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.
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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
表
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】