光纖通信技術：Chapter 3 Signal Propagation in Fibers

Chapter3

SignalPropagationinFibersVocabularyChapter32SOEI,HUSTTotalinternalreflection全內反射Step-indexfiber階躍折射率光纖Graded-indexfiber漸變折射率光纖Core-claddinginterface芯層和包層界面Modaldispersion模式色散Numericalaperture數(shù)值孔徑Impulse沖激Meridionalrays子午光線Parabolic-indexfiber拋物線折射率分布光纖Refractiveindex折射率Absorptioncoefficient吸收系數(shù)Chromaticdispersion色度色散Opticalmode光模式Modeindex模式折射率Effectiveindex有效折射率Cutoffcondition截止條件Normalizedfrequency歸一化頻率Single-modecondition單模條件Eigenvalueequation本征值方程Birefringence雙折射Propagationequation傳播方程NLS非線性薛定諤方程Gaussianapproximation高斯近似

PMD偏振模色散Confinementfactor限制因子Fieldradius模場半徑Attenuationcoefficient衰減系數(shù)Impurity雜質Intrinsicabsorption本征吸收Rayleighscattering瑞麗散射Miescattering米氏散射Waveguideimperfection波導不完善Macrobending宏彎Microbending微彎GVD:群速度色散Intramodaldispersion:模內色散Intermodaldispersion：模間色散Dispersionparameter：色散參數(shù)Materialdispersion：材料色散Waveguidedispersion：波導色散Sellmeierequation：塞米爾方程Zero-dispersionwavelength：零色散波長Dispersion-shiftedfiber：色散位移光纖Chapter33SOEI,HUSTDispersion-flattenfiber：色散平坦光纖Dispersiondecreasingfiber：色散漸減光纖Dispersioncompensationfiber：色散補償光纖Dispersionslope：色散斜率Differential-dispersionparameter：微分色散參數(shù)Polarizationmodedispersion：偏振模色散Pulsebroadening脈沖展寬ChirpedGaussianpulse啁啾高斯脈沖FWHM:半高全寬Ramanscattering喇曼散射Brillouinscattering布里淵散射SRS受激喇曼散射SBS受激布里淵散射Electrostriction電致伸縮效應Brillouinshift布里淵頻移Acousticphonon聲學聲子Inhomogeneous非均勻的Germania鍺Isotropic各向同性Self-phasemodulation自相位調制Cross-phasemodulation交叉相位調制Largeeffective-areafiber大有效面積發(fā)光Phase-matchingcondition相位匹配條件Opticalphaseconjugation光相位共軛Elasticscattering彈性散射Inelasticscattering非彈性散射FiberManufacturing：光纖制作Doublyclad：雙包層Depressed-claddingfiber:凹陷包層光纖Cylindricalpreform：預制棒MCVD：改進的化學汽相沉積OVD：軸外汽相沉積VAD：軸向沉積PCVD：等離子體化學汽相沉積Flamehydrolysis火焰裂解Sintering：燒結Light-dutycable輕型光纜Heavy-dutycable重型光纜Connector連接頭Furnace熔爐Chapter34SOEI,HUST3.1Basicpropagationequation3.2Impactoffiberloss3.3Impactofdispersioninfiber3.4Impactofpolarizationmodedispersion(PMD)infiber3.5Impactoffibernonlinearity3.6SupplementaryChap.3SignalPropagationinFibersChapter35SOEI,HUST3.1.1FiberFundamentals

Totalinternalre?ectionatthecore-claddinginterface.

Spatialmodedistribution:approximatelyGaussianSpotsizeforSMF:Single-modepropagationfor:BasicconceptsrelatedtoSMFRetrospectionforequationsderivationChapter36SOEI,HUSTMaxwell’sEquationsWaveEquationGuidedWaveEquationHelmholtz’sEquation

(x,y,z)tcylindricalcoordinatesGeneralSolutionEigenvalueEquationseparatevariablesboundaryconditionstangentialcomponentsnumericalsolvingChapter27SOEI,HUSTHelmholtzequationAfterusingthemethodofseparationofvariables,

theradialdirectionhastheform:TheFouriertransformoftheZdirection,canbegivenas:光纖光學光纖通信技術Chapter28SOEI,HUSTWhathappenstoopticalsignal?Fiberloss:limitingthetransmissiondistance(minimumlossnear1.55μm).Chromaticdispersion:limitingthebitratethroughpulsebroadening.Nonlineare?ects:limitingthemaximuminputpower.Chapter39SOEI,HUST3.1.2BasicPropagationEquation?ω=ω?ω0

F(x,y)representsspatialpro?leofthe?bermode

Chapter310SOEI,HUSTexpandβL(ω)isaTaylorseriesaroundω0:

Chapter311SOEI,HUSTPulseenvelopeisobtainedusing

Chapter312β1

termcorrespondstoaconstantdelayexperiencedbyapulseasitpropagatesthroughthe?ber.Sincethisdelaydoesnota?ectthesignalqualityinanyway,itisusefultoworkinareferenceframemovingwiththepulse.Thiscanbeaccomplishedbyintroducingnewvariablest’andz’ast’=t?β1z

andz’=z.Thusthebasicpropagationequationcanbegivenas:

SOEI,HUST(G.P.Agrawal,“NonlinearFiberOptics”,the4thversion,2009,pp34,ElsevierPteLtd.)NonlinearcontributionChapter313Nonlineartermcanbewrittenas

SOEI,HUST

Sothebasicpropagationequationcanalsobewrittenas:Chapter314Ifthethird-orderdispersiveeffectscanbeneglected,i.e.β3=0,wewillobtain:Ifwesetα=0,weobtaintheso-calledNLSequation:3.1.3NonlinearSchrodingerEquation

Chapter315Chap.3SignalPropagationinFibers3.1Basicpropagationequation3.2Impactoffiberloss3.3Impactofdispersioninfiber3.4Impactofpolarizationmodedispersion(PMD)infiber3.5Impactoffibernonlinearity3.6SupplementarySOEI,HUSTChapter3163.2.1SourcesofFiberLossLossSourcesMaterialabsorption(silica,impurities,dopants)Rayleighscattering(variesasλ-4)Bendingloss(macroandmicro-bending)SOEI,HUSTChapter217SOEI,HUSTG.657FiberChapter318

AttenuationCoefficientPinPoutSOEI,HUST

Canbederivedfromthebasicpropagationequationα:AttenuationCoefficient,1/km3.2.2LossCompensationChapter319Fiberlossmustbecompensatedfordistance>100km.AOEOrepeatercanbeusedforthispurpose.Opticalbitstreamis?rstconvertedintoelectricdomainandthenregeneratedwiththehelpofanopticaltransmitter.Itbecomesquitecumbersomeandexpensivebecauseofthewavelengthdependence.Alternativesolution:usingopticalampli?ers.SOEI,HUSTChapter320Severalkindsofopticalampli?ersweredeveloped.Erbium-doped?berampli?ersRamanampli?ersSemiconductoropticalampli?ersOpticalampli?ersaredividedintotwocategories:lumpedanddistributedampli?ers.AllmodernWDMsystemsemployopticalampli?ers.TheyamplifymultipleWDMchannelssimultaneously.Ampli?ercanbecascadedandenableustotransmitoverdistancesaslongas10,000km.SOEI,HUSTChapter3213.1Basicpropagationequation3.2Impactoffiberloss3.3Impactofdispersioninfiber3.4Impactofpolarizationmodedispersion(PMD)infiber3.5Impactoffibernonlinearity3.6SupplementarySOEI,HUSTChap.3SignalPropagationinFibersChapter2223.3.1ImpactofDispersioninFiberInter-symbolinterference!!!Bit2Bit1Bit2Bit1Bit2Bit1SMFSOEI,HUSTChapter323

SOEI,HUST

dispersionparameterdispersionslopeChapter3243.3.2PulseBroadeningChirpedGaussianPulseChirpedGaussianPulseatz=0:

SOEI,HUST

Chapter325UsingtheFourier-transformmethod,generalsolutionis

SOEI,HUST

Pulsespectrum:Itisrelatedtothebandwidthoftheopticalsignal,notcorrespondingtotheopticalsource!26 ?Optical?eldatadistancezisfoundtobe:

Chapter3MaintainingGaussianshapebutthewidth,chirpandamplitudewillbechangedbythefactorSOEI,HUSTPulseBroadening(Forbriefness,β3=0)Thewidthchangedto:Thechirpchangedto:

Chapter327Broadeningdependsonthesignofβ2C.Unchirpedpulsebroadensbyafactor

SOEI,HUSTChapter3283.3.3DispersionInducedlimitationsSOEI,HUSTVω

=2σωσ0isadimensionlessparameterL:fiberlengthσ0:RMStemporalwidthoftheinputGaussianpulse:dispersion-introducedbroadeningσω:RMSspectralwidthofthesourceConsideringthecombinedimpactsofβ2,β3,Candsourcespectralwidth:Note:Ifβ3isconsidered,theaforementionedintegralcanstillbeperformedinclosedformintermsofanAiryfunction.However,thepulsenolongerremainsGaussiananddevelopsatailwithanoscillatorystructure.SuchpulsescannotbeproperlycharacterizedbytheirFWHM.ApropermeasureofitistheRMSwidth.

Chapter229SOEI,HUSTOpticalSourceswithaLargeSpectralWidth,ex.LEDnon-zero-dispersionwavelength,neglectingβ3

Chapter230SOEI,HUSTzero-dispersionwavelength,β2=0OpticalSourceswithaSmallSpectralWidth,ex.LDnon-zero-dispersionwavelength,neglectingβ3

Chapter231SOEI,HUSTzero-dispersionwavelength,β2=0

Chapter3323.3.4DispersionCompensationBasicidea:Compensatedispersionalong?berlinkinaperiodicfashionusing?berswithoppositedispersioncharacteristics.

SOEI,HUSTConditionforperfectdispersioncompensation(onlyforβ2

):Chapter233SOEI,HUSTD’=-100ps/(nm·km)L2=?①SMF②DCFD=16ps/(nm·km)L1=50kmABCllonglshortExample:DispersioncompensationDSFandDCFDispersionslopecompensation(forβ3)?ProblemChapter234SOEI,HUST某光纖通信線路使用線寬很窄的單縱模激光器作為光源，發(fā)射機輸出光功率為0.5mw，線路工作速率為10Gbit/s。假定光纖的色散系數(shù)D＝16ps/(nmkm)@1550nm且只考慮二階群速度色散的影響。若光纖的損耗為0.2dB/km，接收機的靈敏度要求為-22dBm，請問此時該線路是何種因素受限（損耗或色散）？

Chapter3353.1Basicpropagationequation3.2Impactoffiberloss3.3Impactofdispersioninfiber3.4

Impactofpolarizationmodedispersion(PMD)infiber3.5Impactoffibernonlinearity3.6SupplementarySOEI,HUSTChap.3SignalPropagationinFibers363.4.1BirefringenceinFibersGeometricbirefringence:smalldeparturesincylindricalsymmetryduringmanufacturing(?bercoreslightlyelliptical).Stressbirefringence:anisotropicstressonthe?bercoreduringmanufacturingorcablingofthe?ber.

Chapter3SOEI,HUSTStateofpolarization(SOP)ofopticalsignaldoesnotremainfixedinpracticalopticalfibers.Itchangesrandomlybecauseoffluctuatingbirefringence.Chapter3373.4.2PolarizationModeDispersion

Wheninputpulseispolarizedalongaprincipalaxis,itsSOPdoesnotchange.Wheninputpulseisnotpolarizedalongaprincipalaxis,itsenergyisdividedintotwopolarizationmodes.Twoorthogonallypolarizedcomponentsofthepulseseparatealongthe?berbecauseoftheirdi?erentgroupvelocities.SOEI,HUSTAphenomenonknownaspolarization-modedispersion(PMD)inducespulsebroadening.Chapter3383.4.3PMDinPMFDelay?τ

(di?erentialgroupdelay,DGD)inthearrivaloftwocomponentsisgivenby

ForaPMF,?β1～1ns/km.

SOEI,HUSTChapter3393.4.4PMDinSMFSOEI,HUSTConventionalfibersexhibitmuchsmallerbirefringence(?n=10?7).Birefringencemagnitudeanddirectionsofprincipalaxeschangerandomlyatalengthscale(correlationlength)lc~10m.Chapter3

SOEI,HUST

40

Chapter3413.4.5High-orderPMD

DGDfluctuateswiththewavelengthoflight.MeasuredvaluesofDGDvaryrandomlyfrom2pstomorethan

30psdependingonwavelengthoflight.SOEI,HUSTChapter3423.1Basicpropagationequation3.2Impactoffiberloss3.3Impactofdispersioninfiber3.4Impactofpolarizationmodedispersion(PMD)infiber3.5Impactoffibernonlinearity3.6SupplementarySOEI,HUSTChap.3SignalPropagationinFibersChapter3433.5.1FiberNonlinearitySOEI,HUST

100Gandbeyond40GLinearityNonlinearity10GSEForlong-haulsystems：NoiseaddedbytheamplifierchaindegradestheSNRandrequireshighlaunchedpowers.Nonlineareffectsaccumulateanddistortthebitstream.FiveMajorNonlinearEffectsarepossibleinopticalfibers:StimulatedRamanScattering(SRS)，StimulatedBrillouinScattering(SBS)，Self-PhaseModulation(SPM)，Cross-PhaseModulation(XPM)，F(xiàn)our-WaveMixing(FWM)Chapter344SOEI,HUSTImpairmentsonopticalsignalsChapter345TransmittedwaveformReceivedwaveformLowopticalpowerHighopticalpowerSMFafterdispersioncompensationThenonlinearitiesinsilicafibers:Stimulatedscattering:intensitydependentgainorloss,SRSandSBS.NonlinearKerreffect:intensitydependentphaseoftheopticalfield,SPM,XPMandFWM.SOEI,HUSTChapter346SOEI,HUST1.Nonlinearphaseshiftpropagationconstantnonlinearrefraction3.5.2Self-PhaseModulationChapter347Pulsepropagationinsideanopticalfiberisgovernedby

SOEI,HUST

U(z,t)satisfiestheNLSequationChapter348

SOEI,HUST

InthelimitChapter349OEI,HUST

2.FrequencychirpNewfrequencycomponentsaregeneratedcontinuouslyandbroadenspectrumofthebitstream.Chapter350

SOEI,HUSTDispersiveandnonlineareffectscanactonbitstreamsimultaneously.3.SolitonsChapter3513.5.3Cross-PhaseModulationNonlinearrefractiveindexseenbyonewavedependsonthe

intensityofothercopropagatingchannels.Nonlinearindexfortwochannels:

SOEI,HUSTTotalnonlinearphaseshiftformultiplechannels:XPMinducesanonlinearcouplingamongchannels.XPMisamajorsourceofcrosstalkinWDMsystems.1.Nonlinearphaseshift2.CoupledNLSequationsChapter352

SOEI,HUST3.LimitationonchannelpowersChapter353

Assumeinputpoweristhesameforallchannels.

Maximumvalueofphaseshiftoccurswhen1bitsinallchannels

overlapsimultaneously.Allowedpowerlevelreducestobelow1mWfor>10channels.

SOEI,HUSTChapter3543.5.4Four-WaveMixingFiberExample:thetwoinputsignalsarelocatedat

1and

2,andtraverseafiberoflength(L).Theoutputisfourdifferentsignalslocatedat1,

2,21-2,and22-1.FWMisnonlinearKerrprocessthatgeneratephasemodulationtoallinvolvedsignals.SOEI,HUSTChapter355Easilytorealizephase-matchingatzero-dispersionwavelength!SOEI,HUSTFormorecommoncase:Chapter356Input(a)andoutput(c)opticalspectraforequallyspaced

channelsInput(b)andoutput(d)opticalspectrainthecaseofunequal

channelspacings.SOEI,HUSTHowtosolvealltheaboveproblemsinDWDMapplication?largeeffectiveareanon-zerodispersion-shiftedfiberisavailable!!!Chapter257SOEI,HUSTRayleighScattering:ElasticscatteringnottogeneratenewfrequencyRamanScattering:InelasticscatteringPumpingphoton→stokesphoton+opticalphononBrillouinScattering:

InelasticscatteringPumpingphoton→stokesphoton+acousticphononbothdirections,frequencyshiftandgainbandwidtharealllarge.backwarddirectioninSMF,frequencyshiftissmall,andgainbandwidthisnarrow.3.5.5StimulatedScattering1.ScatteringChapter258SOEI,HUSTInter-channelinterferenceintimedomainTiltinfrequencydomain2.ImpairmentsChapter259SOEI,HUSTRamangainspectrumoffusedsilicaatλp=1μm

CanopticalamplifierorfibersensingutilizeRamanscattering?Stokesphoton3.SRSenergylevelsparticipatingintheSRSprocess.Chapter260SOEI,HUSTThresholdChapter361Brillouin-gainspectrameasuredusinga1.525-μmpumpforthreefiberswithdifferentgermaniumdoping(a)silica-corefiber;(b)depressed-claddingfiber;(c)dispersion-shiftedfiber.Verticalscaleisarbitrary.Brillouingainspectrumisquitenarrow(<50MHz).Multiplepeaksareduetotheexcitationofdifferentacousticmodes.AndeachacousticmodepropagatesatadifferentvelocityVAandthusleadstoadifferentBrillouinshift.SOEI,HUS