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非对称量子阱中二次极化率的研究

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非对称量子阱中二次极化率的研究非对称量子阱中二次极化率的研究 第7卷 2008年 第2期 4月 广州大学(自然科学版) JournalofGuangzhouUniversity(NaturalScience Vo1.7 Apr. No.2 2008 文章编号:1671-4229(2008)02-0042-05 Secondorderonlinq,pticalI:ibilit3econa-oraernonlinearooticalsusceotibilitv inasymmetricalquantumwell ZHENG...

非对称量子阱中二次极化率的研究
非对称量子阱中二次极化率的研究 第7卷 2008年 第2期 4月 广州大学(自然科学版) JournalofGuangzhouUniversity(NaturalScience Vo1.7 Apr. No.2 2008 文章编号:1671-4229(2008)02-0042-05 Secondorderonlinq,pticalI:ibilit3econa-oraernonlinearooticalsusceotibilitv inasymmetricalquantumwell ZHENGYun—bao,GUOKang—xian, LIUZuo—lian,ZHANGChao-jin,LIBin (SchoolofPhysicsandElectronicEngineering,GuangzhouUniversity,Guangzhou510006,China) Abstract:Withintheframeworkofthecompact—density— matrixapproachandaniterativemethod,the second?ordersusceptibilitycoeffcientforasymmetricalquantumwellareinvestigated.Finally,thenu. mericalresultsarepresentedforatypicalGaAs/A1GaAsasymmetricquantumwel1.Thelargersecond. ordersusceptibilitycoefficientwasobtainedinthisspecialquantumwel1.Thisisafeasiblewaytoget finenonlinearmaterialsinexperiment. Keywords:quantumwell;second?ordersusceptibility;density—matrix;nonlinear CLCnumber:0472Documentcode:A 0Introduction Infhelastthreedecadesmuchattentionhasbeenfocused onthenonlinearopticalpropeaiesoflow?dimensionalsemicon. ductorsystems,includingquantumwells(QW's)卜, quanlumwellwires(QWW's)andquantumdots(QD's) .Becauseoftheirrelevanceforstudyingpracticalappli. cationsandasaprobefortheelectronicstructureofmedia.A. mongthenonlinearopticalproperties,moreattentionhadbeen paidtothethird.ordernonlinearopticalproperties,. All0flheeffectsmentionedabovealeofthethirdorderin electricfield,becausethesystemofsymmetricquantumwell possessesaninversionsymmetryleadingtoabsenceofsecond— Ol'dereffects.Ontheotherhand,second.ordereffectssuchas fequency.mixing,includingsecond?harmonicgeneration (SHG)andlinearelectro?opticaleffectareofgreatpractical interestintheareasofintegratedopticsandopticalcommuni? cations. Ingeneral,theexistingtheoreticalandexperimentalstud? iescanbedividedintotwogroups,dependingonthelightfre? quentcy:thosewhichhavephotonenergyintheregionofintra? band(intersubband)transitions(nearinflared)andasecond groupdealingwithenergiesintheregionofinterband(valence toconductionband)transitions(visiblelight). Asweknow,theopticalsecond—ordersusceptibilityison? lynonzeroifthequantumwellissymmetric.Designingan asymmetricquantumwellisveryimportant.Withthedevelop- mentofthetechnologyofthemolecularbeamepitaxy(MBE) andmetalorganicchemicalvapordeposition(MOVCD), asymmetricquantumwellcanbemade. Inthispaper,weadaptanespecialasymmetricquantum Receiveddate:2007一o9—05;Reviseddate:2007—10—10 Foondafionitems:Supp0rtedbytheNati.halNaturalScienceFoundafionofChina(underGr antNo.60478010):TheScienceandTechnology CommitteeofGuangdongProvince(underGrantNos.2007B010600061and07001899) Biography:ZHENGYunbao(1976 一),male,mastercandidate,mainlyresearchesontheoptica1n0nlinearitiesinlow-dimensio nalsernjc0n. ductorstructures. 第2期zHENGYun-ba.,eta1.:Second一.rdern.nlinear.pticalsuscepcibilityinasymme 【rjcalquan【um! wel1.withintheframeworkofthecompact—density—matrixap' 0r0achandaniterativemethod,weobtainthesecond—order susceDtibilitvcoefficient.InSection1,theHamihonian,rele— vantwavefunctionsandenergylevels,andtheanalyticalex— oressionofthesecond—harmonicgenerationaredescribed.In Section2.thenumericalresultsofthesecond—ordersuscepti— bilitvcoefficientarepresentedforGaAs/A1Ga1一Asasymmet_ ricalquantumwells. 1Theory Letust}1inkaboutanasymmetricquantumwell[.]: U?=Uo(A一音)(>0)() wherenandcanbeadjusted,thechangeoftheasymmetric quantumwellastheparameternandsuchasFig.2.Using theenvelopfunctionandeffective—massapproximation,the Schr~dingerequationhasaform: 【一嘉詈一音)))(2) wheremistheeffectivemassoftheelectronintheconduc— tionband.Thecorrespondingsolutionsofthisequationcanbe writtenas: 叫一?Uo 2疗 n F+, 謦 l2Un\1?+ }(~UO—a2+l一])疗疗JJ (3) ..cith.ormaliz.nconstant,u:? +11,Fisthec.n仃uenthype蜡e.metri functionTheformulaofsecond—ordersusceptibilityinquan' tumwellbythecompact—density—matrixmethodandtheitera— tiveprocedureLetUSCOnsiderthesystemwhichisexcitedby anelectromagneticfieldE(,)=Ee+L'e"Theevolution ofdensitymatrixisgivenbythetime—dependentSchrrdingere— quation 0p0 : ~(14o一(,),p]一(p—p'.)(5) dt疗 Forsimplicity,weonlyassumethattherelaxationF0.:Fo, Eq(5)iscalculatedbythefollowingiterativemethod p(f)=?P(f)(6) with, 0p(n+1) =m}一 [qp,p'n']E(f)(7) i方 TheelectricpolarizationoftheQWduetoE(t)canbeex pressedas P(f)=(80'e一+so''ll+ 0:'e一+cc(8) where' ,,:'arethelinear,opticalrectification,sec ond-harmonicgeneration,respectively0isthevacuumdie 1ectricc0nstant.Theelectronicpolarizationofthenthorderis gwenas ()=1n(ep)(9) whereisthevolumeofinteractionandTrdenotesthetraceor summati0noverthediagonalelementsofthematrixP'epIn ourpaper.thesecond—ordersusceptibilityperunitvolumeis givenbyusingtheresonanceconditionsas (2)一 2一 0 疗 1120 (一l0+iFlo)(2to—tO2【】+,2(1) (10) whereisthedensityofelectronsintheQW,=(Ei— E)/疗isthetransitionfrequencY,andM=l<lP 1>1istheoff-diagonalmatrixelement Thesecond—ordersusceptibilityhasaresonantpeakinthe energypositionofdupleresonanceie疗=疗1. 疗21,andassumingFo=F1o=,2oexpressioneq.(1O)be— nmPS , = e3M01M12M2o 疗F.) 广州大学(自然科学版)第7卷 2Resultsanddiscussions ThentheabovetheoryisnOWappliedtostudysecond-?or-? dersusceptibilitynumericallyinaGaAsquantumwel1.Weuse thefollowingparametersforGaAs:m=0.067m0, whereisthefree—electronmass;o-=5x10Nm,;厂n= 0.2ps.詹=1.055x10. InFig.1.weshowthesecond—harmonicgenerationcoeffi- cientversusthephotonenergy7『forthreedifferentvat— uesoftheUo:(1)=O.05eV,(2)M0:O.15eVand(3) =0.25eV.Weobse,~ethreeresonantpeaksforthesecond— harmonicgenerationsusceptibilityat0.23eV.fo= 0.38eV,=0.51eVforthedifferentvaluesofz.When increasingtheparameter"othephotonenergypeakshavea blushilt Photonenergy/eV Fig.1Thesecond—harmonicgenerationcoefficientX. t2 versus thephotonenergy(cJforthreedifferentvaluesofthe ):(1)u()=0.05eV,(2)u0=0.15eVand(3)u0: 0.25eV TheshapesofthequantumwellareshowninFig.2fora = 2nmandUo:(1)uo=0.05eV,(2)Mo=0.15eVand(3) M『1=0.25eV,respectively.Fromthefigure,wecaneasilyfind thattheasymmetryisincreasingwiththeincreaseofUo.And theshapeofthewellismorelikethesemi—parabolicquantum wellwhentheUobecomesbigger一..Wecanvalidatethatthe biggersymmetUisthesmallerthesecond-ordernonlinearcoef- ficientwillbe.Theshapesofthequantumwellisapproximated tothefact,anditisrelativelysimpletoimplement.Soitisim— portantforourresearchbothinexperimentandintheory. Fig.2Thedifferentshapesofthequantumwellwitha=2nm forUo:(1)u0=0.05eV,(2)%=0.15eVand(3) "0=0.25eV,respectively. Fig.3showsthesecond—harmonicgenerationcoefficient versusthephotonenergyforthreedifferentvaluesof a:(I)a=5nm,(2)a=4nmand(3)a=3nm.Wecan findthattherearethreedifferentresonantpeaksat 0.225eV,:0.320eV,=0.380eV,respectively. Withtheincreaseofn,thepeak'sintensityofincreases greatly.Butthepeakhasalittleshifttowardslowerenergydi- rection.Fromthechangeofthepeaks,wecancometothe conclusionthatthegreatertheasymmetUofthequantumwell is,thebiggerthepeakswillbe.SowecangainbiggerSHGby increasingthevalueofa. Photonenergy/eV Fig.3Thesecond,harmonicgenerationcoefficientX(2'versus thephotonenergytoforthreedifferentvaluesofthe a:(1)a=5nm,(2)a=4nmand(3)a=3nm. 3Conclusion Inthispaper,wehavestudiedtheoreticallythesecond.or 第2期ZHENGYun-ba.,eta1.:Second_I)rdern.nlinear【】 pticalsusceptibilityinasymmetrica1quantomwell4 dernonlinearopticalsusceptibilityinasymmetricalquantum wel1.Byalteringtheparameters8andU0.wegetlargesecond— ordersusceptibility.Fromourresults,wecanconcludethat therearelargesecond?-ordersusceptibilityexistentintheasym— metricalquantumwel1.Theresultsareingoodagreementwith thesemi—parabolicquantumwellwhenthebecomes small[. Whatisimportantisthatwecandesigntheasym- metricalquantumwellaswehavediscussedtoobtainbigger second—ordernonlinearopticalsusceptibilitybychangingthe parameters8andU0. References: [1]ChoiKK,LevineBF,MalikRJ,eta1.Periodicnegativeconductancebysequentialresonan ttunnelingthroughanexpan— dinghigh—fieldsuperlatticedomain[J].PhysRevB,1987,52:4172. 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[10jLinDL,ChenR,GeorgeTF.Interface—phonon— mediatedmagnetopolaroniceffectonimpuritytransitionenergiesinquart— tumwells[J].PhysRevB,1991,43:9328. [11]AtanasovR,BassmliF,Agranovich.V.M.Second— ordernonlinearopticalsusceptibilityofasymmetricquantumwells[J]. PhysRevB,1994,50:7809. [12]ZhangCJ,GuoKX.Polaroneffectsonthesecond— ordersusceptibilitiesinasymmetricalsemi—parabolicquantumwells 【J].PhysicaE,2006,33:363. [13]YoffeAD.Semiconductorquantumdotsandrelatedsystems:electronic,optical,lumine ecenceandrelatedpropertiesoflow dimensionalsystems[J].AdvanPhy,2001,50(1):1. [14]CanhamLT.Siliconquantumwirearrayfabricationbyelectrochemicalandchemicaldis solusionofwafers[J].ApplPhys Lett,1990,57:1046. [15] [16] [17] [18] [19] [20] GrygielK.SzlachetkaK.Chaosinsecond— harmonicgenerationoflightffThecaseofatrainofpulses[J].OptComm,1992, 91:241. PyragasK.Observingchaos:deducingandtrackingthestateofachaoticsystemfromlimitedobservation[J].PhysLettA, 1992,6:421. RosencherE.BoisPh.Modelsystemforopticalnonlinearities:Asymmeticquantumwells[J].PhysRevB,1991,44:11 3l5. ChurnsideJH.Secondharmonicgenerationusingpartiallycoherentlight[J].OptComm,1984,51:207. PettiansNP.Instabilitiesofthedegenerateopticalparametricoscillator[J].OptComm,1989,72:256. SuRukeng.QuantumMechanics[M].FudanUniversityPress,1997:61—100. 广州大学(自然科学版)第7卷 [2I]WangGH,GuoKX,GuoQ.Studyonlinearandthird— ordernonlinearopticalabsorptioninspecialasymmetricquantum wells[j].ChinJQuantElectr,2004,21:429. [22]DiazDC,SchowCL,QiJM,eta1.Si/Sio2resonantcavityphotodector[j].ApplPhysLett,1996,69:2798. [23]ZhangCJ,GuoKx.Polaroneffectsontheopticalrectificationinasymmetricalsemi— parabolicquantumwells[J].Physiea B,2007,387:276. [24]CuiDF,ChenZH,PanSH,eta1.Absorptionsaturationofintersubbandoptie~transitioninGaAs=A1GaI一Asmultiple quantumwells[J].PhysRevB,1993,47:6755. [25]WangGH,GuoKX.1nterbandopticalabsorptionsinaparabolicquantumdot[J].PhysieaE,2005,28:14. [26]QueWM.Exeitionsinquantumdotswithparabolicconfinement[J].PhysRevB,1992,4 5:11036. [27]PeetersFM,DevreeseJT.Sealingrelationsbetweenthetwo—andthethree—dimensionalpolarons[J].PhysRevB,1987, 36.4442. 非对称量子阱中二次极化率的研究 郑允宝,郭康贤,刘佐濂,张超金,李 (广州大学物理与电子工程学院,广东广州510006) 斌 摘要:利用密度矩阵的方法研究了一种非对称量子阱的光学非线性,推导出了二次谐波解析 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式,最后利 用典型的GaAs/AIGaAs非对称量子阱进行数值计算.数值结果表明,"-3非对称性增大时,可得到比较大的二次 谐波,从而为实验上制作比较大的非线性材料提供一种可行办法. 关键词:量子阱;二次极化率;密度矩阵;非线性 中图分类号:0472文献标识码:A 收稿日期:2007,09—05;修回日期:2007—10—10 基金项目:国家自然科学基金资助项目(60478010);广东省科技厅资助项目(2007B01060OO61,07001899) 作者简介:郧允宝(1976一),男,硕士研究生,主要从事低维量子系统非线性光学领域的研究. 【责任编辑:方碧真】
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