1、第39卷第4期2010年4月光 子 學 報Vol.39No.4April2010ArticleID:100424213(2010)042063924ModulationInstabilityinSupercontinuumGenerationUsingthePhotonicCrystalFiberPumpedbyQuasi2ContinuumWave*ZHANGTing1,2,ZHAOWei1,YANGZhi1,WANGYi2shan1,LIChen1,FANGPing1,2(1StateKeyLaboratoryofTransientOpticsandPhotonics,XicanInsti

2、tuteofOpticsandPrecisionMechanics,ChineseAcademyofSciences,Xican710119,China)(2GraduateUniversityofChineseAcademyofSciences,Beijing100049,China)Abstract:Aphenomenonexperimentallyemerginginsuper2continuumgenerationwithapieceofphotoniccrystalfiberpumpedbyquasi2continuumwaveisreported.Accordingtothenum

3、ericalsimulationwhichcontainsusingthegainspectrumtheoryofmodulationinstabilityandsolvingnonlinearSchrÊdingerequation,itisprovedthatthisphenomenonisgeneratedbymodulationinstability.Aftertheresultsofthesimulationandtheexperimentbeingcontrastedandanalyzed,itisfoundthatthesimulationresultincludingt

4、womentionedmethodsisinexcellentagreementwiththeexperimentresultwhichthewavelengthdifferencebetweenthetwospectrumlobesandthecentralwavelengthare27.08nmand32.72nmrespectively.Keywords:Supercontinuumgeneration;GeneralizednonlinearSchrÊdingerequation;Modulationinstability;Quasi2continuumwaveCLCN:TN

5、253 DocumentCode:A doi:10.3788/gzxb20103904.06390 IntroductionRecentyears,thereisgrowinginterestinsupercontinuumgeneration.Supercontinuumgenerationisacollectionofthenonlineareffectwhichcausesaverybroadspectralbandwidthgeneration1.Thiscollectionisusuallyobtainedbypropagationofshortlaserimpulsesbystro

6、nglynonlineardevices.Andtheultra2broadbandlightgeneratedhasavarietyofpotentialapplications,includinginopticalcoherencetomography2,opticalcommunication3,andfrequencymetrology4.AlthoughthesupercontinuumgenerationpumpedCWwasreported5,majorityexperimentsexhibitthatsupercontinuumgenerationwasachievedwith

7、femto2secondpulse,orseveralpicosecondspulsepumpingthe6microstructurefiber,dispersionshiftfiberand7taperedfiberevenSF6softglassphotoniccrystal8fiber.Sosupercontinuumgenerationhadbeendefinedtothephenomenageneratedbythepulse.Experimentalandtheoreticalinvestigationsonsupercontinuumgenerationshowthatthei

8、nterplayofmanynonlineareffectstakesanimportantrole.*SupportedbytheNationalNaturalScienceFoundationofChina(60537060)Tel:029288887613Email:zhangting712Receiveddate:2009204214Reviseddate:2009205227Thisscenarioisrichbutnottobecompletelyunderstood.However,modulationinstability(MI)wasnumericallymentionedw

9、henthelightpumpedthefiberatabnormaldispersionregiontogeneratesupercontinuum.Inthesituationofsupercontinuumgenerationpumpedbythecontinuouswaveorquasi2CWsource,theimportantpartisgenerationoftheultra2shortpulse.Atitsgenerationprogress,however,itiswellknownthatwithaproperchoiceoffiberlengthandthepumppow

10、er,MIwillpayanimportantroleinthegenerationofatrainofopticalpulseswhoserepetitionratecanbeexternallycontrolled9210.Andthenthesupercontinuumisgeneratedundertheinterplayofsomehigh2nonlineareffects.Inref11,MIinphotoniccrystalfiberhasbeenmentionedwithnumericalsimulation,buttheexperimentcharacterhasnotbee

11、npresented.Inthismanuscript,thesub2nanosecondpulseisadoptedtopumpthehighnonlinearphotoniccrystalfiberforsupercontinuumgeneration,andsomenonlinearopticaleffectssuchastheMI/Four2WaveMixing(FWM)werediscussedandanalyzed.Atlastwecomparedwiththeexperimentalandthesimulationresults,andfoundthatthesimulatedr

12、esultsareexcellentagreementwiththeexperimentalones.640光 子 學 報39卷1 ExperimentsetupandresultTheexperimentalsetupisbasedonamode2lockedYb2fiberlaserseedingadouble2cladytterbium2dopedfiberthatprovideda500pspulsetrainwitharepetitionfrequencyof4MHzandacentralwavelengthof1061nm.Thelightaveragepowerwhichputo

13、utfromthedouble2cladfiberendis4W,andthencoupleinthehighnonlinearphotoniccrystalfiberwhichnonlinearcoefficientisC=11km-1/WandthedispersioncoefficientwhichprovidebythemanufacturerisgivenintheFig1.Andafternumericalcalculation,wecanreceivethecoefficientlikeB2=-2.305ps2/km,34B3=7.107ps/km,B4=-1.095ps/km.

14、Fromthedispersioncurvethezerodispersion(ZDW)isconformedat1040nm.ThisimpliesthepumplightpropagatingintheanomalousdispersionregionofthehighnonlinearPCF.correspondingtothetwosidespectrumpeaksandthepumpwavelengtharealmostequal.Andthedifferencesbetweenthesidepeakandthecentralwavelengthare27.08nmand32.72n

15、mrespectively.Fig.3 Experimentspectrumofthe0.5Wsupercontinuum2 MItheoryandsimulationItiswellknownthatthegainspectrumofMIisobtainedfromtheref11,andtheexpressionisshowasfollows21/2g(8)=|B28|(8c-8)(1)where8:thefrequencyofperturbation,the82c=4CP0/&B2&=4/(|B2|LNL),andtheLNL=1/CP0.Thegainspectrumi

16、ssymmetricwithrespectto8=0suchthatg(8)vanishesatthispoint.Thegainbecomeatfrequenciesgivenby01/2c(2)8max=?|B2|2wheretheP0isthepeakpoweroftheinputpulse.Fromformula(3),weachievedthatthepositionofthespectrumlobesexhibitedinthelightspectrumattheendofthenonlinearfiberare1017.65nmand1106.11nmrespectively,a

17、ndfoundthatthepositioncalculatedbyformula(3)isagreementwiththespectrumreceivedfromtheexperiment.MIisawellunderstoodinstabilityphenomenonofthenonlinearSchrÊdingerequation(NLS)whichgovernstheunderlyinglightwavepropagationinanopticalfiberinthepresenceofchromaticdispersionandself2phasemodulation(SP

18、M).Intheanomalousdispersionregion,thedominantunstableMIfrequenciescanbeshowntobeproportionaltotheCWamplitudeandinverselyproportionaltothesquarerootofthedispersionliketheformula(2).ThusthemodulationwhichgrowsontheCWfieldorthequasi2CWfieldisofincreasingfrequencyasthegroupvelocitydispersion(GVD)goestoz

19、ero.EveninthenormalFig.1 DispersioncurveofnonlinearfiberprovidedbythemanufacturerandtheB2iscalculateusingtheformulaD=-(2Pc/K2)B2Afterpropagatingthephotoniccrystalfiber,thelightwiththepowermeasuredbythefiberpowermeteris1.1WandthespectrumwhichmeasuredbyAQ26315AopticalspectrumanalyzerisprovidedinFig2.F

20、ig.2 SupercontinuumspectrumattheendofthehighnonlinearphotoniccrystalfiberInFig3,threepeakswereexhibitedandthe4期ZHANGTing,etal:ModulationInstabilityinSupercontinuumGenerationUsingthePhotonicCrystalFiberPumpedbyQuasi2ContinuumWave641andfourth2orderdispersioncorrections.MIisresponsibleforinitiatingsupe

21、rcontinuumgenerationbydestabilizingthelaunchedCWlight12andthequasi2CWlight.InordertomoreclearlyunderstandMIandthesupercontinuumgenerationmechanisms,wehavenumericallysolvedtheone2dimensionalgeneralizednonlinearSchrÊdingerequation(GNLSE)bythestandardsplit2stepFouriermethod.Assumethatthepulsepropa

22、gatesalongthez2axis.ThegeneralformoftheNLSEfortheslowlyvaryingcomplexenvelopeA(z,t)ofapulsecenteredatfrequencyX0isgivenbymaxkk+A-ik6Bkk=i1+=2K!9z29tX09tspectrumlobepeakwavelengthislargerthanthedifferencebetweenthepumppeakwavelengthandtheleftone$K2=33nm.However,becausetheothernonlineareffectsuchassol

23、itonself2frequencyshift(SSFS)andthedispersionaffectionareactivebutdonotpayanimportantroleintheexperiment,thered2shiftspectrumislargerandflatterthantheblue2shiftspectrum,whichalsoisthecausewhichmakesmoreenergydistributinginthered2shiftspectrumintheexperimentresult.k(3)(A(z,t)R(tc)|A(z,t-tc)|02dtc)whe

24、reA(z,t)expresstheelectricfieldenvelope,BkisthedispersioncoefficientsatthepumpfrequencyX0andCisthenonlinearcoefficientofthefiber.TheR(t)intheintegraloperatorfornonlinearresponseofmediumistakenfromexperimentsinref13,itcontainsbothelectronicandvibrational(Raman)contributions.R(t)canbeexpressedasR(t)=(

25、1-fR)D(t)+fRh(t)=222(1-fR)D(t)+fR(S1+S2)/S1S2#(4)exp(-t/S2)sin(t/S1)(t)wherefR=0.18isthefractionalcontributionofthedelayedRamanresponse,S1=1.22fs,andS2=32fs.(t)istheHeavisidestepfunction.ExpansionofthedispersionoperatorintotheTaylorseriesinthefrequencyiscarriedouttothetermskmax,inthisplaceweassumekm

26、ax=4.Theitemintheright2handsideofGNLSEisresponsiblefornumbersofnonlinearopticaleffectssuchasSPM,MI,stimulatedRamanScattering(SRS),four2wavemixingandsoon.Thefiberandthepumpsourceparametersinourexperimentareadoptedinthenumericalsimulation.Duetothefiberistooshort,weneglectedthefiberlossinoursimulation.

27、AfterthecalculationoftheGNLSEbythesplit2stepFouriermethod,theresultwhichisthespectrumfigureattheendofthephotoniccrystalfiberisexhibitedinFig.4.Fig.4issimilartothespectrumfigureinFig.3,whichistheexperimentalresult.FromFig.4,wealsoreceivethreepeakswhicharepumppeakandtwolobepeaksgeneratedbyMIrespective

28、ly,andthewavelengthdifference$K1=38Fig.4 CalculationspectrumofaninitiallyGaussianpulse3 ConclusionInaword,weexperimentallyreportedthemodulationinstabilityinthesupercontinuumgenerationpumpedinabnormaldispersionregionbythequasi2CWlight.Andthenweutilizedthemodulationinstabilityspectrumgaintoprovetheexp

29、erimentspectrumwhichwegotismodulationinstabilityandsolvedtheGNLSEtofittheexperimentspectrum.Afterabovecontrast,wecanmakeaconclusionthatMIisanimportantnonlineareffectinthesupercontinuumgenerationpumpedbythequasi2CWlightandtheCWlight.Asmentionedbefore,thecalculationresultsofmodulationinstabilityisexce

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