《光通信技術(shù)》課件：Lecture2 Fiber-Optic Communications Technology

Fiber-OpticCommunicationsTechnologyLecture3DepartmentofOpticalEngineering,ZJUTopicsLightguidinginfiberRectangularwaveguide:ananalogyCircularwaveguideDepartmentofOpticalEngineeringDepartmentofOpticalEngineeringLightPropagationinWaveguidesMaxwell’sequationsRectangularwaveguideDeterminedbyboundaryconditionApplytoz-componentFirstfindEzandHz,andyouhavealltherestDepartmentofOpticalEngineeringZJUNoTEM:Ez=Hz=0thenEx=Ey=Hx=Hy=0TE:Ez=0,E-fieldlinesaxisofwaveguideTM:Hz=0,B-fieldlinesaxisofwaveguideTEandTMmodesTE:TM:DepartmentofOpticalEngineeringh2

h2=TEandTMFieldForTMmodes,l=0andm=0arenotpossible,TM11isthelowestTMmode.DepartmentofOpticalEngineeringCutofffrequencyandwavelength=+jh2=2＋k2，k＝/vIf>0,waveguideattenuationoccurs,notsupportpropagationCutofffrequencyCutoffoccursEvanescent:nopropagationPropagation:allowtraveling

DepartmentofOpticalEngineeringCutofffrequencyandwavelengthCutofffrequencyPhaseconstantWith’=√()Threewavelengths:Unboundedwavelength=v/f:freespace,noboundaryGuidedwavelengthg=/[1-(f/fc)2]1/2:Allowtotravel!Cutoffwavelengthc=v/fc

:attenuation/evanescent

ModesinslabwaveguideDepartmentofOpticalEngineeringModalTheoryofStepIndexfiberGeneralexpressionofEM-waveinthecircularfibercanbewrittenas:Eachofthecharacteristicsolutionsiscalledmthmodeoftheopticalfiber.ItisoftensufficienttogivetheE-fieldofthemode.DepartmentofOpticalEngineeringModepropagationconstantThemodalfielddistribution,,andthemodepropagationconstant,mareobtainedfromsolvingtheMaxwell’sequationssubjecttotheboundaryconditionsgivenbythecrosssectionaldimensionsandthedielectricconstantsofthefiber.MostimportantcharacteristicsoftheEMtransmissionalongthefiberaredeterminedbythemodepropagationconstant,m（）,whichdependsonthemode&ingeneralvarieswithfrequencyorwavelength.Thisquantityisalwaysbetweentheplanepropagationconstant(wavenumber)ofthecore&thecladdingmedia.DepartmentofOpticalEngineeringAteachfrequencyorwavelength,thereexistsonlyafinitenumberofguidedorpropagatingmodesthatcancarrylightenergyoveralongdistancealongthefiber.Eachofthesemodescanpropagateinthefiberonlyifthefrequencyisabovethecut-offfrequency,cutoff,(orthesourcewavelengthissmallerthanthecut-offwavelength)obtainedfromcut-offconditionthatis:Tominimizethesignaldistortion,thefiberisoftenoperatedinasinglemoderegime.Inthisregimeonlythelowestordermode(fundamentalmode)canpropagateinthefiberandallhigherordermodesareundercut-offcondition(non-propagating).DepartmentofOpticalEngineeringDepartmentofOpticalEngineeringAttenuationandphaseshiftintotalinternalreflectionTotalinternalreflectionisnottotal:evanescentwave:Attenuatione-y,FresnelformulasReflectancesTransmittances

exampleDepartmentofOpticalEngineeringMoreaboutmodesTruemodesNaturalmodesTE,TMLinear-polarizedmodesLPmodesWhymodes,notfield?ThreetypesofmodesGuided:

internallyreflectedREPETIVELY!:2krequirementRadiation:notinternallyreflected+no2krequirement(continuum)LeakynotrealmodesMoreaboutmodesDepartmentofOpticalEngineeringModepropagationasafunctionoffrequencyModepropagationconstant,lm(),isthemostimportanttransmissioncharacteristicofanopticalfiber,becausethefielddistributioncanbeeasilywrittenasafunctionof.Inordertofindamodepropagationconstantandcut-offfrequenciesofvariousmodesoftheopticalfiber,firstwehavetocalculatethenormalizedfrequency,V,definedby:DepartmentofOpticalEngineeringa:radiusofthecore,

istheopticalfreespacewavelength,aretherefractiveindicesofthecore&cladding.Plotsofthepropagationconstantasafunctionofnormalizedfrequencyforafewofthelowest-ordermodesDepartmentofOpticalEngineeringDepartmentofOpticalEngineeringPhasevelocityv.s.Groupvelocity

c/n2c/n1minmaxGuidedmodesNomodesLeaky&radiationDepartmentofOpticalEngineeringGroupvelocityandpowertransportGroupandphasevelocityforE0cos(t-z)Phasev=/=c/n;puresinewave,notrealGroupvg=/,signalandpowertravelingvPowertransportanddistributionMultimodefiberV=40:Pclad/Ptotal=2%SinglemodefiberV=2.4:Pclad/Ptotal=40%DepartmentofOpticalEngineeringPowerconfinement&cutoffconditionLimitingthenumberofmodesMethodsAsolution:weakboundingCutoffwavelengthDepartmentofOpticalEngineeringDispersioninmultimodefibers:generalTwotypesofdispersion:intermodalandintramodal

TotaldispersionPulsewidth:

Fullwidthathalfthemaximum(FWHM)(fig.4.19)Opticalbandwidth:

Half-power(intensity)0.5PowerfrequencyrangeElectricalbandwidth:

0.707Powerfrequencyrange

DepartmentofOpticalEngineeringDispersioninmultimodefibers:intermodalIntermodaldispersion:1storderapproximation:

80ns/km(v.s.30ns/kmtruevalue)Problematicassumptions:AllmodesexcitedEachmodecarriesequalpowerModesdoesnotinteractwithoneanotherAllmodestravelatthesamevelocitynisindependentonDepartmentofOpticalEngineeringDispersioninmultimodefibers:intramodal

(chromatic,material)Sellmeierequations

Sellmeierequationsareessentiallyempiricalfitstotheactualrefractiveindexofamaterial,usingtheresultfor'forLorentzoscillatorsasbasisfunctionsDepartmentofOpticalEngineeringDepartmentofOpticalEngineeringSellmeierEquationforFusedSilicawithdopingModel:Three-polewithpolesatapproximately9.9m,116nmand68nmDepartmentofOpticalEngineeringDepartmentofOpticalEngineeringDispersioninmultimodefibers:intramodal

(chromatic,material)Propagationdelayperkilometer:g=1/vg

Materialdispersioncoefficient: Dmat()=g/examplePulsedelaycausedbymaterialdispersion tm=Dmat(),

wheretofindS0and0? fig3.20onp.78, table4.1onp.130

DepartmentofOpticalEngineeringBandwidthofmultimodefibersOverallbandwidth:

BW=1/(4ttotal)Intermodalbandwidth(GIfiber):(consideringn()forvg)Material(intramodal)bandwidth:

BWmat=1/[4D()L]

(aroughestimation!)ExampleExampleDepartmentofOpticalEngineeringDm()CalculationDepartmentofOpticalEngineeringIntermodalbandwidthforGIDepartmentofOpticalEngineeringDepartm