TechnicalEnglishForInformationScienceandElectronicEngineeringUnit8OpticalCommunicationsPartIElectromagneticSpectrum3NewWordsperusal精讀，細讀gigahertz吉赫（109Hz）impress印，銘刻，加載directionality方向性resonator諧振器tTerahertz特赫（1012Hz）atwill隨心所欲incur招致，蒙受，引起synchronous同步的interleave交織throughput吞吐量nonlinearity非線性femtosecond毫微微秒(1015sec)coherent相干的obviate避免，使成為不必要micron微米miniature小型的miniaturization小型化counterpart對等物，對等的角色cladding光纖包層4NewWordsproximity接近，親近fruition結果實，成就photon光子granular顆粒狀bias偏置benign良性的51VariousobservationsrelatingtothepotentialofopticaltechnologyfortransmissionofinformationcanbemadefromperusalofthefrequencylineofTable8.1.與用于信息傳輸的光學技術的潛力有關的仔細研究表8.1中的頻率表可以看到各種用于信息傳輸的光學技術的潛力。61Table8.1Afrequencylinewhichgivesthewavelengthsλ,thefrequenciesν,andthephotonenergyεpforthevariousregionsofthefrequencyspectrumNameaudioradioμwavemmwaveIROPT/UVx-rayGammaλ300km300m30cm3mm30μm0.3μm30?0.03?ν(Hz)10310610910111013101510171020εp3μeV0.3meV30meV3eV300eV0.3MeV72Theinformationratesinwhichoneisinterestedinconventional“modern-day”communicationssystemsgenerallycorrespondtoaudioratesintelephonesystems,radioratesincommercialbroadcastsystems,ordigitaltelevisionratesinthemostadvancedvideodistributionsystems.1

…

的信息傳播速率通常相應于

…“現代”常規通信系統中人們所感興趣的信息傳輸速率通常對應于電話系統中的音頻，商用廣播系統中的無線電頻率，或是在最先進的視頻節目分配系統中的數字電視信息速率。82TheseratesaregenerallybelowseveralGHz.Ifoneweretotransmitsuchinformationwithoutimpressingitonanopticalcarrierbutinsteadonaradiofrequency(RF)carrierabithigherthanthemaximumrate,thetransmissionwavelengthoftheRFcarrierwouldbecentimetersorlarger.2

如果要傳輸這樣的信息而不將它加載于光纖上，而是加載在略高于最大速率的射頻載波上，則此射頻載波就會是厘米波或波長再長一些的波。

92Therecan,however,begreatadvantagestousingopticalcarriers.Anobviousoneisthelowlossanddirectionalityoftheopticalfiber.Clearly,thecarriermusthaveahigherratethantheinformationrate.Amajorprinciplethathasappearedincommunicationssystemshasbeenthatthehigherthefrequency,thegreaterthetechnicalcomplexity.Microwavesarehardertohandlethanareradiowaves.通信系統的一個基本原則是102Aswavelengthsdecreasetoapproachthesizeofcircuitcomponents,circuitelementsarenolongerlumped,andleadscanactasreflectivecomponentsand/orantennasandlumpedelementsaselectromagneticresonators.3

隨著……,電路單元就不再是集總的，導線可起到反射元件以及（或）天線的作用，集總單元則成為電磁諧振器。

112Thishasgenerallymeantthatsendingmoreinformationwouldcostmoreandtherewasthereforeacostperbit/sec(bps)oftransmittedinformationinthesensethatgoingtoahigherinformationraterequiresahigherfrequency.Thus,thefirstobservationfromthefrequencylinewouldbethat,foropticalcarriers,whichhavefrequenciesinthehundredsofTHz,informationbandwidthisinsomesensefree.因此在較高的信息率要求較高的頻率這層意義上，要考慮傳輸信息的每個bps成本問題信息的帶寬在某種意義上是免費的122Thatistosay,theopticalwavelengthissosmallcomparedtomostdevicesthatthetechnologyhaschangeddrasticallyfromelectricalandmicrowave.Onceweassumethatwehavesuchtechnology,nomatterhowhighaninformationrateonemightwantitwillnotbenecessarytochangethecarrier,asthecarrierfrequencyishigherthananyrealisticinformationratecoulde.所用技術與電和微波有根本的不同無論信息率有多高，再也沒有必要改變載波了132Bandwidthisnotcompletelyfree,though,asencodersanddecodersmustnecessarilyoperateattheinformationrate,butmuchoftherestofthesystemmustnecessarilyhandleonlythecarrierplusmodulation.而系統其余部分大都只需要處理載波和調制142Ifacomponentcanhandleafrequencyof5×1014Hz,aninformationshiftinthatfrequencyofapartinathousand(correspondingtoa500GHzinformationrate)willhavelittleornoeffectondeviceperformance.在這個頻率，信息偏移千分之一（相應于500吉赫茲的信息率）對器件的性能將沒有什么影響

152Therefore,oncethesystemisalreadysetup,onecanupgradesystemspeedmoreorlessatwillwithoutthekindofcostsincurredbychangingtheelectromagneticcarrierinconventionalsystems.就可以隨意升級系統而不會涉及常規系統中改變電磁載波所需付出的那種代價163Aconsequenceofthesizeoftheopticalbandwidthisthattheopticalcarriercanbeusedtocarrymanydifferenttelephoneconversations,televisionprograms,etc.,simultaneously.Theprocessbywhichthisisgenerallycarriedout(atleastinsynchronousformat)iscalledtimedivisionmultiplexing(TDM).通常實現這種同時傳輸多路信息的過程（至少以同步格式實現）稱為時分復用173Theideaisthat,ifonewishestomultiplex16differentchannelseachtransmittingat1Mbps,onecouldperformthisbydividingeachbitperiodby16andtheninterleavingthebitsintoacomposite1μsecbit(1Mbpsrate)whichactuallycarries16bitsofinformationonit.4

其原理是：如果要復用16個1Mbps的不同信道，可將每一比特所占時間除以16，然后將16個數據比特交織成一個持續1微秒的復合比特（即比特率為1Mbps），這一復合比特實際上帶有16比特的信息。183Withtelephoneconversationsrepresentingarateof64kbps,the100sofTbpsbandwidthoftheopticalcarrierholdsgreatpromiseforTDM.Ofcourse,TDMisnottheonlymultiplexingschemeonecanimagineusing.Onecouldimagineimpressinganumberofsubcarriers,spacedbyperhapssomeGHz,ontotheopticalcarrier.使實現TDM有了極大的可能也許相隔幾個吉赫茲193Eachofthesecarrierscouldthenbemodulatedataninformationrateandthenre-separatedaccordingtotheirdifferentcarrierwavelengthsattheoutput.Suchaschemeisreferredtoaswavelength-divisionmultiplexing(WDM)orsubcarriermodulation,dependingontheimplementation.在輸出端按其不同的載波波長重新分離203Manyofthepresent-dayschemesforincreasinglinkthroughputwithincreasingtrafficinvolvecombiningmanyTDMsignalsontoWDMcarriers.Infact,thelimitationondensityofWDMturnsouttobenotbandwidthbutpower.Thatis,eachchannelrequiressomeamountofpower.Themorechannels,then,thehigherthepowerrequirement.涉及到將許多TDM信號與WDM載波結合的技術213Atsomepowerlevel,opticalfibernonlinearityesimportant,andthisnonlinearitytendstomixthesignalstogether.Thereispresentlymucheffortgoingonintryingtofindwaystoequalizesuchnonlinearities.目前正在進行大量的研究，努力尋求對這種非線性的均衡處理。224Thehighcarrierfrequencyoftheopticalcarrieralsohasdrawbacks,especiallyasitrelates,throughthespeedoflight,totheopticalwavelength.Theopticalperiodcorrespondstolessthantwofemtoseconds.Thismeansthatphasecontrolcorrespondstomanipulationofsub-femtosecondperiodsoftime.當它通過光速與光的波長相聯系時尤其如此毫微微秒（1015秒）234Althoughtechniquestodosuchareemerging,theyarecomplicated–muchmorecomplicatedthanmanipulatingmicrowaveorradiofrequencywaveforms.Forthisreason,coherentopticalreceptionisstillalaboratorytechnology.Thedevelopmentoftherareearth-dopedopticalfiberamplifierseemstohaveobviatedtheneedforcoherenttechniquesinmunicationasfarasimprovedsignal-to-noiseratiogoes.隨著信噪比的提高，看來稀土元素摻雜光纖放大器的發展使通信中不再需要用相干技術。245Theshortperiodoftheopticalwavealsoimpliesashortwavelengthcenteredaroundhalfofamicron.Thesmallnessoftheopticalwavelength,therefore,allowsfortheminiaturizationoftransmitandreceivemodules,whichshouldallowconsiderablereductioninsize,weight,andcostofopticalcommunicationsystemswithrespecttomicrowave/radiowavecounterparts.5

光波波長之小使發射和接收模塊得以小型化，這就使光通信系統的尺寸、重量以至價格與相應的微波、無線電波通信系統相比都大為降低。255Inthecaseofmicrowaves,thehigherthepackagingdensityofopenmicrowavechannels,theworsethecrosstalk.Nomatterhowtightlyonepacksfiber,ontheotherhand,thecrosstalkisessentiallyzeroifthecladdingisproperlydesigned.Thisleadstothecharacteristicthatfiberisanexcellentmediumforspacedivisionmultiplexing(SDM)–thatis,packaginganumberofchannelswithdifferentinformationstreamsincloseproximity.開放的微波信道排列的密度愈高，竄音就愈嚴重將多個傳輸不同信息流的信道緊密地封裝在一起266Althoughalltheadvantagesofcoherentopticalcommunicationsystemshaveyettobebroughttofruition,anotherpropertyofopticalradiationhasmadetoday’sopticalcommunicationsystemsnotdesirableforapplications.6Theimportantpropertyhereisthatofphotonenergy.雖然相干光通信系統的所有優點還有待于落實在具體成果中，光輻射的另一性質卻使目前的光通信系統不利于應用。276AsisseenfromTable8.1,thephotonenergyrangesfromroughly2eVtoroughly4eV.Thiswouldseemtobeanadvantageinefficiency.However,thereisapenaltytobepaidforhavingsuchphotonenergy.Becausesinglephotonsaredetectable,theemission/receptionprocessmusttakeonagranularnature.具有這樣的光子能量需要付出高昂的代價286Asiswell-known,eveninasteadyrain,theprobabilityofaraindroplanding(asafunctionoftime)followsaPoissondistribution,implyingthatthereisraindropbunching.7

如所周知，即使在一場穩定的降雨中，雨滴落地的概率（作為時間的函數）服從Poisson分布，意味著有成串的雨滴。296

Araindropwouldratherfallrightaftertheonebefore.Raindropsareimpatientanddon’tliketowait.Inmuchthesamemanner,alaserlikestospitbunchesofphotonsevenunderconstantbiascurrent.Suchbehaviorleadstoatypeofnoisecommonlyreferredtoasshotnoiseorquantumnoise.即使在恒定偏置電流條件下，激光也發出光子束306Ontheemission/detectionprocess,whichturnsouttobequiteseriousforanalogcommunicationsalthoughmuchmorebenigninthedigitalcase.在發射/檢測過程中，這一問題對于模擬通信變得相當嚴重，盡管在數字通信中要輕微得多317Opticalquantumdetectorscanoperateatroomtemperature,assinglephotonsaremeasurable.Therefore,opticaldirectdetectioncanbequitesensitiveifshotnoise-limited.Directdetection,further,istotallycompatiblewithintensitymodulationschemes–schemesinwhichthesourceisessentiallyjustturnedonandoff.8Suchmodulationschemesaretheeasiesttoimplement.進而言之，直接檢測與強度調制方案完全兼容，在這些方案中光源實質上只是簡單地接通和斷開。327Whencoupledwithlight’sshortwavelengthwhichallowsforminiaturesourcesanddetectorsandmicron-sizedwaveguides,directdetectionschemeshaveallowedforsmall,lightweight,highbandwidthsystemswhicharecompetitiveinmanyareas,mostnotablytothepresentmunicationstransmission,althoughamyriadofotherapplicationsarecontinuallyopeningup.9光波長很小，可以用小型的光源和檢測器以及微米級的波導，于是用直接檢測方案可實現在許多領域具有競爭力的小巧的寬帶系統。特別引人注目的是當前在電信傳輸中的應用，盡管無數其他應用也在不斷涌現出來。337Asmentionedpreviously,theseapplicationshavetendedtoopenupmoreslowlythanoriginallypredicted,ascostwasreallynotmuchofaconsiderationinmunications,whereequipmentcostsareswampedbyotherconsiderations.10如前所述，（線路）成本并非電信系統中真正重要的考慮因素，通信設備的成本主要受到其他因素的制約，因此這些應用比預料的出現得慢。

347Withconsumerelectronics,oneneednotworryaboutrightofwayorinstallation.Atpresent,thecostofconnectingtopersonalcomputersafewmetersfromeachother

opticallyissoexpensivethatfiberhasnotyetcometotheconsumermarket.用光技術將相距幾米的個人計算機連接起來357Thehighcostofthelinkinsuchacase,though,isnotfundamentalbutmorehistorical.Present-daydevelopmentsinmillimetercoreplasticisanexampleofamuchcheapertechnologythan,forexample,glassfiber.Thecostsofcomponentstogointofiberlinksaswellas

packagingcostsarepresentlybeingreducedandnewapplicationsareopeningup.PartIIOpticalFiber37NewWordscore纖芯diameter直徑confinement限制waveguide波導graded-index漸變（梯度）折射率step-index階躍（突變）折射率singlemodefiber單模光纖dispersion色散multimodefibers多模光纖polarization偏振，極化crystal晶體splice結合，焊接melt熔化doped摻雜質的preform預制品flexible柔順的，靈活的bundle捆，包扎attenuation衰減repeater中繼器，轉發器circa(c.,ca.,cir.circ.)大約38NewWordsduct管道immune免疫的，不受影響的wiretapping搭線竊聽concentric同心的tap-proof防竊聽的ignition燃燒，點火strain應力hydrophone水聽器seismic地震的sonar聲納towedstreamer拖曳飄帶式水聽器陣gyroscope陀螺儀co-located位于同一地方的endoscope內窺鏡，內診鏡invasive入侵的，侵略性的erbium鉺cylindrical圓柱形的dielectric介電的，電介質的abrupt突然的indexofrefraction折射率39NewWordsnormal垂直的，法線的aperture孔徑，光圈refractive折射的profile輪廓，分布parabolic拋物線的speckle散斑，斑點coherent相干的transverse橫向的evanescent漸逝的micron微米401Anopticalfiber(orfiber)isaglassorplasticfiberdesignedtoguidelightalongitslengthbyconfiningasmuchlightaspossibleinapropagatingform.1Infiberswithlargecorediameter,theconfinementisbasedontotalinternalreflection.Insmallerdiametercorefibers,(widelyusedformostcommunicationlinkslongerthan200meters)theconfinementreliesonestablishingawaveguide.光纖是一種玻璃的或塑料的纖維，用來沿其長度方向引導光，把盡可能多的光限于一種傳播形式。411Fiberopticsistheoverlapofappliedscienceandengineeringconcernedwithsuchopticalfibers.Opticalfibersarewidelyusedinfiber-opticcommunication,whichpermitstransmissionoverlongerdistancesandathigherdataratesthanotherformsofwiredandwirelesscommunications.Theyarealsousedtoformsensors,andinavarietyofotherapplications.數據速率比有線和無線通信的其它形式更高422Thetermopticalfibercoversarangeofdifferentdesignsincludinggraded-indexopticalfibersandstep-indexopticalfibers.Basedonthewayinwhichlightsarepropagatedthoughthefiber,therearesinglemodefibersincludingnonzerodispersion-shiftedfibersanddispersion-shiftedfibers,andmultimodefibers.漸變折射率光纖和階躍折射率光纖非零色散位移光纖和色散位移光纖432Afibermayeitherbesingle-modeormultimode,dictatedbythespecificdesignandthewavelengthofthelightpropagatinginthefiber.2Becauseofthemechanicalpropertiesofthemorecommonglassopticalfibers,specialmethodsofsplicingfibersandofconnectingthemtootherequipmentareneeded.一根光纖根據其設計和在其中傳播的光的波長，可以是單模的也可以是多模的。

需要用特別的方法熔接光纖以及把它們連接到其它設備442Manufactureofopticalfibersisbasedonpartiallymeltingachemicallydopedpreformandpullingtheflowingmaterialonadrawtower.3Fibersarebuiltintodifferentkindsofcablesdependingonhowtheywillbeused.光纖制造過程是將化學摻雜的預制棒部分融化，并在一個抽絲塔上拉長流動的原料。453Opticalfibercommunication

Opticalfibercanbeusedasamediumformunicationandnetworkingbecauseitisflexibleandcanbebundledascables.Itisespeciallyadvantageousforlong-distancecommunications,becauselightpropagatesthroughthefiberwithlittleattenuationcomparedtoelectricalcables.Thisallowslongdistancestobespannedwithfewrepeaters.由于光纖的柔韌性以及可捆扎成光纜463Additionally,thelightsignalspropagatinginthefibercanbemodulatedatratesashighas40Gbps,andeachfibercancarrymanyindependentchannels,eachbyadifferentwavelengthoflight(wavelength-division-multiplexWDM).4

此外在光纖中傳播的光信號可以調制到高達40Gbps的速率，每一根光纖能作為許多獨立的信道，每個信道用不同波長的光來調制（波分復用）。473Intotal,asinglefiber-opticcablecancarrydataatratesashighas14.4Pbps(circa14millionGbps).Overshortdistances,suchasnetworkingwithinabuilding,fibersavesspaceincableductsbecauseasinglefibercancarrymuchmoredatathanasingleelectricalcable.總體上，單根光纜可攜帶數據高達14.4Pbps（大約1400萬Gbps）483Fiberisalsoimmunetoelectricalinterference,whichpreventscross-talkbetweensignalsindifferentcablesandpickupofenvironmentalnoise.5

光纖也不會受電干擾的影響，防止了不同光纜中信號之間的串話以及環境噪聲的介入。493Also,wiretappingismoredifficultcomparedtoelectricalconnections,andthereareconcentricdualcorefibersthataresaidtobetap-proof.Becausetheyarenon-electrical,fibercablescanbridgeveryhighelectricalpotentialdifferencesandcanbeusedinenvironmentswhereexplosivefumesarepresent,withoutdangerofignition.6

因為光纖是不用電的，它能橫跨很高的電位差，能用于存在爆炸煙霧的環境下而沒有燃燒的危險。504Althoughfiberscanbemadeoutoftransparentplastic,glass,oracombinationofthetwo,thefibersusedinlong-distancemunicationsapplicationsarealwaysglass,becauseoftheloweropticalattenuation.Bothmulti-modeandsingle-modefibersareusedincommunications,withmulti-modefiberusedmostlyforshortdistances(upto500m),andsingle-modefiberusedforlongerdistancelinks.光纖可用透明塑料、玻璃、或兩者的結合制成514Becauseofthetightertolerancesrequiredtocouplelightintoandbetweensingle-modefibers(corediameterabout10micrometers),single-modetransmitters,receivers,amplifiersandothercomponentsaregenerallymoreexpensivethanmulti-modecomponents.7

由于將光耦合到單模光纖或在單模光纖之間耦合（纖芯直徑大約為10微米）的允差較小，單模發射器、接受器、放大器和其它元件的價格通常比多模元件的貴。525Fiberopticsensors

Opticalfiberscanbeusedassensorstomeasurestrain,temperature,pressureandotherparameters.Thesmallsizeandthefactthatnoelectricalpowerisneededattheremotelocationgivethefiberopticsensoradvantagestoconventionalelectricalsensorincertainapplications.小的尺寸以及在偏遠位置不需要電力536Opticalfibersareusedashydrophonesforseismicorsonarapplications.Hydrophonesystemswithmorethan100sensorsperfibercablehavebeendeveloped.Hydrophonesensorsystemsareusedbytheoilindustryaswellasafewcountries’navies.Bothbottommountedhydrophonearraysandtowedstreamersystemsareinuse.TheGermancompanySennheiserdevelopedamicrophoneworkingwithalaserandopticalfibers.

船底裝有水聽器陣列和拖纜系統已投入使用547Opticalfibersensorsfortemperatureandpressurehavebeendevelopedfordownholemeasurementinoilwells.Thefiberopticsensoriswellsuitedforthisenvironmentasitisfunctioningattemperaturestoohighforsemiconductorsensors.

因為它能工作在對半導體傳感器而言太高的溫度下558AnotheruseoftheopticalfiberasasensoristheopticalgyroscopewhichisinuseintheBoeing767andinsomecarmodels(fornavigationpurposes)andtheuseinhydrogenmicrosensors.

光學陀螺569Fiber-opticsensorshavebeendevelopedtomeasureco-locatedtemperatureandstrainsimultaneouslywithveryhighaccuracy.Thisisparticularlyusefultoacquireinformationfromsmallcomplexstructures.以很高的精確度同時測量同一點的溫度和張力5710Otherusesofopticalfibers

Fibersarewidelyusedinilluminationapplications.Theyareusedaslightguidesinmedicalandotherapplicationswherebrightlightneedstobeshoneonatargetwithoutaclearline-of-sightpath.Insomebuildings,opticalfibersareusedtoroutesunlightfromtherooftootherpartsofthebuilding.Opticalfiberilluminationisalsousedfordecorativeapplications,includingsigns,art,andartificialChristmastrees.

需要明光照亮目標而不需要一個清晰的直線路徑5811Opticalfiberisalsousedinimagingoptics.Acoherentbundleoffibersisused,sometimesalongwithlenses,foralong,thinimagingdevicecalledanendoscope,whichisusedtoviewobjectsthroughasmallhole.Medicalendoscopesareusedforminimallyinvasiveexploratoryorsurgicalprocedures(endoscopy).Industrialendoscopesareusedforinspectinganythinghardtoreach,suchasjetengineinteriors.

醫學內窺鏡用于微創探測或外科手術（內窺鏡檢查法）5912Anopticalfiberdopedwithcertainrare-earthelementssuchaserbiumcanbeusedasthegainmediumofalaseroropticalamplifier.Rare-earthdopedopticalfiberscanbeusedtoprovidesignalamplificationbysplicingashortsectionofdopedfiberintoaregular(undoped)opticalfiberline.摻雜某些稀土元素如鉺通過一小段摻雜光纖熔接到正常（非摻雜）光纖6012Thedopedfiberisopticallypumpedwithasecondlaserwavelengththatiscoupledintothelineinadditiontothesignalwave.8Bothwavelengthsoflightaretransmittedthroughthedopedfiber,whichtransfersenergyfromthesecondpumpwavelengthtothesignalwave.Theprocessthatcausestheamplificationisstimulatedemission.

除了信號波外，耦合到光纖線路的另一個激光波長被泵浦（注入）到摻雜介質的光纖中。6113Opticalfibercanbeusedtosupplyalowlevelofpower(aroundonewatt)toelectronicssituatedinadifficultelectricalenvironment.Examplesofthisareelectronicsinhigh-poweredantennaelementsandmeasurementdevicesusedinhighvoltagetransmissionequipment.

光纖可用于給處于用電困難環境的電子設備提供低的功率（約一瓦特）6214PrincipleofoperationAnopticalfiberisacylindricaldielectricwaveguidethattransmitslightalongitsaxis,bytheprocessoftotalinternalreflection.Thefiberconsistsofacoresurroundedbyacladdinglayer(Figure8.1).Toconfinetheopticalsignalinthecore,therefractiveindexofthecoremustbegreaterthanthatofthecladding.光纖是一個圓柱形的電介質波導，通過全內反射沿其軸傳播光光纖由一個被包層包圍的纖芯組成6314Theboundarybetweenthecoreandcladdingmayeitherbeabrupt,instep-indexfiber,orgradual,ingraded-indexfiber.

Figure8.1Atypicalopticalfiberconsistingofatransparentmaterialofrefractiveindexn1andsurroundedbyacladdingofaslightlylowerrefractiveindexn2.Mostofthepropagatingenergyisconfinedtothecoreregionandthefielddecaysexponentiallyinthecladding.Cladding(n2)Core(n1)6415Multimodefiber

Fiberwithlarge(greaterthan10μm)corediametermaybeanalyzedbygeometricoptics.Suchfiberiscalledmultimodefiber,fromtheelectromagneticanalysis.Inastep-indexmultimodefiber(Figure8.2),raysoflightareguidedalongthefibercorebytotalinternalreflection.由于全內反射光線沿光纖纖芯傳播6515Figure8.2Astep-indexmultimodefiberinwhichtherefractiveindexinthecoreisconstant.Lightraysimpingingonthecore-claddinginterfaceatananglegreaterthanthecriticalanglearetrappedinsidethecoreofthewaveguide.Insuchafiberraystravelingatlargeranglestotheaxishavetotraversealargerpathandhencetakealongertimethanthoserayswhichpropagatewithlesseranglestotheaxis.Thisleadstoasubstantialamountofbroadeninginapulsepropagatingthroughthefiber.xn(x)qCore:n1Cladding:n2(<n1)z6615Raysthatmeetthecore-claddingboundaryatahighangle(measuredrelativetoalinenormaltotheboundary),greaterthanthecriticalangleforthisboundary,arecompletelyreflected.9

當光線射到纖芯和包層之間界面的角度（與垂直于邊界的直線之間的夾角）大于臨界角時，光線被完全反射。

6715Thecriticalangle(minimumanglefortotalinternalreflection)isdeterminedbythedifferenceinindexofrefractionbetweenthecoreandcladdingmaterials.Raysthatmeettheboundaryatalowanglearerefractedfromthecoreintothecladding,anddonotconveylightandhenceinformationalongthefiber.10

以小角度射到分界面上的光線被折射，從纖芯進入包層，它們并不沿著光纖傳輸光，因而也不傳輸信息。6815Thecriticalangledeterminestheacceptanceangleofthefiber,oftenreportedasanumericalaperture.Ahighnumericalapertureallowslighttopropagatedownthefiberinraysbothclosetotheaxisandatvariousangles,allowingefficientcouplingoflightintothefiber.11

大的數值孔徑使光能以接近于軸線的方式沿光纖傳播，也能以不同的角度傳輸，從而使得光能有效地耦合進入光纖。

6915However,thishighnumericalapertureincreasestheamountofdispersionasraysatdifferentangleshavedifferentpathlengthsandthereforetakedifferenttimestotraversethefiber.12Alownumericalaperturemaythereforebedesirable.

然而，大的數值孔徑增加了色散的總量，因為以不同角度傳播的光線具有不同的光程長度，因而化了不同的時間穿過光纖。7016Inagraded-indexfiber(Figure8.3),theindexofrefractioninthecoredecreasescontinuouslybetweentheaxisandthecladding.Thiscauseslightraystobendsmoothlyastheyapproachthecladding,ratherthanreflectingabruptlyfromthecore-claddingboundary.這使得光線到達包層時是平滑地彎曲，而不是在纖芯包層邊界上突然反射7116Theresultingcurvedpathsreducemulti-pathdispersionbecausehighanglerayspassmorethroughthelower-indexperipheryofthecore,ratherthanthehigh-indexcenter.Theindexprofileischosentominimizethedifferenceinaxialpropagationspeedsofthevariousraysinthefiber.Thisidealindexprofileisveryclosetoaparabolicrelationshipbetweentheindexandthedistancefromtheaxi