthissection,Ireporttheopticalvisualizationofmacroscopicquantizedstatesfromanopticallyinducedharmonicinahighlyphotoexcitedmicrocavityatroomtemperature.Pho-toexcitationcreatesmainlyfreepairsofelectronsandholesinanIII-V-basedsemiconductorQWasaresultofthermalionizationathightemperature[119,120].Inthehighlyphotoexcitedmicro-cavitystudiedhere,thenonlinearlyphoto-modulatedrefractiveindexresultsinasizableeffectivecavityresonanceshift,whichenablesopticallyinducedInanopticalinitiatedbyspatiallymodulatednonresonantpspulseexcitation,sequentialmultiple-pulselasingradiationcommencesatseveralquantizedenergylevels.Thetransverseopticalmodesinaspa-tiallymodulatedrefractiveindexcanalsobeunderstoodasanopticallyinducedpotentialforaquasiparticle,e.g.,correlatede-hpairsresultingfromtheeffectivecouplingtothecavitylightMultiple-pulselasingradiationfromquantizedstatesinaharmonic(po-tential)manifestsasaresultofthetime-andenergy-dependentcompetitionbetweenthegainandreservoircarrierrelaxation.Inthefollowing,Iwilldetailtheseresults.Theexperimentalsetupisthesamementionedinchapter4,butthebeamisswappedbyadouble-hump-shapedbeamtotheorientationoftheopticallypotential(Fig.6.1(aŒb)).6.1VisualizationofharmonicoscillatorsinopticaltrappingReal-space(r-space)imagingspectraprovidedirectvisualizationoftheopticalpotential.Fig.6.1(cŒd)showsther-spaceimagingspectraofanarrowcross-sectionalstripacrossthetrap.Anearly74Figure6.1Visualizationofthemacroscopicharmonicstates.(a)Intensityimageofthering-shapedpumplaserbeam.(b)Photoluminescence(PL)imageunderapumpofabout1.3Pth,wherethethresholdpumpPth=1:8108photonsperpulse.Thewhitedashedlinerepresentstheintensitypeakofthepump.PLemergesatthecenterwithaminimaloverlapwiththeannularpumplaserbeam.(cŒd)r-spaceimagingspectraatP=0.8Pthand1.3Pth.TheblackdashedlinerepresentstheharmonicpotentialV(x),whereasthewhitelinesrepresentthespatialprobabilitydistributionsofthelowestthreestatesofacorrespondingharmonicoscillator.(eŒf)k-spaceimagingspectra.Theenergysplittingis¯hwˇ2meV,consistentwiththequantizedenergyofaquantumoscillatorforaparticlewithmassm=3105me,asdeterminedbytheEvs.kkdispersion(dotedgreyline).Thequantizedmodesspectrallyblueshiftabout1meVfromP=0.8to1.3Pth,whereasthequantizedenergysplittingremainsthesame.Thepotentialandspectralshiftsareduetoadensity-dependentincreaseinthechemicalpotentialofthehigh-densitye-hplasmainthereservoir.parabolicpotentialwellof˘10meVacross3mmisrevealed.Suchaquasi-1Dharmonicpotential,V(x)=1=2ax2,isspontaneouslyformedunder2pspulseexcitation.Theresultantradiationappearsin-betweenthetwohumps,afewmicrometersawayfromthepumpspot.Ther-spaceintensitysagreewiththeprobabilitydistributionsofthequantizedstatesofaharmonicoscillator(harmonicstates).Thedeviationsoftheactualpotentialfromaperfectlyharmonictrapresultinslightlyasymmetricluminescenceintensitydistributions.Thesestandingwavepatternsformintheself-inducedharmonicopticalpotentialwhenamacroscopiccoherentstateemerges.Atacriticaldensity,theoccupationnumberofcorrelatede-hpairs(ni)inthesequantizedharmonicstatesapproachesunitywhentheconversionfromthereservoir(Neh)overcomesthedecayoftheharmonicstates.Consequently,whenastimulatedprocess(µNehni)prevails,niandtheresultantradiationincreasenonlinearlybyafewordersofmagnitudewiththeincreasingNeh.75Figure6.2Quantizedstatesinopticallycontrolledpotentials.(aŒc)Opticalimagesofpumpbeamatthefrontsamplesurfacefortwodouble-hump-shapedandonefocalspots.Thefalsecolorrepresentsthephotoexciteddensity(cm2)perquantumwellperpulseat0.4Pthfor(a)andat0.8Pthfor(b).Pth=1:8108perpulse,asinthemaintext.Thelasingthresholdsare0.4Pthfor(a)and0.8Pthfor(b).Thepeak-to-peakdistancesofthesetwodouble-hump-shapedpumpbeamsare5mmand3mm,respectively.(d,f,h)Real-spaceimagingspectrameasuredbelowthethreshold.Theblackdashedlineshowstheeffectiveharmonicpotential,whereasthewhitelinesrepresentthespatialprobabilitydistributionsofthelowestfewstatesofacorrespondingquantumoscillator.Thequantizedenergysplittingsfor(d)and(f)are4:0and2:2meV,respectively.Thefalsecolorrepresentsthesquarerootofintensity.(e,g)Real-spaceimagingspectraunderabove-thresholdpump.(i-n)Correspondingk-spaceimagingspectraunderbelow-threshold(i,k,m)andabove-threshold(j,l)Anevenmoreregularpatternappearsink-spaceimagingspectra(Fig.6.1(eŒf)).TheEvs.kkdispersionmeasuredbelowthethresholdallowsthedirectmeasurementoftheeffectivemassm=3105me,wheremeistheelectronrestmass.Moreover,thestrengthoftheopticallyharmonicpotentialacanbetunedthroughavariationinthespatialdistancebetweentwohumpsofthepumpbeam(Fig.6.2).Theenergyquantization(¯hw)varieswithpa=m,whiletheemissionpatternsevolveintotheprobabilitydistributionsforaparticlewithaneffectivemassminV(x)(Fig.6.2).766.2Dynamicsofmultiple-pulselasingFigure6.3Dynamicsofharmonicstates.(a)Time-dependentluminescenceink-spaceatP=1:0,1:1,1:2and1:6Pth.TheE3,E2andE1statesappearsequentiallywiththeincreasingpumpTherisetimesdecreasewiththeincreasingpumpforallstates.(b)Time-dependentspectrainr-space.Thefalsecolorrepresentsnormalizedintensities.Temporally,theseharmonicstatesemergesequentiallyanddisplaydistinctdensity-dependentdynamics.InFig.6.3(a),westudythetimeevolutionsofthreeharmonicstatesinthek-space,andFig.6.3(b)isthetime-resolvedspectrarevealingtheenergyrelaxationofthesethreestates.Thecorrespondingtime-integratedimagingspectraink-spaceareshowninFig.6.4.Atacriticalphotoexciteddensity,thehigh-energyE3statearises˘25psafterpulseexcitationandlastsfor˘20ps.Thecorrespondingpumpisasthethreshold(Pth).WiththeincreasingpumptheE2stateemerges˘25psafterE3at1.1Pth,whereasthegroundE1stateappear50psafterE2at1.2Pth.Intheopticallyinducedharmonicstudiedhere,theeffectivecavityreso-77nanceE0cdecreaseswithtimeasaresultofthedecayofreservoircarriers.However,theconversionfromthereservoirtoEistatecanbeefonlywhenE0cisresonantwithEi.SuchatemporaldecreaseinE0cresultsinatime-andenergy-dependentconversionefyfortheseharmonicstates(Fig.6.5)andconsequentmultiple-pulselasingradiationabovethecriticaldensitythreshold.Figure6.4K-spaceimagingspectra.Theenergyvs.in-planemomentumkjjdispersioncorrespondingtothedatasetinthemainpaperwiththeincreasingpumpfrom0.9to1.3Pth.ThequantizedE3,E2,andE1stateslaseinsequencewiththeincreasingpumpE3-statelasingcommencesfollowedbyE2-statelasingatabout1.2Pth,andthenE1-statelasingappearsat1.3Pthanddominatesovertheothertwostatesatahigherpump6.3HarmonicoscillatorspropertieswithdensitydependenceWefurtheranalyzetheemissionandenergyoftheseharmonicstatesbyusingtime-integratedspectrameasuredwithincreasingphotoexciteddensity(Fig.6.6andFig.6.7).Farbelowthelasingthreshold(P<0:4Pth),emissionisdominatedbyluminescencefromGaAsspacerlayers.Whenthepumpisincreased,theemissionsfromthecorrelatede-hpairsstatesbecomeincreasinglydominant,andtheE3stateeventuallylasesatthethreshold.Theemissionesofallthreestatesincreasenonlinearlybymorethantwoordersofmagnitudeacrossathresholdandthenreachaplateauatasaturationdensity(Fig.6.6(a)).Ontheotherhand,theemissionenergyofthesethreestatesincreasestoaconstantwiththeincreasingpump(Fig.6.6(b)).Theenergyspacing¯hw78Figure6.5Harmonicoscillator:below-thresholddynamics.(a)Time-dependentspectrallyandspatiallyintegratedluminescenceatP=0.9Pth.Theluminescencedecayswitha>500pstimeconstantlargelybecauseofthenonradiativeloss.(b)Spatialluminescencedistributionintegrateduptoadelayof50psafterpulseexcitation,revealingadouble-hump-shaped(c)Time-dependentluminescencespectraatP=0.9Pth.Thefalsecolorrepresentsthesquarerootoftheluminescenceintensity.(d)Time-dependentluminescenceintensityfortheE3(black),E2(red)andE1(blue)harmonicstates.Theintensityisintegratedoveraspectralrangeof1meVcenteringtheenergies,asindicatedbythedashedlinesin(c).onlyincreasesslightlywithdensity.ThespectrallinewidthsincreaseslightlyfortheE1state,byaboutafactorof10fortheE3state.Next,westudythedensity-dependentdynamics.Fig.6.6(c)showstherisetimesandpulsedurationsforE3,E2,andE1.Theproductofthevariancesofthespectrallinewidth(DE)andthepulseduration(Dt)isfoundtobeclosetothatofatransform-limitedpulse:&4¯handˇ1¯hfortheE3=E1andE2states,respectively.Theseharmonicstatesaremacroscopicallycoherentstateswithphaseandintensityinducedbyinteractions.79Figure6.6Densitydependenceofharmonicstates.(a)Temporallyandspectrallyintegratedemissionvs.pumpAllthreemodesdisplaynon-linearincreasesinintensitybymorethantwoordersofmagnitude,andsaturateat1:1,1:2and1:3Pth,respectively.(b)Peakenergy(solidshapes)andlinewidths2DE(errorbars)vs.pumpThesestatesspectrallyblueshiftby1to4meV.Thespectrallinewidths(DE)andpulsewidths(Dt)arereciprocalwithaproductofDEDtˇ4¯h(¯h)forE3andE1(E2),whichisclosedtotheuncertainty(Fourier-transform)limit.(c)Risetimevs.pumpforthethreestatesE1(blue),E2(red)andE3(black).Theerrorbarrepresents2Dt.Figure6.7resonanceenergyandpolarizedluminescencespectra.(a)Resonanceenergy(theenergyofemissionmodeatkkˇ0inK-spacespectralmapping)versusphotoexciteddensityunderatightly-focusedcircularpumpingbeam(radius˘1mm).Thespectralpeakcanbeconsideredastheeffectivecavityresonanceanddisplaysasizablespectralblueshiftwithincreasingthephotoexciteddensity.Suchanenergyshiftwithphotoexciteddensityisthebasisofopticallyinducedharmonic(potential)usingaspatiallymodulatedpumpbeamDˇ41012cm2perquantumwellperpulse.(b,c)Normalizedspectraintegratedoverk-spaceasafunctionofpumpinthedouble-hump-shapedpumpingcase:Co-circularly(b)andcross-circularly(c)polarizedcomponent.Quantizedharmonicstatesareformedabove˘0:8Pth.Belowthethreshold,theluminescencefromallstatesisunpolarized.Abovethethreshold,theE3stateishighlycircularlypolarized,whereastheE1statehasadiminishingcircularpolarization.Thefourthquantizedstate(E4)isweakly806.4TheoreticalmodelHereIpresentatheoreticalexplanationofsection6.1fromaviewofquasiparticle,andgivesimu-lationresultsofluminescencedynamicsandtime-integrated6.4.1OpticallyinducedpotentialandrefractiveindexchangesThetransverseopticalmodesbyaspatiallymodulatedrefractiveindexcanalsobeunder-stoodasanopticallyinducedpotentialforaquasiparticle.ConsideringtheelectromagneticinaplanarFabry-Pérotcavitywithamediumofa2Dspatiallymodulatedeffectiverefractiveindexn(r),wecanexpresstheHelmholtzequationfortheelectricinthefollowingform:¶2F(r;j;z)¶r2+n2(r)k20F(r;j;z)=0(6.1)TheelectricFinthecavitycanbedecomposedintolateralandtransversecomponents,andapproximatedasF(r;j;z)µy(r)exp[in(r)kz(r)z)],wherek20=k2z(r)+k2k(r),andkk(r)andkz(r)aretransverseandlongitudinalwavenumbersinthevacuum,respectively.Forsimplicity,weconsiderthe1DcaseandreduceEq.6.1to:¶2F(x;z)¶x2+n2(x)[k20k2z(x)]F(x;z)=0(6.2)Applyingtheeffective-massapproximationforsmallkk,weexpressthein-planedispersionEc(kk)intermsofaneffectivemassmfortheexcitation:Ec(kk)=Ec0+Ejj=(n¯hkz)22m+(n¯hkk)22m,wherem¯h2n2k2z2Ec0=¯hn2kz2c.Eq.6.2canthenbemappedtoatime-independentSchrödingerequationbyreplacingtheelectricamplitudewiththeprobabilitywavefunctionfofahypotheticalquasiparticlewithaneffectivemassminthepresenceofapotentialV(x),thus:¯h22m¶2f(x)¶x2+[V(x)Ec]f(x)=0(6.3)81Replacingtheeffectivemassforanopticalcavitymodewithlongitudinalwavenumberkz,weobtain¶2f(x)¶x2+n2kz¯hc[EcV(x)]f(x)=0(6.4)ComparingEqs.6.2and6.4givesV(x)=¯hckz(x)=Ec0(x)(6.5)Therefore,Ec0(x)andEkcorrespondtothepotentialV(x)andthekineticenergyofaquasi-particleofmassm.ConsideringEc0(x)µ¯hcn(x)Lc,whereLcistheeffectivecavitylength,wecanrelatethepotentialtothespatiallymodulatedrefractiveindexDn(x)¯nasfollows:V(x)=V[1+DV(x)V]=Ec01+Dn(x)=¯nˇEc0(1Dn(x)¯n),where¯nand¯Varetherefractiveindexandpotentialatx=0.Thus,thespatialmodulationofthepotential(DV(x))andrefractiveindex(Dn(x))haveaone-to-onecorrespondence:DV(x)¯VˇDn(x)¯n.6.4.2PhenomenologicalmodelingAsdiscussedinsection6.4,thespatialmodulationoftherefractiveindexcanbeconsideredaspatiallydependenteffectivepotentialforaquasiparticlewithaneffectivemassassociatedwiththebarecavityresonanceandmeanrefractiveindex.Themultipletransverseopticalmodesareequivalenttoharmonicstatesinharmonic(potential).Weuseasetofrateequationsthatconsiderastimulatedprocessandthespatialdistributionofe-hcarriers.WeconsiderthetemporalevolutionofthereservoirdistributionNR(x;t)andquantizedsatesni(t).Thee-hpairsphotoexcitednon-resonantlybya2pspulselasercooldownrapidly(<5ps)tothebandedge.ThecooledcarriersinthereservoirNR(x;t)aresubjecttonon-radiativeloss(Gnr)andthusresultinaslowdecrease(˘0.1meV/ps)inthechemicalpotentialm.Afractionofthereservoircarriers[Neh(x;t)=bNR(x;t)]couldcoupleeffectivelytothecavitylightwhenmadvancestowardthecavityresonanceEc(Fig.6.8),resultinginquasiparticlescoinedascorrelatede-hpairs.Thedouble-hump-shapedspatialdistributionofe-hplasmaresultsintheestablishmentofaharmonicchemicalpotential(V(x)µx2)inwhichthestandingwavesofamacroscopic82Figure6.8Schematicdiagramsforthetheoreticalframework.(aŒb)Energyleveldiagramsatdelayst1andt2(t1<t2)afterinjectionofe-hcarriersinthereservoir.Thechemicalpotentialm(t)ataedlocationdecreaseswithtimelargelybecauseofthenonradiativeloss.Theformationefyofthecorrelatede-hpairsisapproximatedbyaLorentzianfunctioncenteringatthecavityresonanceEc,whereastheconversionefyofcorrelatede-hpairsintoquantizedharmonicstatesisrepresentedbyaGaussianfunctioncenteringatquantizedenergiesE3,E2,andE1.(c)(toppanel)Theinitialspatialdistributionofe-hcarriersinthereservoir(NR(x;t=0+)µGp(x;t=0+)).(bottompanel)ThepotentialV(x)(solidblueline),whichisassumedtobestationary.Thespatialmatt1(solidblackline)andt2(dashedblackline).Thecorrelatede-hpairswithmclosetotheenergiesofEicanscattereffectivelyintotheEistates.coherentstateareformed.However,onlythecorrelatede-hpairsnearinresonancewiththequantizedstatesoftheharmonicpotentialcanspontaneouslybescatteredintoaEistateatarateWs.Abovethreshold,thepopulationofEistatesincreasesnonlinearlyasaresultofspin-dependentstimulation(µWssNehni).Theconsequentleakagephotonsfromthedecayofthesecorrelatede-hpairsatarateassociatedwiththecavityphotondecayrateGcarethenmeasuredexperimentally.Thedynamicsofthequantumoscillatorofcorrelatede-hpairscanthenbedescribedbythefollowingsetofcoupledrateequations:dNR(x;t)dt=Gp(x;t)PGnrNR(x;t)3åi=1hizNeh(x;t)[Wssni(t)+Ws];(6.6)dni(t)dt=ZdxhizNeh(x;t)[Wssni(t)+Ws]Gcni(t):(6.7)ThespatialgenerationrateG(x;t)followsthe2psGaussiantemporalanddouble-hump-shaped83ParameterParameterb0.0125Ws1:0104ps1Gnr1=700ps1Wss1:0102ps1.Gc0.5ps1Dm10meVE11.401eVDE11meVE21.403eVDE21meVE31.405eVDE31meVEc1.410eVTable6.1Fittingparametersbeam(Fig.6.8(c)andFig.6.9(c)).Pisthepumpofhelicity.zisanenergydepen-denteffectiveformationefyofthecorrelatede-hpairs.WeapproximatezasaLorentzianfunctionz=1=[1+(mEc)2=Dm2],whereDmistheenergyrangethatcorrelatede-hpairsareformed.hi=exph(mEi)2=(2DE2i)iisthecouplingefyofthecorrelatede-hpairstotheEistate,whereDEiisthespectrallinewidthoftheEistate.Theparametersarelistedinthetable.6.1.Inthissimulation,weneglectthespindegreeoffreedomandonlyconsiderthedensityregimeabove0.8NthRandjm(x;t)Ecj<15meV(NthR˘500,correspondingtotheoccupationnumberatP=Pth).Weapproximatem(x;t)=m0+gNeh(x;t),wherem0andgaredeterminedbythefollowinginitialconditions:m(x=0;t=0)=1.4eVandm(x=3mm;t=0)=1.407eV.Figure6.9Simulateddynamicsoftheharmonicstates.(a)Thetime-dependentoccupationnumberofharmonicstatesE3(solidblackline),E2(solidredline),E1(solidblueline),andthesumofthethreestates(dashedblackline)forP=0.8Pth.(bŒc)Similarto(a),butforP=1.15and1.5Pth.Forsimplicity,thespindegreeoffreedomisneglectedinthesecalculations.Additionally,theradiativedecayratesofthesestatesareassumedtobeidenticalandequaltoGc,resultinginanidenticalpulseduration.84Figure6.10Simulatedrisetimesandtime-integratedoftheharmonicstates.Thecalculatedrisetimes(a)andtime-integrated(b)oftheE3(solidblackline),E2(solidredline),andE1(solidblueline)statesasafunctionofpumpThismodelreproducesthetimeevolutionofthequantizedstateswithincreasingphotoex-citeddensity(Fig.6.9).Belowthethreshold,thescatteringofthecorrelatede-hpairsintothequantizedstatesoccursthroughaspontaneousdecayprocess.Theradiativequantumefyislow(<104)becauseofthedominantnon-radiativerecombinationloss.Abovethethreshold,thequantumefyincreasesbytwotothreeordersofmagnitudeasaresultofstimulation.Thismodelreproducesqualitativelytherisetimesandthetime-integratedemissionesofthemultiplepulselasingfromthequantizedstateswhenthepumpisvaried(Fig.6.10).6.5ConclusionanddiscussionInconclusion,Ireporttheobservationofmacroscopicharmonicstatesinanopticallyinducedinahighlyphotoexcitedsemiconductormicrocavityatroomtemperature.Thespa-tiallyphoto-modulatedrefractiveindexchangesresultinthevisualizationofharmonicstatesinamicrometer-scaleopticalpotential.Thequantizedenergiesoftheharmonicstatescanbeupto4meV,evenintheweak-couplingplasmalimit.Icharacterizethetimeevolutionoftheharmonicstatesdirectlyfromtheconsequentpulseradiationandidentifysequentialmultiple˘10pspulselasingwithdifferentemittinganglesandfrequencies.Ourgroupdevelopstherate-equationmodeltodescribethedynamicformationofquantizedstatesinanopticallyharmonic(Sec.6.4).Thisphenomenologicalmodel85reproducesqualitativelythedynamicsandintegratedemissionoftheharmonicstateswhenphotoexciteddensityisvaried(Figs.6.8,6.9,and6.10).Non-equilibriumpolaritoncondensateshavebeenmodeledbyaGrossŒPitaevskii(GP)(orcomplexGinzburgŒLandau[cGL])equationthataccountsforthelifetimeofpolaritons[121,104].However,cGL-typeequationsareinapplicableforthemultipledynamicstatesexaminedinthisstudy.Additionally,theformationofaBEC-likecondensatethatunderpinstheGP-orcGL-typeequationisnotnecessarilyinroom-temperatureexperiments.Transversepatternsandopticalmodeshavebeeninnonlinearopticalsystems[122],VCSELs[123,124],andmicroscalephotonicstructures[125].Inprinciple,themultipletransversemodelasinginahigh-densityEHPdescribedinthepresentstudycanbemodeledbyaself-consistentnumericalanalysiswithMaxwell-Blochequationsdevelopedforcon-ventionalsemiconductorlasers[126,127].ThisapproachisvalidprovidedthatthestrongopticalnonlinearitiesinducedbyCoulombmany-bodyeffects,suchasscreening,bandgaprenormaliza-tion,andphase-spaceareallconsidered.Forexample,onecanconsidertheformationofindex-guidedmultipletransversemodesasaresultofanoptically-inducedrefractiveindexreduc-tion(Dnc(x)).Thecavityresonanceshift(dE)canbeestimatedfromdEc=Ec=Dnc=nc,wherencistheeffectiverefractiveindexaveragedoverthelongitudinalcavityphotonmodewhichspansover˘mminthegrowthdirection.Therefore,dE˘10meV(Figs.6.1and6.2)correspondstojDnc=ncj˘1%.Sucharefractiveindexisprobablywithresonance-enhanceopticalnonlinearityfromthee-hcorrelation[12,128,129,102]orcarrier-inducedchangeinrefractiveindexatahighcarrierdensity(of˘1019cm3ormore)[130,90,131].Furthercharacterizingthephotoexciteddensitydistributionisnecessarytouncoverthemicroscopicformationmechanisms,andthemechanismsincludeasizablespatialmodulationinrefractiveindexorequivalenteffec-tiveharmonicunderpulseexcitation.Thiscanbeimplementedwiththeuseofotherultrafastspectroscopictechniques,suchasapump-probespectroscopy,isnecessary.86CHAPTER7OPTICALLYINDUCEDRESONANCESINASEMICONDUCTORMICROCAVITYSofarIhavedemonstratedspin-polarizedlasinginahighlyphotoexcitedsemiconductormicro-cavity,andthelargeenergyshiftwithincreasingpumpisattributedtothecombinationeffectofbothEcshiftandelectron-holeinteraction.TheEcshiftcanbeequivalenttorefractiveindexchangewithsimpleformuladEcEc=dncnc.Theessentialquestioniswhethercoherentstateexistsundersuche-h-gsystem.Ontheotherhand,theoreticalworkonQWssystempredictedthataquasiparticlegapformsattheconduction-electronandvalence-holeFermisurfaceinaninteract-ingsystem[12,13],whichcanbeontheabsorptionspectrum.Toexploretheexistenceofcoherentstateaswellasthequasiparticlegapinoursystem,thatmotivateustoperformtheopticallytime-resolvedpump-probespectroscopymeasurement.Theprincipleofpump-probetechniquehereisinthefollowing.Thestrongpumpingpulsegenerateshigh-densityphotoexcitedcarriersinthesample.Thepresenceofcarriersmaymodifytheopticalpropertiesofasample,whichcanberevealedonthetransmissionorbyshiningaweaklight(probe)onthesample.Bymonitoringtheprobesignalasafunctionoftimedelaybetweenpumpandprobe,itispossibletocharacterizethetime-dependentopticalchangeduetothepump.Intheexperiment,themeasurementrevealsatransientopticallyinducedresonancenearthecavityresonance(Ec)afternon-resonantpumpingwithafewpicosecondpulsedexcitation.Suchresonanceredshiftsinenergyanddecaysslowlywithalongtimeconstant.Iwilldetailthecharacteristicsoftheresonanceinthefollowingsection.Theexperimentalsetupismentionedinsection3.2.5withshowninFig.3.7.Fig.7.1demonstratestheopticalpumpingschemeinthepump-probemeasurement.Thepumpischosenas2-pslaserpulsewithpeakenergy0.2eVaboveEc.Theprobeisa20-fslaserpulsewithbroadbandenergycoveringfrom1.39to1.55eV.Therepetitionratesofpumpandprobelaserpulsesaresynchronizedthroughapiezo-drivenendmirrorinthelightpathinsidetheprobelaser87Figure7.1Pumpingschemeofpump-probemeasurement.Intheexperiment,themicrocavitysampleisnon-resonantlypumpby2-pslaserpulseandisprobedbya20-fsbroadbandlaserpulse.Thepumpenergyisabout0.2eVabovecavityresonanceEc˘1:41eV.Theenergybandofprobelasercoversfrom1.39to1.55eV.Thegrayarearepresentstheaccumulationofe-hcarrierswiththetopedgeaschemicalpotentialm.system.However,thearrivaltimeoftwolaserpulsesatsamplesurfaceiscontrolledbytuningthelightpathofprobelaser.ThetimedifferenceofthesetwoarrivaltimeisastimedelayDt=trtp,whichtrandtparethetimeofprobeandpumppulsearrivingatsamplesurface,respectively.Thepumpandprobelaserbeamsarelinearlyorellipticallypolarized,andtheirpolarizationsarealwaysorthogonaltoeachother.Thepumpis˘3109photonsperpulse,whiletheprobeisadjustedtoabouttwo-thousandthofthepump.Thepumpbeampassesthroughaholographicphase-only2Dspatiallightmodulator(SLM),andisfocusedonthesamplewithashapeof1010mm2orafocusedspotof2mmdiameter.Theprobebeamisalwaysfocusedtoaspotof2mmdiameterwithoutpassingthroughtheSLM.Intheexperiment,theluminescenceandprobelaserweremeasuredinrealspaceormomentumspacebyaFourier-transformopticalsetupequippedwithanimagingspectrometerandpsstreakcamerasystem.Thetimeresolutionislimitedbythe2psofpumplaser(Ti:sapphirelaser).887.1ResonanceinmicrocavityFigure7.2Differentialr(a)spectrawithnopump(black)andwithpump(red),denotethemasRandR'respectively.(b)CalculateddifferentialDR=R=(R0R)=R,whichindicateapresenceoflargeresonanceunderhighelectron-holeplasmadensity.First,Iwilldiscussthechangeofmicrocavitysampleundernon-resonantlyopticalpumping.Fig.7.2(a)showstheofmicrocavityintheabsenceofpumping(blackline,R(E))andinthepresenceofpumping(redline,R0(E))atDt˘5ps.Thepumpinghereisabout0.85Pth,whichPthcorrespondstophotoexciteddensity˘11019cm3.Thevityofstopbandisenhancedunderpumping,andalargedipappearsatEc.TheseresultsdemonstratetheQ-factorofmicrocavitybecomesbetterwithalargedensityofphotoexcitedcar-riers.ThedifferentialchangeasDR=R=[R0(E)R(E)]=R(E)canexceed50%showninFig.7.2(b).Forconvenience,theDR=Riscalledasresonanceinthefollowingsec-tions.ThelargejDR=RjandenhancementofQ-factorareattributedtothecombinationeffectofdecreasinglightabsorptioninDBRlayersande-hcorrelation.ThereductionoflightabsorptioninDBRincreasesthetransparencyneartheEcandthevityinstopband,whichisprovenbysimulationintroducedinlasersection.Thee-hcorrelationeffectisnotobvious,whichneedsmoreexperimentalresultstobeillustrated.TheresonanceshapeisasymmetricinFig.7.2(c),andisquitedifferenttothesymmetricLorentzianshapeinmostconventionallasersystems.Suchasymmetricshapecanbewell89byaDrudemodelwithaFano-shapedLorentzoscillator,thissimulationwillbedemonstratedinthelatersection.TheFano-resonancetypicallyoccursinaninteractingsystemresultingfromthelightinterferencebetweenabackgroundandaresonantscatteringprocess.Thisresultindirectlyimpliesthephotoexcitedcarriersgeneratedinthemicrocavitysampleisnotpurelyfreeelectronsandholes.Figure7.3Dynamicoftheresonance.(a)2DimageofdifferentialspectrawithdelaytimedependenceatpumpingP=0:85Pth.EachslicerepresentstonormalizedspectrumatparticulardelaytimeDt=trtp,whichtrandtparethetimeofprobeandpumppulsearrivingatsamplesurface,respectively.Thepumphereisafocusedspotof2mm.(b)Selecteddifferentialatpumping0.85Pth.Theresonanceexistsinalongtimeabout1ns.(c)Theenergypeak(black)anddepth(ref)ofresonanceasafunctionofDt.Thelong-livedresonancered-shiftsinenergyinabout20meV.TheinsetisenergyshiftingdE(thedifferencebetweenenergypeakandbottomenergy)asafunctionofDtinlogscale.Itillustratestwo-stepdecayprocesswithfastrelaxationtimet1˘60psandslowrelaxationtimet2˘380ps.(d)DifferentialwithselectedpumpTheresonanceblueshiftsinenergyaccompaniedwithdepthincrementaspumpincreases.Next,Idiscussthedynamicsoftransientopticallyinducedresonance,itislong-livedandcanhaveaspectralshiftwithtime.Toinvestigatehowtheresonanceevolveswithrelaxing90carriersinenergy,herethebeamofthepumpischosenasatightlyfocusedspot.Fig.7.3(a)illustratesthe2DimageofresonanceasafunctionofDtandenergyatpumppower0.85Pth.Theopticallyinducedresonancecanlastmorethan500ps.Fig.7.3(b)showsdifferentialspectraatselectiveDt.AsDtincreases,theresonancered-shifts20meVinenergyaccompaniedwithbroadeninglinewidthofdepth.Fig.7.3(c)trackstheenergypeakofresonance(black)andthemagnitudeofdepth(red)withDtdependence.Theresonanceappearswithin5psafterpumpingandthendecayswithfastandslowprocesses.ThedecaytimeconstantofthesetwoprocessesshownintheinsetofFig.7.3(c)are60psand380ps,respectively.Ontheotherhand,themagnitudeofdifferentialcanmaintain0.4evenatDt>500ps.Fig.7.3(d)representsdensity-dependentresonanceatDtˇ0+andselectivepumpnearandbelowthreshold.Theenergypeakofresonanceblueshiftsinabout3meVwhenpumpincreasesfrom0.5to1Pth,andthelinewidthofdepthnarrowsgradually.Theenergypeakoftheresonancevarieswithdifferentprobingangles,andsuchangle-resolvedresonanceappearstobeaparaboliccurve.Thiscurveresemblestheangle-resolvedspectrumofluminescencefromthemicrocavitysample.Fig.7.4demonstratestheangulardispersionoftheresonanceunderpumppower0.9PthatDt=10ps(black)and680ps(red).Theerrorbarsrep-resenttheFWHMofthedepth.Theblackandreddashedlinesareparaboliccurvesforangle-resolvedresonanceenergypeak,whilethebluelinerepresentsthecurveoflumines-cencespectralpeakatdifferentanglesshownintheinset.Theconsistencyoftheblackdashedlineandthebluelineindicatestheluminescencespectrummatchestotheresonanceat10Œ50psaftertheexcitation.7.2Polarization-dependentresonanceinmicrocavityUndercircularlypolarizedpumping,thedifferentialechangebyprobingwithorthogonalcircularlypolarizedcomponentsaredifferent,indicatingourmicrocavityunderhighphotoexcita-tionischiralcharacteristics.Fig.7.5(a)showsthedifferentialchangebelowlasing91Figure7.4Angulardispersionoftheresonance.Angle-resolvedresonances(thepeakofthedifferentialspectrum)atDt=10ps(black)and˘700ps(red)underpumpingP=0.9Pth.Theerrorbarrepresentthefullwidthhalfmaximum(FWHM)ofthedifferentialDashedlinesaresimulatedparaboliccurves,whilebluelineisparaboliccurveofangulardispersionspectrum(insetofphotoluminescenceat0.9Pth.threshold(0.9Pth)atDt=0undercircularlypolarizeds+andlinearlypolarizedsxpumping.Aenergypeakdifferenceabout0.8meVappearsbetweens+=s+(red)ands+=s(blue)compo-nentsoftransientinducedresonance.Fig.7.5(b)tracesdowntheenergypeakofresonancefordifferentcomponents.Thetransientspin-dependentsplittingdecreasesfrom0.8meVtozerowithdecaytimeinabout50ps.Thesplittingoftransientresonancerevealsthattheopticalresponsesofmicrocavityfortwoorthogonalcircularlypolarizedlightaredifferent.Undercircularlypolarizedpumping,itcreatesanunbalancedpopulationofspin-upandspin-downcarriersinreservoirwithin0-50ps.Whenthemicrocavityisprobedbycircularlypolarizedlight,thes+canonlyrespondtospin-upcarriers.Therefore,theunequalspin-polarizedcarriersresultsinenergysplittinginpump-probespectroscopy,andsuchsplittingdecreasesduetothereducingpopulationdifferenceofspin-polarizedcarriers.Thedelaytimeisrelatedtospinrelaxationtimeofpho-toexcitedcarriers,andislargerthanlasinglifetime˘10ps.Theunbalancedspincarriersisthe92essentialrequirementtoinitiatespin-dependentstimulationandthespin-polarizedlasingpresentedinChapter4.Figure7.5Polarization-dependentresonance.(a)Differentialspectraundercircularlypolarized=sigma+pumpingandlinearlypolarizedsxpumping.Theco-circulars+=s+(polarizationofpump/probe)andcross-circulars+=scomponentsarerepresentsasredandbluedots,respectively.Thecross-linearcomponentisshownasblackdots.(b)Energypeaksofthedifferentialspectrain(a)withashapeof1010mm2.ThedifferenceDEofenergypeaksoforthogonalcircularcomponentsappearsatDt=0,anddiminishestozerowithdecaytimeapproximatedabout25ps.7.3SimulationResultThelargejDR=Rjcanbeseenastheeffectofcarrier-inducedrefractiveindexchangeinphotoex-citedmicrocavity.Inthefollowingparagraphs,Iwillpresentafewmethodstosimulatespectrumandexploretheeffectofrelaxingcarriersinthewholesystem.Thediscussionaboutpo-tentialexistenceoftheexistingcorrelatede-hpairswillbementionedlater.7.3.1Drude-LorentzmodelBeforepresentingthetheoreticalmethods,Iwouldliketooutlinetheconnectionbetweentheandthedielectricconstante.Theformeroneisacommonmeasurementinoptics,andthelatterisoneofimportantpropertiesinmaterials.ThedielectricconstanteaffectstheCoulomb93forcesbetweentwopointchargesinmaterials,soitcanmodifytheopticalpropertiesofmaterialsifechanges.Therefractiveindexnistypicallyusedtorepresenttheopticalparameterofmaterials,andrelatestothedielectricconstantbyn=pe.Therefractiveindexisnormallyafrequencydependencedenotedasn(w),wherewisthelightfrequency.Themicrocavitysamplewiththestructureofmultiplelayeredmaterialscanberegardedasawholesamplewitheffectiverefractiveindexofsamplen(w).Thecanbededucedby:R(w)=n(w)1n(w)+12accordingtoFresnelequation.Ifthedielectricconstantisrealnumber,thenitcanbeexperimentallydeterminedbymeasuringR(w).However,thedielectricconstantistypicallyacomplexnumberinmathandcannotbededucedbyspectrumonly.Althoughe(w)cannotbeobtainedpreciselyfromthespectrum,wecouldapplyfewsimplemodelstostudythesystempropertiesunderintenseopticalpumping.ThemodelweuseisDrude-Lorentz(DL)model.Itdescribesthattheopticalresponseofchargecarriersinmaterialsisrepresentedasasetofharmonic(damped)oscillators,andthee(w)willbe:e(w)=e(¥)+åiw2piw2oiw2igiw(7.1)Heree(¥)isas"high-frequencydielectricconstant",whichrepresentsthecontributionofalloscillatorsatveryhighfrequencies(comparedtothefrequencyrangeinconsideration).Theparameterswpi,woi,andgiarethe"plasma"frequency,thetransversefrequency(eigenfrequency)andthelinewidth(scatteringrate),respectivelyofi-thLorentzoscillators.The"Drude"inmodel'snamedescribestheresponseoffree(unbound)chargecarriers,andthewoiiszerointhiscase.IntheDLmodel,theLorentzoscillatorsareindependent,andthespectrumnormallycanberepresentedbythesumofindependentLorentzoscillators.Fig.7.6(a)giveanexampleshowingaspectrum(blackdots)obtainedinourexperimentwithoutpumping.ThesimulationcurvebasedonDLmodelisshownasredline.TheDLmodeldescribesamaterialsystemwithfreecarriers;however,theDLmodelcannotwellwiththeunderpumping.Thisresultindicatesthattheoscillatorsdescribedbyclassicalopticsinthemodelareinteractinginsteadofbeingindependent.Onecouldalso94Figure7.6Simulationofrspectrawithoutandwithpresenceofpumpingin(a)and(b),respectively.Theblackdotsrepresentmeasuredandredlinesaresimulation.Thesimulationmethodusedin(a)isclassicalDrude-Lorentz(DL)model,whilein(b)aFano-shapedoscillatorisaddedinDLmodel.witnessthedifferencefromtheresonanceshape.TheresonanceintheDLmodelistypicallysymmetricresemblingtheLorentzshape,buttheoneinourmeasurement(Fig.7.2)isasymmetric.TheasymmetricshapeofresonanceissimilartotheFano-resonancereportedinotherinteractingsystems.Therefore,weDLmodelbyswappingoneoftheLorentzoscillatorswithaFano-shapedLorentzoscillator,whichtheformofdielectricconstantis:e=w2pw2ow2igw1+iwpw2+wpwqwow2(7.2)Herewqisaninsertedparameterthatgivesasymmetricshape.Ifwq=0,theaboveequationrecoverstotheaforementionedDLform.Thewqrelatestoq-factorinFano-resonancetheoryby:q=wo=wq.Ifthewq(orsmallerq)islarger,thenasevereasymmetricresonanceshapeisobtained.ThesimulationresultofDLmodelwithFano-resonanceisshowninFig.7.6(b).Afteropticalpumping,thepopulationdistributionofphotoexcitedcarriersvariesintimeandenergy,thuswewillexplorethesecarriers'dynamicsincludingnon-radiativecarriersthroughstudyingthetime-dependentdielectricconstant.Fig.7.7demonstratesthe(blackdots)withpumpingindelaytimeDtat(a)0psand(b)670ps.ThesimulatedcurveshowninredlineisbasedonDLmodelwithadditionalFano-shapedLorentzresonance.Fig7.7(c)representsdi-electricconstantinrealparter(black)andimaginarypartei(red),withthesolidandshortdashed95Figure7.7Timedependentdielectricconstant.underpumping(blackdots)withsimulation(redline)basedonDLmodelwithadditionalFano-resonanceshownat(a)Dt=0and(b)Dt=670ps.(c)spectralresolveddielectricconstantinrealpart(e1,blackline)andimaginarypart(e2,redline).ThesolidandshortdashedlinerepresentthecaseatDt=0and670ps,respectively.(d)spectralresolvedrefractiveindexwithsameas(c).linesymbolsthecaseatDt=0andDt=670ps.Fig7.7(d)illustratesthecaseofrefractiveindexandtheextinctionfactork.Thekassociateswithabsorptionabyformulaa=2wck,wherewisthelightfrequency.NearDt=0,theeishowsconcaveshapenearresonanceaccompaniedwithsmallera.Thedepthofeiisclosedbutnotthesametothepeakofresonance,whilethetransitionofer(frompositivetonegative)aswellastheminimumofnissameastheresonancepeak.Astimeincreases,theoverallshapeofdielectricconstantredshiftsinenergywithattenuatedampli-tude.Theconcaveshapeofkimpliesthatthedecreasingabsorptionnearcavityresonanceallowsprobelaserlightpenetratedintosampleinsteadofbouncingback,sothevitydropsnearthecavity.96Figure7.8changefromabsorptioneffect.Differentialchangeresultingfromdifferentdecreasingimaginarypartofrefractiveindexof(a)GaAsand(b)InGaAs.7.3.2Transfer-matrixmethodThesecondwaytosimulateisthetransfer-matrixmethod,anditgivessomeinsightaboutcarriersimpactonthesystem,too.Thetransfer-matrixmethodisbasedonMaxwellequationplusthecontinuousconditionfortheelectricastheelectromagneticacrossboundariesfromonemediumtoanother.Iftheisknown,thestackoflayerscanberepresentedasasystemmatrix.OneexampleofsimulationbythismethodisalreadyshowninFig.3.2,IalsodiscussedtheresonanceshiftwiththerefractiveindexchangeinducedbybandeffectofcarriersinSec.4.5.NowIconsideriftheabsorptionofthesystemisbyalargedensityofcarriers,howthesystembehavesonitsspectrum.Theopticalabsorptionofthesystemassociatestotheimaginarypartoftheeffectiverefractiveindex.Thereducedimaginarypartoftherefractiveindexinthesystemcouldenhancethecontrastoflocalminimumandmaximumofvity.Ourmicrocavitysampleconsistsofthreelayermaterials:GaAs,AlAsandIn0:15Ga0:85As(abbreviatedasInGaAsforconvenience).IwillnotconsidertheabsorptioneffectfromAlAssincethebandgapofAlAsis2.12eV,whichisfarabovethepumpingenergy.Theimaginarypartoftherefractiveindexniofonematerialiszeroiflightenergyisbelowmaterial'sbandgap(noabsorption).Fig.7.8illustratesdifferential97changefromdifferentreduceddegreeofabsorptionpartof(a)GaAslayersand(b)InGaAslayers.GaAsandInGaAsarealsothemainconstituentmaterialsofDBRandMQW,respectively.Inanenergyrangeabovethebandgapofsemiconductors(GaAsorInGaAs),thereducingnicanresultinlargerlocalmaximumandsmallerlocalminimumofectivity.ComparingtheeffectfrombetweenGaAsandInGaAs,theGaAspartgivesmorebecausethethicknessofGaAsismuchlargerthanthatofInGaAs.Intheexperimentalresult(Fig.7.2(c)),the50%magnitudeofDR=Rrequiresthechangeofimaginaryrefractiveindexupto40%inGaAsor60%inInGaAs.Thisdeductionarisestwounansweredquestions:(1)Canalarge-densityfreeEHPresultsin40%changeinabsorptionofGaAs?SofarIhaven'tfoundanyworkreportedaboutlargechangeofabsorptioninsemiconductorsduetohigh-densityEHP.(2)Howtoexplainaninconsistenceofchangebetweentheexperimentalresultandsimulation.TobetheresonanceintheexperimentappearatenergybelowtheGaAsbandgap;however,thechangenear880nmisverysmallinoursimulationmodel.Thesimulationmodelwithtransfermatrixmethodisbasedontheclassicalopticsinthesystemoffreecarriers.Therefore,theinconsistenceindirectlyimpliesthataninteractionbeyondclassicalphysicsexistsinoursystem.7.4TheoriginofopticallyinducedresonanceFromprevioussection,alargedensityoffreecarriercancausecarrier-inducedrefractiveindexchange,butitcannotexplainalltheresultofthelargemagnitudeofDR=R.Theopticallyinducedresonanceisattributedtothecombinationeffectofcarrier-inducedrefractiveindexchangeinDBRlayersandtheenhancementofopticalnonlinearityduetoe-hcorrelationinMQW.Inthissection,IwillpresenttwocontrolexperimentstoexplorehowmuchcontributionofsucheffectcomesfrompurecavityorDBRlayers.ThecontrolexperimentisthemeasurementofDR=RfromacommercialVCSEL,whichisthoughtnoe-hcorrelationplayinginroleandistypicallynoabsorptioninDBRlayers.ThemagnitudeofDR=Rislessthan5%,whichissmallerthanoursimulation.Itdemonstratesagain98Figure7.9Carriereffectonblankcavity.spectra(blackdots)andsimulation(red)under(a)nopumpingand(b)pumping,respectively.ThesimulationisbasedonDLmodel.thattheabsorptioninDBRlayersindeedchangestheopticalpropertiesofmicrocavitysample.ThesecondcontrolexperimentisthemeasurementofDR=Rfromamicrocavitysamplewithquantumdots(QDs).Thissampleisobtainedfromourcollaborators,Lin'sgroup,anditcontains19topDBRlayersand24bottomDBRlayerswiththesamecompositestructurewithmicrocavitysamplepresentedbefore.ThebareEcisshiftedtoaround˘885nm.Thesamplehasmuchsmalleractiveregion(thetotalvolumeofQDs)comparedtopreviousmicrocavitysamplewithMQW;therefore,thee-hcorrelationissuppressed.Forconvenience,IcallthemicrocavitysamplewithQDsasblankcavity.Fig.7.9demonstratestheofblankcavityunderaconditionof(a)theabsenceofpumpingand(b)thepresenceofpumping.Undertheopticalpumpingbeamasmalldipappearsat˘883nm,whichisblueshiftcomparedtobarecavityresonance.TheredlinesarethesimulationbasedonDLmodel,whichwellwiththesetwospectra.ThisimpliestheblankcavitycanbedescribedbythesumofindependentLorentzoscillatorsnomatterifthesystemisopticallypumpedornot.TheopticalresponseofthemicrocavitywithMQWandblankcavityarequitedifferent,andtheircomparisonisshowninFig.7.10.TheleftpanelsshowDR=Rmeasuredinoursample,andtherightpanelsshowDR=Rmeasuredintheblankcavity.Thetopandbottompanelsareusingandtightlyfocusedspotbeamofpumping,respectively.Underthesameorder99Figure7.10ComparisonofblankcavitywithandwithoutMQWs.(aŒb)DifferentialspectraofthemicrocavitywithMQWsunderorfocusedexcitation.(cŒd)Sameconditionsas(aŒb)butthesamplesarethemicrocavitywithoutMQWsintheactiveregion.photoexciteddensity,theenergyshiftintheblankcavityis10meV,whichismuchshorterthanthatinoursample.Moreover,thelinewidthofresonanceinthesampleisbroaderthanthatintheblankcavity.Itgivesanevidencethatthelight-inducede-hcorrelationinMQWtheopticalpropertiesnearEc,andthee-hcorrelationmakesmorethan50%contributionsonjDR=Rj.7.5ConclusionandDiscussionInconclusion,atransientoptically-inducedresonanceappearsnearEcwithin5psafter2pspulsepumpexcitationwithnearly0.2eVexcessenergyaboveEcandthendecaysslowlywithmorethan500psdelaytimeconstant.ThedifferentialchangeDR=Rmeasuredintwo-color100pump-probespectroscopycanexceed50%,whichisthreetofourordersofmagnitudehigherthantypicalphotoexcitedmeasurementintheGaAs-basedquantumwellorsemiconductormicrocavity.Theopticallyinducedresonanceisattributedtothecombinationeffectofcarrier-inducedrefractiveindexchangeinDBRande-hinteractioninMQW.Theenergypeakofsuchresonancecanshiftin5meVundertightlyfocusedpumpingwithtwodecayrates.Ontheotherhand,theresonancehasenergysplittingundercircularlypolarizedpumpingwithbeamindicatingourmicrocavityischiralcharacteristics.Anyspectrumchangeassociateswitheffectiverefractiveindexchangeinasystem,butsuchcarrier-inducedindexchangecannotbetotallyattributedtoopticalconstantchangeduetofreecarriers.Isimulatethepump-probebyDLmodelwithanadditionalFano-shapedLorentzoscillator.Theofasymmetricshapeoftheresonanceindirectlyimpliesourmicrocavityisaninteractingsystemunderopticalpumping.Next,thesimulationwithtransfer-matrixmethoddemonstratesthat50%DR=Rneeds40%changeinabsorptionofGaAs,whichseemsunlikelyinafreeEHPsystem.Last,IpresentcomparisonofDR=RmeasurementbetweenmicrocavitywithMQWandblankcavity,whichboththeenergyshiftwithphotoexciteddensityaswellasthemagnitudeofDR=Rinourmicrocavityarelargerthantheothercase.Itrevealsthatthelight-inducede-hcorrelationcanmodifytheopticalresponsenearEcwiththecontributionofthemagnitudeofDR=Rexceeding50%.101CHAPTER8DISCUSSIONANDFUTUREDIRECTION8.1SummaryanddiscussionInthissection,Iwillillustratetheofourworkandsummarizetheessentialexperi-mentalresults.Inmythesiswork,myco-workersandIexploredthecooperativephenomenacausedbye-hcorrelationinahighlyphotoexcitedmicrocavityatroomtemperature.ThephotoexcitedcarriersformEHPwithFermilevelabout80meVabovethebandgapEgofQWinmicrocavity.AfractionofelectronsandholesinEHPcantransformtolight-inducedcorrelatede-hpairswithenergynearbutnotlockedtocavityresonanceEc.Thesecorrelatede-hpairsresultsinlasingradiationwhenthephotoexciteddensityexceedsthecriticaldensity.Fewexperimentalresultsarelistedanddiscussedinthefollowingtosupportthatthelasingradiationstudiedhereisthestimulatedemissionofcorrelatede-hpairsinsteadofcavityphotons:DynamicsofPLunderexcitation:WhenthemicrocavitysampleispumpedbyexcitationwithpowerfarabovelasingthresholdPth,abroad-bandlasingradiationcom-menceswithtransientlasingenergyred-shiftingintimedomain(Fig.4.10-c).TheeffectiveEcdeterminedbytherefractiveindexofDBRisalmostedwithin100psafterexcitation.Therefore,thered-shiftoflasingradiationcanexcludethelasingmechanismfromconven-tionallaserinwhichthelaserenergyislockedtoEc.TheenergyshiftofPLresultsfromthechemicalpotentialdropofcorrelatede-hpairsduetothedissipationofEHP.Thedy-namicsofPLresemblestheinthesemiconductorQW[14,15,16]withthesimilarphotoexciteddensitybutatcryogenictemperature.Spontaneousconstructionofquantumcorrelationisacrucialfactorresultinginthesemacroscopiccooperativephenom-ena.SuchcorrelationcanbeenhancedwiththeassistanceofEcandmakeitpossible102torealizequantummany-bodyphenomenaatroomtemperature.Therefore,theenergylevelofcorrelatede-hpairsisnearbyEcwithestimatedDE˘15meVrangenearbyEc.DynamicsofmultiplelasingfromharmonicThemultiplelasingwithdiscreteenergiesfromharmonicappearwithseparaterisingtimeinanorderofhightolowenergy(Fig.6.3).Theconditionforlasingfromeachenergystaterequiresthattheenergyofcorrelatede-hpairsisresonanttothetraversecavitymodeinducedbytheopti-callyinducedThechemicalpotentialofcorrelatede-hpairsdropsduetothedissipationofe-hpairsinEHP,sothesequentialmultipleslasingcommencefromhightolowenergystates.Inconventionallasertheory,itisexpectedthatthegroundstateoftraversemodescommenceslasingradiationwhichisinconsistenttoourexperimentalresult.Largedifferentialtancechangeinpump-probespectroscopy:Themagnitudeofdiffer-entialchangeDR=Rinpump-probespectroscopyisaslargeas0.5(Fig.7.2).TheDR=Ristheresultofeffectiveveindexchangeduetothecombinationoftwoeffects:thereductionoflightabsorptioninDBRmaterials,andtheenhancementofnonlinearitycausedbye-hcorrelation.FromtheresultofFig.7.10,theDBRcontributestoabout40%DR=R,andthee-hcorrelationleadsto60%DR=R.Besidestheexplorationofcorrelatede-hpairsatroomtemperature,ourworkprovidescom-prehensiveanalysisandpotentialimpactforapplications.Theselectivemeritsofmyresearchinclude:Theangle-resolvedspectroscopywithincreasingpumpismeasuredtocharacterizetheenergy-momentumdispersionofphotoexcitedcarriers.ThedynamicofluminescenceaswellasthetransientopticalconstantchangeareexploredthroughStreakimageandpump-probespectroscopy.Thepump-probeexperimentalsetupincludessynchronizedtwolasersystems,whichincreasesthefeasibilityofdynamicalinvestigationinsemiconductorsespe-ciallywhentheenergydifferencebetweentheexcitedpumpandPLexceeds200meV.These103measurementdeterminesthetransientEcandthedynamicsofthecorrelatede-hpairswithphotoexciteddensity.Theluminescencedisplayshighlycircular-polarizedlasingradiationeventhemicrocavitysampleisexcitedbynonresonantellipticallypolarizedlight(Fig.4.6).Itisuncommonbe-causethespinrelaxationtimeofphotoexcitedcarriersisless10psandthelasercommencesat20-30psafterexcitation,sothelasingradiationisexpectedtobeunpolarized.Thespin-polarizedlasingfrommicrocavityisattributedtoaspin-dependentstimulatedprocessofcorrelatede-hpairs.Theluminescencepolarizationchangewithpumppolarizationcancon-tributetopolarization-controlofspinlasers.Themicrocavityunderopticallyinducedharmonicproducessequentialmultiplelasing.Thedispersionofluminescenceresemblesthequantumharmonicoscillator,andthepatternofharmonicstatescanbeadjustedbytuningthebeamsize(Fig.6.2).Thebeamshapingtechniquecanbeutilizedtogenerateotherdesiredopticalpotentialtocontrolthebehaviorofluminescence.Ilistmypublicationsrelevanttoourworkinthefollowing:Ch.4:Ultrafastspin-polarizedlasinginahighlyphotoexcitedsemiconductormicro-cavityatroomtemperature.[F.Hsu,W.Xie,Y.Lee,S.Lin,andC.Lai,Phys.Rev.B91,195312(2015)]Ch.5:Transientdual-energylasinginasemiconductormicrocavity.[F.Hsu,W.Xie,Y.Lee,S.Lin,andC.Lai,Sci.Rep.5,15347(2015)]Ch.6:Multiple-pulselasingfromharmonicstatesinahighlyphotoexcitedmicrocavity.[W.Xie,F.Hsu,Y.Lee,S.Lin,andC.Lai,arXiv:1502.00040(2015)]Ch.7:Transientrstudiesofopticallyinducedresonancesinasemiconductormicrocavity.[inpreparation]1048.2FuturedirectionFromprevioussections,wehaveaconjecturetointerpretexperimentalresults:thecorrelatedelectron-holepairsformatbelowtheFermi-edgeofelectron-holeplasmainthepresenceofthecavitylightd.Thesecorrelatede-hpairsformamacroscopiccoherentstatethroughaspin-dependentstimulatedprocess,resultingincircularlypolarizedsuperradiance-likeradiation(las-ing).Lasingenergydependsonthedensityofcorrelatede-hpairsandredshiftswithtimeasaresultofdissipationviaradiation.Figure8.1Diagramofterahertzexperiment.Theparabolic-likecurvesherearethebandofquasiparticle(ortheelectron-holepairings)inquantumwells.Photoexcitedelectron-holepairsthebandabovethesecondquantizedlevels.Thecorrelatede-hpairsareassumedtoformbelowtheFermi-edgesurfaceofquasiparticle.Thecorrelatede-hpairsareexpectedtobeionizeduponFermi-edgesurfaceifthesampleisexcitedbyasecondlasingpulsewithcontrolledenergymatchingthedifferencebetweenFermi-edgesurfaceandtheenergylevelofcorrelatede-hpairs.Tocorrelatede-hpairsandtheenergylevelofe-hpairs,weproposeanexperimentshowninFig.8.1.Atunableterahertz(THz)lightsourceisusedtoexcitethehigh-densityplas-mas,andtheconsequentluminescence/radiationgeneratedbythe2-pspulsepumpexcitationismonitored.IfthereisagapcausedbytheBCS-likewithcorrelatede-hpairsoragapbetweenthecondensede-hpairsandthequasi-Fermilevel,theradiationwouldbegreatlysuppressedwhenTHzlightsourceisinresonancewiththegapthatmightbeashighas20meV.105Thereisstillalackofmicroscopictheoreticalunderstandingofthedensitydependentlasingenergyandlinewidthcausedbythepossibleformationofcorrelatede-hpairsatroomtemperature.Wehopetheresultsonlasinginhighlyphotoexcitedmicrocavitiesasreportedinthisthesiswouldleadtofurtherdevelopmentstoharnessmany-bodyeffectsandspindegreeoffreedomtocontrollasingorsuperradiance.106APPENDICES107APPENDIXATYPICALVERTICAL-CAVITYSURFACE-EMITTINGLASERCHARACTERISTICFigureA.1spectrumofVCSEL.thespectrumofVCSELprovidedfromGlobalCommunicationSemiconductors,LCCcompany.Thebarecavityresonanceisaround850nm.Theredarrowshowsexcitationwavelength785nmusingintheexperiment.Herewecompareluminescencecharacteristicsofourmicrocavitysamplewithconventionalvertical-cavitysurface-emittinglaser(VCSEL).ThecomparedlaserprovidedbyGlobalCommu-nicationSemiconductorsInccompanyis10Gps850nmVCSEL(Do188-VCSEL).ThespectrumisshowninFig.A.1.Intheexperiment,weopticallypumpVCSELwiththesameexci-tationof785-nmTi-sapphirelaserpulse.TheVCSELexhibitsnonlinearincreaseoutputvs.inputwithrelativehighlasingthresholdcomparedtoourcase(Fig.4.2).Thelargestefy(sameinSec.4.1)ofoutputintheexperimentwecanachieveislessthan0.5%at1.3Pth(Fig.A.2(b)).ComparedtoourresultFig.4.2(b),theefyreaches3%at1.3Pth,andthedifferencecanbelargerifwecomparethemwiththesametransmittedpumpTheVCSELstudiedhereexhibitslinearlypolarizedradiationinpreferenceatabovelasingthreshold,whichisdifferentthatourmicrocavitylaserpreferscircularpolarization.ThecrucialdistinctionbetweenourmicrocavitylaserandconventionalVCSEListhelarge108FigureA.2NonlinearincreaseandinVCSEL.(a)outputversusinputunderlinearlypolarizedexcitation.Thebluearrowsdenotesthelasingthreshold,correspondingto5108photoncountsperpulsetransmittedintoVCSEL.(b)Outputefyasafunctionofpumpwithlinear(black)andcircular(red)polarizations.Theefyiscalculatedfromtheratiobetweentheoutputandinputshownontheleft.energyshift.Fig.A.3demonstratetheangle-resolvedspectroscopyatselectedpumpinVC-SEL.Belowlasingthreshold,parabolic-likedispersionemergesatthebarecavityresonance1.456eV(l=852nm).Nearandabovethreshold,radiationbecomesspectrallyandangularlynarrowwithenergyexactlyatbarecavity.Comparedtospectralcharacteristicsofourresult(Fig.4.4),theenergypeakofoursampleexhibits10meVwithincreasingpumpTheoriginoflargeenergyshiftisthelargedetuningbetweenquantumwellbandgapandcavityresonance,whichenhancesaccumulationofe-hdensityresultinginphotomodultedindexchange.109FigureA.3Angle-resolvedspectroscopyinVCSEL.(a)Angle-resolvedspectroscopyinVCSELwithselectedpower0.8,1and1.3Pthmeasuredfromsx=sxcomponent.(b)2DimageofspectraversuspumpEachslicerepresentsnormalizedspectrumobtainedfromtime-integratedspectrumneark'0.110APPENDIXBREFERENCEOFTERMINOLOGYABBREVIATIONThefollowingtableliststheabbreviatedwordsorterminologyfrequentlyusedinthisdissertation:BEC)Bose-EinsteincondensationDBR)distributedBraggDoCP)degreeofcircularpolarizationFWHM)fullwidthhalfmaximume-h)electron-holee-h-g)electron-hole-photonEHP)electron-holeplasmaMQW)multiplequantumwellPL)photoluminescenceQD)quantumdotQW)quantumwellSLM)spatiallightmodulatorVCSEL)vertical-cavitysurface-emittinglaserDR=R)differentialchange111BIBLIOGRAPHY112BIBLIOGRAPHY[1]M.H.Anderson,J.R.Ensher,M.R.Matthews,C.E.Wieman,andE.A.Cornell,fiObser-vationofBose-Einsteincondensationinadiluteatomicvapor,flScience269,198(19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