準(zhǔn)連續(xù)光抽運(yùn)光子晶體光纖產(chǎn)生超連續(xù)譜中的調(diào)制不穩(wěn)定性_英文_

1、第39卷第4期2010年4月光 子 學(xué) 報(bào)ArticleID:100424213(2010)042063924ModulationInstabilityinSupercontinuumGenerationUsingthePhotonicCrystalFiberPumpedbyQuasi2ContinuumWave*ZHANGTing1,2,ZHAOWei1,YANGZhi1,WANGYi2shan1,LIChen1,FANGPing1,2(1StateKeyLaboratoryofTransientOpticsandPhotonics,XicanInstituteofOpticsandPrec

2、isionMechanics,ChineseAcademyofSciences,Xican710119,China)(2GraduateUniversityofChineseAcademyofSciences,Beijing100049,China)Keywords:Supercontinuumgeneration;GeneralizednonlinearSchrdingerequation;Modulationinstability;Quasi2continuumwaveCLCN:TN253 DocumentCode:A doi:10.3788/gzxb20103904.06390 Intr

3、oductionRecentyears,thereisgrowinginterestinsupercontinuumgeneration.Supercontinuumgenerationisacollectionofthenonlineareffectwhichcausesaverybroadspectralbandwidthgeneration1.Thiscollectionisusuallyobtainedbypropagationofshortlaserimpulsesbystronglynonlineardevices.Andtheultra2broadbandlightgenerat

4、edhasavarietyofpotentialapplications,includinginopticalcoherencetomography2,opticalcommunication3,andfrequencymetrology4.AlthoughthesupercontinuumgenerationpumpedCWwasreported5,majorityexperimentsexhibitthatsupercontinuumgenerationwasachievedwithfemto2secondpulse,orseveralpicosecondspulsepumpingthe6

5、microstructurefiber,dispersionshiftfiberand7taperedfiberevenSF6softglassphotoniccrystal8*Thisscenarioisrichbutnottobecompletelyunderstood.However,modulationinstability(MI)wasnumericallymentionedwhenthelightpumpedthefiberatabnormaldispersionregiontogeneratesupercontinuum.Inthesituationofsupercontinuu

6、mgenerationpumpedbythecontinuouswaveorquasi2CWsource,theimportantpartisgenerationoftheultra2shortpulse.Atitsgenerationprogress,however,itiswellknownthatwithaproperchoiceoffiberlengthandthepumppower,MIwillpayanimportantroleinthegenerationofatrainofopticalpulseswhoserepetitionratecanbeexternallycontro

7、lled9210.Andthenthesupercontinuumisgeneratedundertheinterplayofsomehigh2nonlineareffects.Inref11,MIinphotoniccrystalfiberhasbeenmentionedwithnumericalsimulation,buttheexperimentcharacterhasnotbeenpresented.Inthismanuscript,thesub2nanosecondpulseisadoptedtopumpthehighnonlinearphotoniccrystalfiberfors

8、upercontinuumgeneration,andsomenonlinearopticaleffectssuchastheMI/Four2WaveMixing(FWM)werediscussedandanalyzed.Atlastwecomparedwiththeexperimentalandthesimulationresults,andfoundthatthesimulatedresultsareexcellentagreementwiththeexperimentalones.640光 子 學(xué) 報(bào)39卷1 ExperimentsetupandresultTheexperimental

9、setupisbasedonamode2lockedYb2fiberlaserseedingadouble2cladytterbium2dopedfiberthatprovideda500pspulsetrainwitharepetitionfrequencyof4MHzandacentralwavelengthof1061nm.Thelightaveragepowerwhichputoutfromthedouble2cladfiberendis4W,andthencoupleinthehighnonlinearphotoniccrystalfiberwhichnonlinearcoeffic

10、ientisC=11km-1/WandthedispersioncoefficientwhichprovidebythemanufacturerisgivenintheFig1.Andafternumericalcalculation,wecanreceivethecoefficientlikeB2=-2.305ps2/km,34B3=7.107ps/km,B4=-1.095ps/km.Fromthedispersioncurvethezerodispersion(ZDW)isconformedat1040nm.Thisimpliesthepumplightpropagatinginthean

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

12、=1/CP0.Thegainspectrumissymmetricwithrespectto8=0suchthatg(8)vanishesatthispoint.Thegainbecomeatfrequenciesgivenby01/2c(2)8max=?|B2|2bythemanufacturerandtheB2iscalculateusingtheformulaD=-(2Pc/K2)B2Afterpropagatingthephotoniccrystalfiber,thelightwiththepowermeasuredbythefiberpowermeteris1.1Wandthespe

13、ctrumwhichmeasuredbyAQ26315AopticalspectrumanalyzerisprovidedinFig2.Fig.2 SupercontinuumspectrumattheendofthehighnonlinearphotoniccrystalfiberInFig3,threepeakswereexhibitedandthe4期ZHANGTing,etal:ModulationInstabilityinSupercontinuumGenerationUsingthePhotonicCrystalFiberPumpedbyQuasi2ContinuumWave641

14、andfourth2orderdispersioncorrections.MIisresponsibleforinitiatingsupercontinuumgenerationbydestabilizingthelaunchedCWlight12andthequasi2CWlight.maxkk+A-ik6Bkk=i1+=2K!9z29tX09tspectrumlobepeakwavelengthislargerthanthedifferencebetweenthepumppeakwavelengthandtheleftone$K2=33nm.However,becausetheothern

15、onlineareffectsuchassolitonself2frequencyshift(SSFS)andthedispersionaffectionareactivebutdonotpayanimportantroleintheexperiment,thered2shiftspectrumislargerandflatterthantheblue2shiftspectrum,whichalsoisthecausewhichmakesmoreenergydistributinginthered2shiftspectrumintheexperimentresult.k(3)(A(z,t)R(

16、tc)|A(z,t-tc)|02dtc)whereA(z,t)expresstheelectricfieldenvelope,BkisthedispersioncoefficientsatthepumpfrequencyX0andCisthenonlinearcoefficientofthefiber.TheR(t)intheintegraloperatorfornonlinearresponseofmediumistakenfromexperimentsinref13,itcontainsbothelectronicandvibrational(Raman)contributions.R(t

17、)canbeexpressedasR(t)=(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.ExpansionofthedispersionoperatorintotheTaylorseriesinthefrequencyiscarriedouttothetermskma

18、x,inthisplaceweassumekmax=4.Theitemintheright2handsideofGNLSEisresponsiblefornumbersofnonlinearopticaleffectssuchasSPM,MI,stimulatedRamanScattering(SRS),four2wavemixingandsoon.Thefiberandthepumpsourceparametersinourexperimentareadoptedinthenumericalsimulation.Duetothefiberistooshort,weneglectedthefi

19、berlossinoursimulation.AfterthecalculationoftheGNLSEbythesplit2stepFouriermethod,theresultwhichisthespectrumfigureattheendofthephotoniccrystalfiberisexhibitedinFig.4.38Fig.4 CalculationspectrumofaninitiallyGaussianpulse3 ConclusionReferences1 HUSAKOUAV,HERRMANNJ.Supercontinuumgenerationofhigher2orde

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