學(xué)習(xí)-chapter2of微納制備與新器件集成研究所

Chapter2DielectricWaveguidesandOpticalDr.DaoliOffice:Room409WestBuildingVoice::zhang_ 微 與新器件集SymmetricPlanarDielectricSlabModalandWaveguideDispersioninPlanarStep-IndexOpticalNumericalDispersionInSingle-ModeDispersionModifiedFibersandBitRate,Dispersion,andElectricalandOpticalTheGradedIndex(GRIN)OpticalAttenuationinOpticalFiber微 與新器件集AdditionalWavelengthDivisionMultiplexing:NonlinearEffectsinOpticalFibersandBraggPhotonicCrystalFibers—HoleyFiberBraggGratingsand微 與新器件集CourtesyoftheChineseUniversity微 與新器件集“Theintroductionofopticalfibersystemswillrevolutionizethecommunicationsnetwork.Thelow-transmissionlossandthelargebandwidthcapabilityofthefibersystemsallowsignalstobetransmittedforestablishingcommunicationscontactsoverlargedistanceswithfewornoprovisionsofintermediateamplification.”[CharlesK.Kao(oneofthepioneersofglassfibersforopticalcommunications)OpticalFiberSystems:Technology,Design,andApplications(McGraw-HillBookCompany,NewYork,USA,1982),p.1]CharlesKaoatthenamingceremonyofMinorPlanet(3463)"Kaokuen"byNanjing'sPurpleMountainObservatoryinJuly1996.CharlesKaoandhiscolleaguescarriedouttheearlyexperimentsonopticalfibersattheStandard municationsLaboratories(theresearchcenterofStandard ephonesandCables)atHarlowintheUnitedKingdom,duringthe1960s.HesharedtheNobelPrizein2009inPhysicswithWillardBoyleandGeorgeSmithfor"ground-breakingachievementsconcerningthetransmissionoflightinfibersforopticalcommunication."Ina tonepaperwithGeorgeHockampublishedintheIEEProceedingsin1966theypredictedthattheintrinsiclossesofglassopticalfiberscouldbemuchlowerthan20dB/km,whichwouldallowtheiruseinlongdistancemunications.Today,opticalfibersareusednotonlyin municationsbutalsoinvariousothertechnologiessuchasinstrumentationandsensing.From1987tohisretirementin1996,professorKaowastheViceChancelloroftheChineseUniversityof.(CourtesyoftheChineseUniversity 微 與新器件集Jean-DanielColladonandtheLightGuidinginaWater

LightisguidedalongawaterjetasdemonstratedbyJean-DanielColladon.ThisillustrationwaspublishedinLaNature,RevuedesSciences,in1884(p.325). Hisfirstdemonstrationwasaround1841.(ComptesRendes,15,800-802,Oct.24,1842).AsimilardemonstrationwasdonebyJohnTyndallfortheRoyalInstitutioninLondoninhis1854 suggestedtheexperimenttoJohnTyndallthoughFaradayhimselfprobablylearnedaboutiteitherfromanotherearlier publication.AlthoughJohnTyndallisoftencreditedwiththeoriginaldiscoveryofawater-jetguidinglight,Tyndall,himself,doesnotmakethatclaimbutneitherdoesheattributeittosomeoneelse.(Thefountain,courtesyofConservatoireNumérique desArtsetMétiers, sciences,Genève,Switzerland.)Reference:JeffHecht,"IlluminatingtheOriginofLightGuiding,"Optics&PhotonicsNews,10,26,1999andhiswonderfulbookTheCityofLight(OxfordUniversityPress,2004)describetheevolutionoftheopticalfiberfromthewaterjetexperimentsofColladonandTyndalltomodernfiberswithhistoricalfactsandreferences.微 與新器件集NarinderSingh

NarinderSinghKapanywasbornin ,studiedattheAgraUniversityandthenobtainedhisPhDfromtheImperialCollegeofScienceandTechnology,UniversityofLondonin1955.Heheldanumberofkey-positionsinbothacademiaandindustry,includingaRegentsProfessorattheUniversityofCalifornia,Berkeley,theUniversityofCalifornia,SantaCruz(UCSC),theDirectoroftheCenterfor

significantcontributionstoopticalglassfibersstartingin1950s,andessentiallycoinedthetermfiberopticsinthe1960s.HisbookFibreOptics:PrinciplesandApplications,publishedin1967,wasthefirstinopticalfibers.(CourtesyofDr.NarinderS.Kapany)微 與新器件集ACenturyandHalfLighthasreplacedcopperincommunications.Photonshavereplacedelectrons.Will“PhotonicsEngineering”replaceElectronics微 與新器件集微納與新器件集成SymmetricPlanarDielectricSlabAplanardielectricwaveguidehasacentralrectangularregionofhigherrefractiveindexn1thanthesurroundingregionwhichhasarefractiveindexn2.Itisassumedthatthewaveguideisinfiniywideandthecentralregionisofthickness2a.Itisilluminatedatoneendbyanearlymonochromaticlightsource.微 與新器件集Lightwaveszigzagalongtheguide.Isthatreallywhat微 與新器件集WavesInsidetheAlightraytravelingintheguidemustinterfereconstructivelywithitselftopropagatesuccessfully.Otherwisedestructiveinterferencewilldestroythewave.Eisparalleltox.(1andk1arethewavelengthandthepropagationconstantinsidethecoremediumn1i.e.1=/n1.)微 與新器件集Twoarbitrarywaves1and2thatareinitiallyinphasemustremaininphaseafterreflections.Otherwisethetwowillinterferedestructivelyandcanceleachother.微 與新器件集2n1(2a)2n1(2a)cosmmk1=kn1=(AC)=k1(AB+BC)2=BC=d/cosandAB=AB+BC=BCcos(2)+BC=BC[(2cos21)+1]=k1[2dcos]2=m=0,1,2,3“Mode微 與新器件集1 k1k 1 k1k mmmmm1m微 與新器件集Togetapropagatingwavealongaguideyoumusthaveconstructiveinterference.Alltheseraysinterferewitheachother.Onlycertainanglesareallowed.Eachallowedanglerepresentsamodeofpropagation.

m

微 與新器件集n(2a)1 mm k1m1mmm=integer,n1=corerefractiveindex,mistheincidenceangle,2aisthecorethickness.Minimummand ummmuststillsatisfyTIR.Thereareonlyafinitenumberofmodes.Propagationalongtheguideforamodem微 與新器件集Togetapropagatingwavealongaguideyoumusthaveconstructiveinterference.Alltheseraysinterferewitheachother.Onlycertainanglesareallowed.Eachallowedanglerepresentsamodeofpropagation.

m

微 與新器件集ModesinaPlanarWecanidentifyupward(A)anddownward(B)travelingwavesintheguidewhichinterferetosetupastandingwavealongyandawavethatispropagatingalongz.Rays2and2belongtothesamewavefrontbut2 esreflectedbefore2.Theinterferenceof1and2determinesthefieldataheightyfromtheguidecenter.ThefieldE(y,z,t)atPcanbewrittenasE(y,z,t)=Em(y)cos(tTravelingwavealongFieldpatternalong微 與新器件集

cos

m=integer,n1=corerefractiveindex,mistheincidenceangle,2aisthecorethickness. k 2n1

E(y,z,t)=Em(y)cos(tTravelingwavealongFieldpatternalong微 與新器件集ModeFieldLeft:Theupwardanddownwardtravelingwaveshaveequalbutoppositemandinterferetosetupastandingelectricfieldpatternacrosstheguide.Right:Theelectricfieldpatternofthelowestmodetravelingwavealongtheguide.Thismodehasm=0andthelowest.Itisoftenreferredtoastheglazingincidenceray.Ithasthehighestphasevelocityalongtheguide微 與新器件集ModalandWaveguideDispersioninPlanarModesinaPlanarTheelectricfieldpatternsofthefirstthreemodes(m=0,1,2)travelingwavealongguide.Noticedifferentextentsoffieldpenetrationintothe微 與新器件集Intermode(IntermodalorModal)Schematicillustrationoflightpropagationinaslabdielectricwaveguide.Lightpulseenteringthewaveguidebreaksupintovariousmodeswhichthenpropagateatdifferentgroupvelocitiesdowntheguide.At oftheguide,themodescombinetoconstitutetheoutputlightpulsewhichisbroaderthantheinputlightpulse.微 與新器件集TEandTMEisalongx,sothatE= Bisalongx,sothatB=Possiblemodescanbeclassifiedintermsof(a)transverseelectricfield(TE)andtransversemagneticfield(TM).Planeofincidenceisthe微 與新器件集V-AllwaveguidesarecharacterizedbyaparametercalledtheV-numberornormalizedfrequencyV

2V</2,m=0istheonlypossibilityandonlythefundamentalmode(m=0)propagatesalongthedielectricslabwaveguide:asinglemodeplanar2=cforV=/2 isthecut-offwavelength,andabovethiswavelength,onlyone-mode,thefundamentalmodewillpropagate.微 與新器件集ExampleonWaveguideConsideraplanardielectricguidewithacorethickness20m,n1=1.455,n2=1.440,lightwavelengthof900nm.Findthemodes1/ n2TIRphase

sin2 2mforTE

tan1

1

TEm m

2n1(2a)

m2ak1cosm微 與新器件集

1/2msin2 2m

TE

n1tanak1cosmm2

f(m 微 與新器件集withd=2a=20m,n1=1.455,n2=1.440(=900m0123456789°°°°°mm=0Criticalanglec=arcsin(n2/n1)=

nnn 2sin2m11/mmNumberofModes

OnemodewhenV</2MultimodewhenV>MInt(2V)微 與新器件集ModeFieldWidthEcladding(y)=

1/i i

sin2

(n

n2)1/2

V

ModeFieldWidthNote:TheMFWdefinitionhereissemi tive.Amorerigorousapproachneedstoconsidertheopticalpowerinthemodeandhowmuchofthispenetratesthecladding.Seeopticalfiberssection.微 與新器件集WaveguideDispersionTheslopeofvs.isthegroupvelocity微 與新器件集ModeGroupVelocitiesfromDispersionGroupvelocityvs.frequencyorwavelengthbehaviorisnotobvious.Forthefirstfewmodes,ahighermodecantravelfasterthanthefundamental.Thegroupvelocityvgvs.foraplanardielectricguidewithacore(2a)=20m,n1=1.455,n2=1.440.TE0,TE1and微 與新器件集APlanarDielectricWaveguidewithMany

c/×108

m=m=

c/Slowerthan

m=

m= m= m=

(c/n1)sinc=cn2/n1 0.5×1016 1.0×1016 1.5×1016Thegroupvelocityvgvs.foraplanardielectricCorethickness(2a)=20m,n1=1.455,n2=Notinthe微 與新器件集DispersioninthePlanarDielectricWaveguidewithTE0andTE1(Nearcut-

c/

Output2vgmaxc/n2;vgmin2

c/

n1

SpreadinarrivaltimesLL

Notinthe微 與新器件集m=m=m=mm=m=m=m=m=m=c/×108

c/Rangeofvelocitiesfor0

0.5×1016 1.0×1016 1.5×1016

(c/n1)sinc=cn2/n12Multimodeoperationin anymodespropagatewithdifferentgroupvgvs.foraplanardielectricguidewithacorethickness(2a)=20m,n1=1.455,n2=1.440[Calculationsbytheauthor]Notinthe微 與新器件集DispersioninthePlanarDielectricWaveguidewithManyModes(Farfromc

c/Rangeof65modes

1

n2n1(nn)n n

1

c n1vcvc cn2nc1 1 1vc1

(Sincen1andn2areonlyslightlyNotinthe微 與新器件集DispersioninthePlanarDielectricWaveguideMany

c

= n1 (Sincen1andn2areonlyslightly

Notinthe n 121Lcn2HowcanahighermodesuchasTE1orTE2travelfasterthanthenearcut- PenetrationPenetrationl TE1nearcut-l 2

IncidenceangleThemodeTE1penetratesintothecladdingwhereitsvelocityishigherthaninthecore.Ifpenetrationislarge,asnearcut-off,TE1groupvelocityalongtheguidecanexceedthatofTE0.Notinthe微 與新器件集GroupVelocityandWavelength:FundamentalTheelectricfieldofTE0modeextendsmoreintothecladdingasthewavelengthincreases.Asmoreofthefieldiscarriedbythecladding,thegroupvelocityincreases.微 與新器件集Step-IndexOpticalThestepindexopticalfiber.Thecentralregion,thecore,hasgreaterrefractiveindexthantheouterregion,thecladding.Thefiberhascylindricalsymmetry.Thecoordinatesr,zareusedtorepresentanypointPinthefiber.Claddingisnormallymuchthickerthan微 與新器件集Meridionalrayentersthefiberthroughthefiberaxisandhencealsocrossesthefiberaxisoneachreflectionasitzigzagsdownthefiber.IttravelsinaplanethatcontainsthefiberSkewrayentersthefiberoffthefiberaxisandzigzagsdownthefiberwithoutcrossing微 與新器件集 Weaklyguidingmodesin<< weaklyguiding

EandBare90otoeachotherand微 與新器件集FundamentalModeistheLP01mode:l=0andm=Theelectricfielddistributionofthefundamentalmode,LP01,inthetransverseplanetothefiberaxisz.Thelightintensityisgreatestatcenterofthe微 與新器件集Theelectricfielddistributionofthefundamentalmodeinthetransverseplanetothefiberaxisz.Thelightintensityisgreatestatthecenterofthefiber.IntensitypatternsinLP01,LP11andLP21modes.(a)Thefieldinthefundamentalmode.(b)-(d)Indicativelightintensitydistributionsinthreemodes,LP01,LP11andLP21.微 與新器件集m=numberof aalongrstartingfromthecorecenter.Determinesthereflectionangle2l=number aaroundal-radialmodel-extentofhelicalpropagation,i.e.theamountskewraycontributiontothe微 與新器件集OpticalFibern=(n1+n2)/2=averagerefractive=normalizedindex(n1n2)/n1(n12

V2a

V<2.405only1modeexists.FundamentalV<2.405or>cSinglemodeVM2V>VM2微 與新器件集ModesinanOptical

b1.1428

0.996Normalizedpropagation(/k)2n2

(1.5<V<b n2n2 k=Normalizedpropagationconstantbvs.V-numberforastep-indexfiberforvariousLPmodes微 與新器件集GroupVelocityandGroupConsiderasinglemodefiberwithcoreandcladdingindicesof1.4480and1.4400,coreradiusof3m,operatingat1.5m. 0.996b1.1428 b(/k)

1.5<V<=nk[1+n1 k=2/=4,188,790m-1and=2c/1.255757×1015rads-V=(2a/)(n12n22)1/2b=0.3860859,and=6.044796×106m-Increasewavelengthby0.1%andrecalculate.Valuesinthe微 與新器件集GroupVelocityandGroupCalculationVk(m-(rads-b(m-=1.500000=1.50150vg (1.2545031.255757)1015vg Thegroup er1kmis4.83微 與新器件集ModeFieldDiameter arbitrarilytoIntensity 微 與新器件集IntensityIntensity arbitrarilyto2w=ModeFieldDiameterMarcuseMarcuseMFD2w2a(0.651.619V3/22.879V6) 0.8<V<2.52w(2a)(2.6V) 1.6<V<2.4微 與新器件集CorrectionnoteAppliestoprintversiononly;e-versionisInsertInsertthis2assuperscripteinFigureInsertthis2inEquation微 與新器件集

IntensityAreaofacircularthinstrip(annulus)withradiusris2rdr.PowerpassingthroughthisstripisproportionaltoFractionofopticalwithin

E(r)2 0.865E(r)20

Notinthe微 與新器件集Fractionofopticalwithin=86Fractionofopticalwithin=8686%ofThisisthesameasthefractionofopticalpowerwithinaradiuswtheaxisofaGaussianbeam(SeeChapter微 與新器件集Example:AmultimodeCalculatethenumberofallowedmodesinamultimodestepfiberwhichhasacoreofrefractiveindexof1.468anddiameterm,andacladdingofrefractiveindexof1.447ifthewavelengthis850nm.Substitute,a=50m,=0.850m,n1=1.468,n2=1.447intoexpressionfortheV-V=(2a/)(n12n22)1/2=(250/0.850)(1.4682=SinceV>>2.405,thenumberofmodesMV2/2=(91.44)2/2=whichis微 與新器件集Example:AsinglemodeWhatshouldbethecoreradiusofasinglemodefiberwhichhasacoreofn1=1.4680,claddingofn2=1.447anditistobeusedwithasourcewavelengthof1.3m?Forsinglemodepropagation,V2.405.WeV=(2a/)(n12n22)1/2[2a/(1.3m)](1.46821.4472)1/2whichgivesa2.01Ratherthinforeasycouplingofthefibertoalightsourceortoanotherfiber;aiscomparabletowhi eansthatthegeometricraypicture,strictly,cannotbeusedtodescribelightpropagation.微 與新器件集Example:Singlemodecut-offCalculatethecut-offwavelengthforsinglemodeoperationforafiberthathasacorewithdiameterof8.2m,arefractiveindexof1.4532,andacladdingofrefractiveindexof1.4485.WhatistheV-numberandthemodefielddiameter(MFD)foroperationat=1.31m?ForsinglemodeV=(2a/)(n12n22)1/2Substitutingfora,n1andn2andrearrangingwe>[2(4.1m)(1.453221.44852)1/2]/2.405=1.251Wavelengthsshorterthan1.251mgivemultimodeAt=1.31V=2[(4.1m)/(1.31m)](1.453221.44852)1/2=Modefielddiameter微 與新器件集ModefielddiameterMFDfromtheMarcuseEquation2(4.1)[0.651.62(2.30)3/22.88(2.30)62w=9.30

86%oftotalpoweriswithinthis2w=(2a)(2.6/V)=2(4.1)(2.6/2.30)=9.282w=2a[(V+1)/V]=11.8This2w=2a[(V+1)/V]=11.8differentthanthatforanoptical微 與新器件集umacceptanceanglemaxisthatwhichjustgivestotalinternalreflectionatthecore-claddinginterface,i.e.when=maxthen=c.Rayswithmax(e.g.ray erefractedpenetratethecladdingandeventuallyNA

n2

2 2 sinmax VV2aNANAisan

2max=totalacceptancefactorinlightlaunchingdesignsintotheoptical微 與新器件集Astepindexfiberhasacorediameterof100mandarefractiveindexof1.480.Thecladdinghasarefractiveindexof1.460.Calculatethenumericalapertureofthefiber,acceptanceanglefromair,andthenumberofmodessustainedwhenthesourcewavelengthis850nm.Thenumericalaperture2NA=2

=

1.460

=From,sinmax=NA/no=Acceptanceanglemax=Totalacceptanceangle2max=V-numberintermsofthenumericalaperturecanbewrittenThenumberofmodes,MV2/2=微 與新器件集Example:AsinglemodeAtypicalsinglemodeopticalfiberhasacoreofdiameter8mandarefractiveindex1.460.Thenormalizedindexdifferenceis0.3%.Thecladdingdiameteris125m.Calculatethenumericalapertureandthetotalacceptanceangleofthefiber.Whatisthesinglemodecut-offfrequencycofthefiber?NA=

=[(n1+n2)(n1n2)]Substituting(n1n2)=n1and(n1+n2)2n1,wegetNA[(2n1)(n1)]1/2=n1(2)1/2=1.46(20.003)1/2=0.113Theacceptanceangleisgivensinmax=NA/no=0.113/1ormax=6.5°,and2max=13TheconditionforsinglemodepropagationisV2.405whichcorrespondstominimumwavelengthcisgivenc=[2aNA]/2.405=[(2)(4m)(0.113)]/2.405=1.18微 與新器件集DispersionInSingle-ModeDispersion=SpreadofMaterialsDispersion:GroupvelocitydependsonNgandhenceonWaveguideDispersion:GroupvelocitydependsonwaveguideChromaticDispersion:Materialdispersion+WaveguideDispersionPolarizationDispersionProfileDispersion:Likematerialandwaveguidedispersion.Add Material+Waveguide+ProfileSelfphasemodulationdispersion微 與新器件集IntermodeDispersionn1n2 (Sincen1andn2areonlyslightly微 與新器件集

c

n1n2

/L50ns/kmDependsonlength!vvc cn 2nc1 1 1vn1 n 121Lcn2微 與新器件集IntramodeDispersionDispersioninthefundamentalGroupDelay=L/ GroupvelocityvgdependsRefractiveindex=V-number==(n1n2)/n1=

MaterialDispersionProfileDispersion微 與新器件集MaterialEmitteremitsaspectrum?ofWavesintheguidewithdifferentfreespacewavelengthstravelatdifferentgroupvelocitiesduetothewavelengthdependenceofn1.Thewavesarriveat ofthefiberatdifferenttimesandhenceresultinabroadenedoutputpulse.Dm

Dm=Materialdispersioncoefficient,psnm-1km-微 與新器件集

22v(gVeryshortlight

vg=c/Group

DependsontheDmDmd2ncd2 Dm=Materialdispersioncoefficient,psnm-1km-微 與新器件集WaveguidebhencedependsonVandhenceon

0.996V

n2

b1.1428 12 12Normalizedpropagation(/k)2n2b n2n2 k= 微 與新器件集WaveguidedispersionThegroupvelocityvg(01)ofthefundamentalmodedependsonV-number,whichitselfdependsonthesourcewavelengthevenifn1andn2wereconstant.Evenifn1andn2werewavelengthindependent(nomaterialdispersion),wewillstillhavewaveguidedispersionbyvirtueofvg(01)dependingonVandVdependinginverselyon.Waveguidedispersionarisesasaresultoftheguidingpropertiesofthewaveguideimposesanonlinearvs.lmwDDw=waveguidedispersionw Dwdependsonthewaveguidestructure,psnm-1km-微 與新器件集Chromatic

Materialdispersioncoefficient(Dm)forthecorematerial(takenasSiO2),waveguidedispersioncoefficient(Dw)(a=4.2m)andthetotalorchromaticdispersioncoefficientDch(=Dm+Dw)asafunctionoffreespacewavelength,Chromatic=Material+(D D 微 與新器件集WaveguideDimensionandChromaticw w2wD(psnm1km1)w

[a(μm)]2nDwDwn d2(bV) cdVWaveguidedispersiondependsontheguide微 與新器件集ProfileGroupvelocityvg(01)ofthefundamentalmodedependson,refractiveindexmaynotbeconstantoverarangeofwavelengths:=pD Dp=Profiledispersionp Dp<0.1psnm-1km-CangenerallybeTotalintramode(chromatic)dispersioncoefficientDchDch=Dm+Dw+DpwhereDm,Dw,Dparematerial,waveguideandprofiledispersioncoefficientsrespectively微 與新器件集ChromaticDch=Dm+Dw+0=dispersionslopeat

D

Chromaticdispersioniszeroat=0S 4Dch 10 微 與新器件集Polarizationndifferentindifferentdirectionsduetoinducedstrainsinfiberinmanufacturing,handlingandcabling.n/n10-6

DPMD=PolarizationdispersionTypicallyDPMD=0.10.5psnm-1km-微 與新器件集Self-PhaseModulationDispersion:NonlinearAtsufficientlyhighlightintensities,therefractiveindexofglassnisn=n+CIwhereCisaconstantandIisthelightintensity.Theintensityoflightmodulatesitsownphase. Whatistheopticalpowerthatwill/L0.1pskm-TakeC=10-14cm2W-I(c/C)(/L)=3Wcm-orn310-Given2a10m,A7.8510-7

Inmanycases,thisdispersionwillbelessOpticalpower2.35Winthe

otherdispersion微 與新器件集DispersionModifiedFibersandNonzeroDispersionShiftedForWavelengthDivisionMultiplexing(WDM)avoid4wavemixing:crosstalk.WeneeddispersionnotzerobutverysmallinEr-ampliferband(1525-1620nm)Dch=0.16psnm-1km-1.NonzerodispersionshiftedVariousfibersnamedaftertheirdispersioncharacteristics.Therange1500-1600nmisonlyapproximateanddependsontheparticularapplicationofthefiber.微 與新器件集DispersionFlattenedDispersionflattenedfiberexample.Thematerialdispersioncoefficient(Dm)forthecorematerialandwaveguidedispersioncoefficient(Dw)forthedoublycladfiberresultinaflattenedsmallchromaticdispersionbetween1and2.微 與新器件集NonzeroDispersionShiftedFiber:MoreFiberwithflatteneddispersionslope(schematic)

Nonzerodispersionshiftedfiber微 與新器件集CommercialFibersforOpticalpsnm-1km-psnm-2km-pskm-SomeStandardsinglemode,T(1550≤<Dch=0at01312nm,MFD=8.6-9.5mat1310nm.c≤1260nm.fiber,ITU-TG.655(1530<at1550<For1500-1600nmrange.WDMMFD=811fiber,ITU-TG.656<at1550<For1460-1625nmrange.DWDMapplication.MFD=711m(at1550nm).PositiveDch.c<1310CorningSMF28e+(StandardSMF)(1550<SatisfiesG.652.01317nm,MFD=9.2m1310nm),10.4m(at1550nm);c≤12602.6-SatisfiesG.655.Optimizedfor1530nm-1625nm.MFD=8.4m(at1550nm);c≤1260nm.OFSREACH5.5-HigherperformancethanG.655specification.SatisfiesG.656.ForDWDMfrom1460to1625nm.0≤1405nm.MFD=8.6m(at1550微 與新器件集SingleModeFibers:Selected微納與新器件集成DispersionTotaldispersion=DtLt+DcLc=(10psnm-1km-1)(1000km)+(100psnm-1km-1)(80=2000ps/nmfor1080Deffective=1.9psnm-1km-微 與新器件集DispersionDvs.wavelengthcharacteristicsinvolvedindispersioncompensation.Inversedispersionfiberenablesthedispersiontobereducedandmaintainedflatoverthecommunication微 與新器件集DispersionCompensationandCompensatingfiberhashigherattenuation.Dopedcore.NeedshorterlengthMoresusceptibletononlineareffects.Useatthereceiverend.Differentcrosssections.Splicing/couplingCompensationdependsontheManufacturersprovidetransmissionfibersplicedtoinversedispersionfiberforawelldefinedDvs.微 與新器件集BitRate,Dispersion,andElectricalandOpticalDispersion umBitB1/

Return-to-zero(RTZ)bitrateordataNonreturntozero(NRZ)bitrate=2RTZ微 與新器件集NRZand10101101001微 與新器件集umBitRateAGaussianoutputlightpulseandsometolerableintersymbolinterferencebetweentwoconsecutiveoutputlightpulses(y-axisinrelativeunits).Attimet=fromthepulsecenter,therelativemagnitudeise=0.607andfullwidthrootmeansquare(rms)spreadisrms=2.(TheRTZcase)微 與新器件集Dispersion umBitumBit B0.25 1/2

1/L

Dch1/BL0.25L0.25 Dch DchBitRate×Distanceinverselyproportionaltodispersioninverselyproportionaltolinewidthoflaser(so,weneedsinglefrequencylasers!)微 與新器件集)2 umBitB0.25 1/ 微 與新器件集OpticalAnopticalfiberlinkfortransmitting ogsignalsandtheeffectofdispersioninthefiberonthebandwidth,fop.微 與新器件集PulseShape umBit微納與新器件集成Example:BitrateandConsideranopticalfiberwithachromaticdispersioncoefficient8pskm-1nm-1atanoperatingwavelengthof1.5m.Calculatethebitratedistanceproduct(BL),andtheopticalandelectricalbandwidthsfora10kmfiberifalaserdiodesourcewithaFWHPlinewidth1/2of2nmisused.ForFWHP1/2/L=|Dch|1/2=(8psnm-1km-1)(2nm)=16pskm-1AssumingaGaussianlightpulseshape,theRTZbitratedistanceproduct(BL)isBL=0.59L/1/2=0.59/(16pskm-1)=36.9Gbs-1Theopticalandelectricalbandwidthsfora10kmfiberfop=0.75B=0.75(36.9Gbs-1km)/(10km)=2.8fel=0.70fop=1.9微 與新器件集TheGradedIndex(GRIN)OpticalMultimodesteppathsaredifferentsothatraysarriveatdifferenttimes.Gradedindexaredifferentbutsoarethevelocitiesalongthepathssothatalltheraysarriveatthesametime.微 與新器件集Arayinthinlystratifedmedium esrefractedasitpassesfromonelayertothenextupperlayerwithlowernandeventuallyitsanglesatisfiesTIR.Inamediumwherendecreasescontinuouslythepathoftheraybends微 與新器件集Therefractiveindexprofilecangenerallybedescribedbyapowerlawwithanindexcalledtheprofileindex(orthecoefficientofindexgrating)sothat,n=n1[1 ;r<n=n2;r= 2(4)(3) 5

L

Minimumintermodal Minimumintermodal微 與新器件集Minimumintermodal 2(4)(3) 5Profiledispersion

Ng1L

Minimumintermodal微 與新器件集(1/21/2)(n2n2)1/12M2V2NANA(r)[n(r)2n22EffectivenumericalapertureforGRINNumberofmodesinagradedindex微 與新器件集Table2.5Gradedindexmultimoded=corediameter(m),D=claddingdiameter(m).Typicalpropertiesat850nm.VCSELisaTypicalsurfaceemittinglaser.isattenuationalongthefiber.OM1,OM3andOM4arefiberstandardsforLANdatalinks(ethernet).arereportedTypicalpsnm-1km-in10Gand40G4700<550m150m2000<300m500200<33m微 與新器件集Example:DispersioninaGRINFiberandBitGradedindexfiber.Diameterof50mandarefractiveindexofn1=1.4750,0.010.ThefiberisusedinLANsat850nmwithavertical surfaceemittinglaser(VCSEL)thathasveryanarrowlinewidththatisabout0.4nm(FWHM).Assumethatthechromaticdispersionat850nmis100psnm-1km-1asshowninTable2.5.Assumethefiberhasbeenoptimizedat850nm,andfindtheminimumrmsdispersion.Howmanymodesarethere?Whatwouldbetheupperlimitonitsbandwidth?Whatwouldbethebandwidthinpractice?Givenandn1,wecanfindn2=0.01=(n1n2)/n1=(1.4750n2=TheV-numberisthenV=[(2)(25m)/(0.850m)(1.475021.46032)1/2=Forthenumberofmodeswecansimplytake=2andM=(V2/4)=(38.392/4)=368Thelowestintermodaldispersionforaprofileoptimizedgradedindexfiberfora1offiber,L=1km,微 與新器件集intermodeL

2

3(3108

=14.20×10-15sm-1or14.20pskm-Assumingatriangularoutputlightpulseandtherelationshipbetweenand1/2giveninTable2.4,theintermodalspreadintermode(FWHM)inthegroupdelayover1kmisintermode=(61/2)intermode=(2.45)(14.20ps)=34.8Wealsoneedthematerialdispersionattheoperatingwavelengthover1km,intramode=L|Dch|1/2(1km)100psnm-1km-1)(0.40nm)=40.0

(34.8)2

=53.0微 與新器件集B0.25 0.61

=11.5Gbs-Opticalbandwidthfop=0.99B=11.4Thisistheupperlimitsinceweassumedthatthegradedindexfiberisperfectlyoptimizedwithintermodebeingminimum.Smalldeviationsaroundtheoptimumcauselargeincreasesinintermode,whichwouldsharplyreducethebandwidth.微 與新器件集Ifthiswereamultimodestep-indexfiberwiththesamen1n2,thenthefulldispersion(totalspread)wouldroughlyn1n2n1 =4.92×10-11sm-1or49.2nskm-TocalculatetheBLweuseintermode BL

0.29(/

(0.29)(49.2109skm1

=17.5Mbs-1LANsnowusegradedindexMMFs,andthestepindexMMFsareusedmainlyinspeed微 與新器件集Example:Dispersioninagraded-indexfiberandbitConsideragradedindexfiberwhosecorehasadiameterof50mandarefractiveindexofn1=1.480.Thecladdinghasn2=1.460.Ifthisfiberisusedat1.30mwithalaserdiodethathasveryanarrowlinewidthwhatwillbethebitratedistanceproduct?EvaluatetheBLproductifthiswereamultimodestepindexfiber.Thenormalizedrefractiveindexdifference=(n1n2)/n1=(1.481.46)/1.48=0.0135.Dispersionforkmoffiberintermode/L=n12/[(20)(31/2)c]=2.610-14sm-1or0.026nskm-BL=0.25/intermode=9.6Gbs-1Wehaveignoredanymaterialdispersionand,further,weassumedtheindexvariationtoperfectlyfollowtheoptimalprofilewhi eansthatinpracticeBLwillbeworse.(Forexample,a15%variationinfromtheoptimalvaluecanresultinintermodeandhenceBLthataremorethan10timesworse.)Ifthiswereamultimodestep-indexfiberwitht