光纤通信(Optical-Fiber-Communication)Optical-Fiber课件

Chapter2OpticalFiber9/26/20231TheSch.OfInformationEngineering,WHUTChapter2OpticalFiber8/5/20OUTLINEThenatureoflightThefabricationofopticalfibersThestructureofanopticalfiberThepropagationprincipleoflightalongafiberThetransmissioncharacteroffiber9/26/20232TheSch.OfInformationEngineering,WHUTOUTLINEThenatureoflight8/5/2.1Thenatureoflight2.1.1thebasicconcept2.1.2

Lightasanelectromagneticwave2.1.3Polarization2.1.4Basicopticallawanddefinitions9/26/20233TheSch.OfInformationEngineering,WHUT2.1Thenatureoflight2.1.1t2.1.1thebasicconcept1.Ray－geometricalorrayopticalItisagooddescriptionwhenitgoesthroughanobjectthatismanytimeslargerthanthewavelength.Inclassicalphysics,lightconsistsof“ray”thatcouldbereflectedandrefractedthroughmirrorsandprismsetc.Theraysshowthedirectionofenergyflowinthelightbeam.Inopticalfibercommunicationsystem,Italwaysbeusedtodiscusslightpropagationinmultimodefibers.Problem:itiscannotexplainmanyphenomenawemakeuseofinopticalfibercommunication.9/26/20234TheSch.OfInformationEngineering,WHUT2.1.1thebasicconcept1.Ray－2.ElectromagenticwavesIn1815,

Fresnelgivedthecorrectexplanationofdiffraction.In1864,Maxwelltheorizedthatlightwavesmustbeelectromagneticinnature.Theobservationofpolarizationeffectsindicatedthatlightwavearetransverse.Itisnodifferentfromaradiowaveexceptthatthewavelengthismuchshorter.9/26/20235TheSch.OfInformationEngineering,WHUT2.ElectromagenticwavesIn1813.PhotonsLightenergyisalwaysemittedorabsorbedindiscreteunitscalledquantaofphotons.Inallexperimentsusedtoshowtheexistenceofphotons,thephotonenergyisfoundtodependonlyonthefrequency.Therelationshipbetweentheenergyandthefrequencyofaphotonisgivenby

WhereisPlanck’sconstant.9/26/20236TheSch.OfInformationEngineering,WHUT3.PhotonsLightenergyisalwa2.1.2

LightasanelectromagneticwaveTheelectomagneticspectrum9/26/20237TheSch.OfInformationEngineering,WHUT2.1.2LightasanelectromagneAnelectromagneticwaveconsistoftwofield:anelectricfieldanmagneticfieldthetwofields(electricandmagnetic)areorientedatprecisely90°tooneanother9/26/20238TheSch.OfInformationEngineering,WHUTAnelectromagneticwaveconsis9/26/20239TheSch.OfInformationEngineering,WHUT8/5/20239TheSch.OfInformati

Thecurvedlineisintendedtorepresentfieldstrength.Thefieldmightstartatamaximuminonedirection,decaytoazeroandthenbuildupintheotherdirectionuntilitreachesamaximuminthatotherdirection.Thefieldstrengthchangessinusoidally.9/26/202310TheSch.OfInformationEngineering,WHUTThecurvedlineisintende2.1.3Polarization1.LinearpolarizationTheelectricandmagneticfielddistributionsinatrainofplaneelectromagneticwavesatagiveninstantintimeareshownasfollowing:Theplanewaveexamplegivenabovehasitselectricfieldvectoralwayspointinginthedirection.Suchawaveislinearlypolarized.9/26/202311TheSch.OfInformationEngineering,WHUT2.1.3Polarization1.LinearpolAnotherlinearlypolarizedwavewhichisindependentofthefirstwaveandorthogonaltoit.

Whereistherelativephasedifferencebetweenthewaves.theresultantwaveisthensimplyasfollowing:Ifiszerooranintegermultipleof,thewavesareinphase.9/26/202312TheSch.OfInformationEngineering,WHUTAnotherlinearlypolarizedwavJustasanytwoorthogonalplanewavescanbecombinedintoalinearlypolarizedwave,anarbitrarylinearlypolarizedwavecanberesolvedintotwoindependentorthogonalplanewavesthatareinphase.9/26/202313TheSch.OfInformationEngineering,WHUTJustasanytwoorthogonalpla2.EllipiticalandcircularpolarizationForgeneralvaluesofthewaveisellipticallypolarized.Thegeneralequationofanellipseis

Theaxisoftheellipsemakesananglerelativetothexaxisasfollowing9/26/202314TheSch.OfInformationEngineering,WHUT2.Ellipiticalandcircularpo9/26/202315TheSch.OfInformationEngineering,WHUT8/5/202315TheSch.OfInformatWhen

Wehavecircularlypolarizedlight.Choosethepositivesignfor,thewaveisrightcircularypolarizedChoosethenegativesignfor,thewaveisleftcircularypolarized9/26/202316TheSch.OfInformationEngineering,WHUTWhenWehavecircularlypolari2.1.4Basicopticallawanddefinitions1.RefractiveindexInfreespacealightwavetravelsataspeed

Typicalvaluesofnare1.00forair,1.33forwater,1.50forglass,And2.42fordiamond.9/26/202317TheSch.OfInformationEngineering,WHUT2.1.4Basicopticallawandde2.Snelllaw(1)Accordingtothelawofreflection,theangleatwhichtheincidentraystrikestheinterfaceisexactlyequaltotheanglethatthereflectedraymakeswiththesameinterface.(2)Theincidentray,thenormaltotheinterface,andthereflectedrayalllineinthesameplane,whichisperpendiculartotheinterfaceplanebetweenthetwomaterials.Thisiscalltheplaneincidence.9/26/202318TheSch.OfInformationEngineering,WHUT2.Snelllaw(1)Accordingtot(3)Externalreflection:lighttravelinginacertainmediumisreflectedoffanopticallydensermaterial(onewithahigherrefractiveindex).Internalreflection:thereflectionoflightoffoflessopticallydensematerial(suchaslighttravelinginglassbeingreflectedataglass-airinterface).9/26/202319TheSch.OfInformationEngineering,WHUT(3)Externalreflection:light2.2Thefabricationofopticalfibers2.2.1FiberMaterials2.2.2fiberfabrication9/26/202320TheSch.OfInformationEngineering,WHUT2.2Thefabricationofoptical2.2.1FiberMaterials1.TherequirementsoffibermaterialsItmustbepossibletomakelong,thinflexiblefibersfromthematerial.Thematerialmustbetransparentataparticularopticalwavelengthinorderforthefibertoguidelightefficiently.Physicallycompatiblematerialsthathaveslightlydifferentrefractiveindicesforthecoreandcladdingmustbeavailable.Materialsthatsatisfytheserequirementsareglassesandplastics.9/26/202321TheSch.OfInformationEngineering,WHUT2.2.1FiberMaterials1.There2.GlassfibersHigh-lossglassfiberswithlargecoresusedforshort-transmissiondistancesVerytransparent(low-loss)fibersemployedinlong-haulapplicationsThelargestcategoryofopticallytransparentglassesfromwhichopticalfibersaremadeconsistsoftheoxideglasses.Ofthese,themostcommonissilica(SiO2),whichhasarefractiveindexof1.458at850nm.9/26/202322TheSch.OfInformationEngineering,WHUT2.Glassfibers8/5/202322TheScToproducetwosimilarmaterialsthathaveslightlydifferentindicesofrefractionforthecoreandcladding,eitherfluorineorvariousoxides(referredtoasdopants),suchasB2O3,GeO2,orP2O5,areaddedtothesilica.TheadditionofGeO2orP2O5increasestherefractiveindex,whereasdopingthesilicawithfluorineorB2O3decreasesit9/26/202323TheSch.OfInformationEngineering,WHUTToproducetwosimilarmateria3.Halideglassfibers4.ActiveglassfibersIncorporatingrare-earthelements(atomicnumbers57-71)intoanormallypassiveglassgibestheresultingmaterialnewopticalandmagneticproperties.Thesenewpropertiesallowthematerialtoperformamplification,attenuation,andphaseretardationonthelightpassingthroughit.Twocommonlyusedmaterialsforfiberlasersareerbiumandneodymiun.9/26/202324TheSch.OfInformationEngineering,WHUT3.Halideglassfibers8/5/202325.ChalgenideglassfibersChalgenideglassisonecandidatefortheseusesbecauseofitshighopticalnonlinearityanditslonginteractionlength.6.PlasticopticalfibersHigh-bandwidthgraded-indexpolymer(plastic)opticalfibers(POF)foruseinacustomerpremises.Althoughtheyexhibitconsiderablygreateropticalsignalattenuationsthanglassfibers,theyaretoughanddurable,thecorediametersofplasticfibersare10-20timelarger,whichallowsarelaxationofconnectortoleranceswithoutsacrificingopticalcouplingefficiencies.9/26/202325TheSch.OfInformationEngineering,WHUT5.Chalgenideglassfibers8/5/22.2.2fiberfabrication1.direct-meltmethodsthismethodsfollowstraditionalglass-makingproceduresinthatopticalfibersaremadedirectlyfromthemoltenstateofpurifiedcomponentsofsilicateglasses.9/26/202326TheSch.OfInformationEngineering,WHUT2.2.2fiberfabrication1.direc2.vapor-phaseoxidationprocessHighlypurevaporsofmetalhalides(eg.SiCl4andGeCl4)reactwithoxygentoformawhitepowderofSiO2particles.Theparticlesarethencollectedonthesurfaceofabulkglassandaresintered(transformedtohomogeneousglassmassbyheatingwithoutmelting)byoneofavarietytechniquestoformaclearglassrodortubethatiscalledapreform.Itistypicallyaround10-25mmindiameterand60-120cmlong.Thepreformisprecision-fedintoacircularheatercalledthedrawingfurnace.Thenthepreformendissoftenedtothepointwhereitcandrawnintoaverythinfilament,whichbecomestheopticalfiber.Anelasticcoatingisappliedtothefiberinordertoprotectthebareglassfiberfromexternalcoontaminants9/26/202327TheSch.OfInformationEngineering,WHUT2.vapor-phaseoxidationproces9/26/202328TheSch.OfInformationEngineering,WHUT8/5/202328TheSch.OfInformat2.3ThestructureofanopticalfiberAnopticalfiberisadielectricwaveguidethatoperatesatopticalfrequencies.Thisfiberwaveguideisnormallycylindricalinform.Itconfineselectromagneticenergyintheformoflighttowithinitssurfacesandguidesthelightinadirectionparalleltoitsaxis.Thetransmissionpropertiesofanopticalwaveguidearedictatedbyitsstructuralcharacteristics,whichhaveamajoreffectindetermininghowanopticalsignalisaffectedasitpropagatesalongthefiber.9/26/202329TheSch.OfInformationEngineering,WHUT2.3Thestructureofanoptica2.3.1fiberstructure1.core-claddingstructureThemostwidelyacceptedstructureisthesinglesoliddielectriccylinderofradiusaandindexofrefractionn1Thiscylinderisknownasthecoreofthefiber.Thecoreissurroundedbyasoliddielectriccladdingwhichhasarefractiveindexn2thatislessthann1.9/26/202330TheSch.OfInformationEngineering,WHUT2.3.1fiberstructure1.core-cl9/26/202331TheSch.OfInformationEngineering,WHUT8/5/202331TheSch.OfInformat2.Thepurposeofusingcore-claddingstructure:thecladdingreducesscatteringlossthatresultsfromdielectricdiscontinuitiesatthecoresurface.addsmechanicalstrengthtothefiberprotectsthecorefromabsorbingsurfacecontaminantswithwhichitcouldcomeincontact.9/26/202332TheSch.OfInformationEngineering,WHUT2.Thepurposeofusingcore-cl2.3.2fibertype1.AccordingthemodewhichpropagateinthefiberSinglemodefiber(SMfiber)2a=2~12µmasinglemodeopticalsource:LDMultimodefiber(MMfiber)2a=5~100µmopticalsource:LEDthelargercoreradiiofmultimodefibersmakeiteasiertolaunchopticalpowerintothefiberandfacilitatetheconnectingtogetherofsimilarfibers9/26/202333TheSch.OfInformationEngineering,WHUT2.3.2fibertype1.Accordingt9/26/202334TheSch.OfInformationEngineering,WHUT8/5/202334TheSch.OfInformat2.Accordingtotherefractiveindexofthecore(1)Step-indexfiber(SIOF)(2)Graded-indexfiber(GIOF)Theparameteriscalledthecore-claddingindexdifferenceorsimplytheindexdifference.Itisnominally0.01.Typicalvaluesrangefrom1to3percentforMMfibersandform0.2to1.0percentforSMfiber.9/26/202335TheSch.OfInformationEngineering,WHUT2.Accordingtotherefractiveaisthecoreradius,theparameterdeterminestheindexprofile:Astep-indexprofileisapproachedinthelimitoflargeAparabolic-indexfibercorrespondsto9/26/202336TheSch.OfInformationEngineering,WHUTaisthecoreradius,thepara2.4Thepropagationprincipleoflightalongafiber

Twomethodtostudythepropagationcharacteristicsoflight:ModetheoryGeometricalopticsofray-tracingapproach9/26/202337TheSch.OfInformationEngineering,WHUT2.4Thepropagationprinciple2.4.1rayopticsrepresentation1.TheclassificationofrayMeridionalraytheyareconfinedtothemeridianplanesofthefiber,whicharetheplanesthatcontaintheaxisofsymmetryofthefiber.meridionalraycanbedividedintotwogeneralclasses:boundrays;unboundraysSkewraytheyarenotconfinedtoasingleplane,butinsteadtendtofollowahelical-typepathalongthefiber.9/26/202338TheSch.OfInformationEngineering,WHUT2.4.1rayopticsrepresentatio9/26/202339TheSch.OfInformationEngineering,WHUT8/5/202339TheSch.OfInformat2.Theanalysisofmeridionalray

inSIOF9/26/202340TheSch.OfInformationEngineering,WHUT2.TheanalysisofmeridionalrRefractionattheair-glassinterface:Totalinternalreflectionatthecore-claddinginterfaceifDefinethenumericalaperture(NA)ofastep-indexfiberformeridionalray9/26/202341TheSch.OfInformationEngineering,WHUTRefractionattheair-glassinMultimodefiberssufferfrommodaldispersion.Shortestpathlength(alongthefiberaxis).Longestpathlengthfortherayclosetothecriticalangle.Pulsebroadening:Modaldispersion:LimitationonthebitrateSingle-modefibersessentialforhighperformace9/26/202342TheSch.OfInformationEngineering,WHUTMultimodefiberssufferfromm3.Theanalysisofmeridionalray

inGIOFWhyintermodalormultipathdispersionisreduceforgraded-indexfibers.ThetrajectoryofaparaxialrayisobtainedbysolvingForAllraysarrivesimultaneouslyatperiodicintervalsLimitationonthebitrate:9/26/202343TheSch.OfInformationEngineering,WHUT3.Theanalysisofmeridionalr2.4.2modetheoryforcircularwaveguides9/26/202344TheSch.OfInformationEngineering,WHUT2.4.2modetheoryforcircularMaxwellequation9/26/202345TheSch.OfInformationEngineering,WHUTMaxwellequation8/5/202345The1.ThebasicconceptofmodeSolvingMaxwell’sequationssubjecttothecylindricalboundaryconditionsattheinterfacebetweenthecoreandthecladdingofthefiber.ThebasicequationofwavingtheoryHereislaplacianfunctor9/26/202346TheSch.OfInformationEngineering,WHUT1.ThebasicconceptofmodeSolLengthwayspropagationfactor:GuidemoderadiationmodeorcladdingmodeLeakymode9/26/202347TheSch.OfInformationEngineering,WHUTLengthwayspropagationfactor:2.ThemodeinopticalfiberTEmodeorTMmodecorrespondtomeridionalrayHEmodeorEHmodecorrespondtoskewrayTEmode:TMmode:HEorEHmode:9/26/202348TheSch.OfInformationEngineering,WHUT2.ThemodeinopticalfiberTEWeakguidingfiberandlinearlypolarized(LP)modeandifisthemainmodeandnoskewrayThemeaningoflandmin

symbol9/26/202349TheSch.OfInformationEngineering,WHUTWeakguidingfiberandlinearlTheVnumberisconnecttothecutoffconditionWhenitrealizethatasinglemodepropagateinfiberTheVnumbercanalsobeusedtoexpressthenumberofmodesMinamultimodefiberwhenVislarge.Forthiscase,anestimateOfthetotalnumberofmodessupportedinafiberis9/26/202350TheSch.OfInformationEngineering,WHUTTheVnumberisconnecttothe2.5thetransmissioncharacteroffiberWhathappentosignal

fiberlosses:limitsthetransmissiondistance

chromaticdispersion:limitsthebitratethroughthepulsebroadening

nonlineareffect:distortthesignalandlimitthesystemperformace9/26/202351TheSch.OfInformationEngineering,WHUT2.5thetransmissioncharacterSignaldegradationinopticalfibersWhatarethelossorsignalattenuationmechanisminafiberWhyandtowhatdegreedoopticalsignalsgetdistortedastheypropagatelongafiber9/26/202352TheSch.OfInformationEngineering,WHUTSignaldegradationinoptical2.5.1attenuationAttenuationofalightsignalasitpropagatesalongafiberisanimportantconsiderationinthedesignofanopticalcommunicationsystem,sinceitplaysamajorroleindeterminingthemaximumtransmissiondistancebetweenatransmitteranareceiveroranin-lineamplifier.9/26/202353TheSch.OfInformationEngineering,WHUT2.5.1attenuationAttenuationo1.AttenuationunitsAslighttravelsalongafiber,itspowerdecreasesexponentiallywithdistance.IfP(0)istheopticalpowerinafiberattheorigin,thenthepowerP(z)atadistancezfurtherdownthefiberiswhere9/26/202354TheSch.OfInformationEngineering,WHUT1.AttenuationunitsAslighttr9/26/202355TheSch.OfInformationEngineering,WHUT8/5/202355TheSch.OfInformat2.AbsorptionAbsorptionbyatomicdefectsintheglasscompositionExtrinsicabsorptionbyimpurityatomsintheglassmaterialIntrinsicabsorptionbythebasicconstituentatomsofthefibermaterial.9/26/202356TheSch.OfInformationEngineering,WHUT2.AbsorptionAbsorptionbyatom(1)Atomicdefectsareimperfectionsintheatomicstructureofthefibermaterial.Usually,absorptionlossesarisingfromthedefectsarenegligible.(2)Thedominantabsorptionfactorinfiberspreparedbythedirect-meltmethodisthepresenceofimpuritiesinthefibermaterial.impurityabsorptionresultspredominantlyfromtransitionmetalions,suchasiron,chromium,cobaltandcopper,andfromOH(water)ions.thepresenceofOHionimpuritiesinfiberpreformsresultsmainlyfromtheoxyhydrogenflameusedforthehydrolysisreactionoftheSiCl4,GeCl4,andPOCl3startingmaterial.9/26/202357TheSch.OfInformationEngineering,WHUT(1)Atomicdefectsareimperfec(3)intrinsicabsorptionisassociatedwiththebasicfibermaterialandistheprincipalphysicalfactorthatdefinesthetransparencywindowofamaterialoveraspecifiedspectralregion.electronicabsorptionbandsintheultravioletatomicvibrationbandsinthenear-infraredregion9/26/202358TheSch.OfInformationEngineering,WHUT(3)intrinsicabsorptionisass9/26/202359TheSch.OfInformationEngineering,WHUT8/5/202359TheSch.OfInformat3.ScatteringlossesScatteringlossesinglassarisefrommicroscopicvariationsinthematerialdensity,fromcompositionalfluctuations,andfromstructuralinhomogeneitiesordefectsoccurringduringfibermanufacture.Densityfluctuationsleadtorandomfluctuationsoftherefractiveindex.Therefractive-indexvariationswhichoccurwithintheglassoverdistancesthataresmallcomparedwiththewavelength.TheseindexvariationscauseaRayleigh-typescatteringofthelight.9/26/202360TheSch.OfInformationEngineering,WHUT3.ScatteringlossesScatteringThescatteringcrosssectionvariesasAsaresult,theintrinsiclossofsilicafibersfromRayleighscatteringcanbewrittenas:WheretheconstantCisintherange0.7-0.9dB/km—dependingontheconstituentsofthefibercore.ThesevaluesofCcorrespondtoatindicatingthatfiberlossisdominatedbyrayleighscatteringnearthiswavelength9/26/202361TheSch.OfInformationEngineering,WHUTThescatteringcrosssectionv2.5.2Dispersion-signaldistortioninopticalwaveguidesintramodaldispersionorchromaticdispersionitispulsespreadingthatoccurswithinasinglemode.Thespreadingarisesfromthefinitespectralemissionwidthofanopticalsource.Thisphenomenonisalsoknownasgroupvelocitydispersion(GVD),sincethedispersionisaresultofthegroupvelocitybeingafunctionofthewavelength.intermodaldispersionitisaresultofeachmodehavingadifferentvalueofthegroupvelocityatasinglefrequency.9/26/202362TheSch.OfInformationEngineering,WHUT2.5.2Dispersion-signaldistor1.InformationcapacitydeterminationAresultofthedispersion-inducedsignaldistortionisthatalightpulsewillbroadenasittravelsalongthefiber.Thispulsebroadeningwilleventuallycauseapulsetooverlapwithneighboringpulses.Afteracertainamountofoverlaphasoccurred,adjacentpulsecannolongerbeindividuallydistinguishedatthereceiveranderrorswilloccur.9/26/202363TheSch.OfInformationEngineering,WHUT1.Informationcapacitydetermi9/26/202364TheSch.OfInformationEngineering,WHUT8/5/202364TheSch.OfInformatAmeasureoftheinformationcapacityofanopticalwaveguideisusuallyspecifiedbythebandwidth-distanceproductinMHz·km.ForSIOF:BLislimitedtoabout20MHz·kmforGIOF:BLismaybeashighas2.5GHz·kmiftheradialrefractive-indexprofilecanbecarefullyselectedsothatpulsebroadeningisminimizedataspecificoperatingwavelength.9/26/202365TheSch.OfInformationEngineering,WHUTAmeasureoftheinformationc2.GroupdelayAsthesignalpropagatesalongthefiber,eachspectralcomponentcanbeassumedtotravelindependently,andtoundergoatimedelayorgroupdelayperunitlengthinthedirectionofpropagation.HereListhedistancetraveledbythepulse,isthepropagationconstantalongthefiberaxis,thegroupvelocityis9/26/202366TheSch.OfInformationEngineering,WHUT2.GroupdelayAsthesignalproThedelaydifferenceperunitwavelengthalongthepropagationpathisapproximatelyorforspectralcomponentswhichareapartandthecentralwavelengthis,thetotaldelaydifferenceoveradistanceLis:ThefactoristheGVDparameter.whichdetermineshowmuchalightpulsebroadensasittravelsAlonganopticalfiber.9/26/202367TheSch.OfInformationEngineering,WHUTThedelaydifferenceperunitIfthespectralwidthofanopticalsourceischaracterizedbyitsrmsvalue,thenthepulsespreadingcanbeapproximatedbythermspulsewidth,Dispersioncoefficientitunitis9/26/202368TheSch.OfInformationEngineering,WHUTIfthespectralwidthofa3.Thetypeofdispersionintermodaldispersionintramodaldispersionchromaticdispersion:materialdispersionwaveguidedispersionPMD(Polarizedmodedispersion)9/26/202369TheSch.OfInformationEngineering,WHUT3.Thetypeofdispersioninterm(1)MaterialdispersionMaterialdispersionoccursbecausetheindexofrefractionvariesasafunctionoftheopticalwavelength.Sincethegroupvelocityofamodeisfunctionoftheindexofrefraction,thevariousspectralcomponentsofagivenmodewilltravelatdifferentspeeds,dependingonthewavelength.9/26/202370TheSch.OfInformationEngineering,WHUT(1)Materialdispersion8/5/2029/26/202371TheSch.OfInformationEngineering,WHUT8/5/202371TheSch.OfInformatBecause,sothedelayisWhenasourceofspectralwidth,thepulsespreadisWheretheismaterialdispersion9/26/202372TheSch.OfInformationEngineering,WHUTBecause9/26/202373TheSch.OfInformationEngineering,WHUT8/5/202373TheSch.OfInformat(2)WaveguidedispersionThecontributionofwaveguidedispersiontothedispersionparameterisgivenanddependsontheVparameterofthefiber.Waveguidedispersiondependsoncoresizeanddopantdistribution.9/26/202374TheSch.OfInformationEngineering,WHUT(2)Waveguidedispersion8/5/2029/26/202375TheSch.OfInformationEngineering,WHUT8/5/202375TheSch.OfInformat9/26/202376TheSch.OfInformationEngineering,WHUT8/5/202376TheSch.OfInformat(3)PMDApotentialsourceofpulsebroadeningisrelatedtofiberbirefringence.Iftheinputpulseexcitesbothpolarizationcomponents,itbecomesbroaderasthetwocomponentsdispersealongthefiberbecauseoftheirdifferentgroupvelocitiesThisphenomenoniscalledthePMDandhasbeenstudiedextensivelybecauseitlimitstheperformanceofmodernlightwavesystems9/26/202377TheSch.OfInformationEnginee