光波導(dǎo)理論2012-7課件

耦合模理論平面介質(zhì)光波導(dǎo)的耦合模微擾理論采用A.Yariv的理論，將耦合系統(tǒng)看作一個(gè)受到某種微擾的理想波導(dǎo)，介質(zhì)光波導(dǎo)中的波動(dòng)方程可以寫(xiě)成以下形式：微擾極化強(qiáng)度對(duì)于y分量，有對(duì)波導(dǎo)的耦合作用，可以看作一種微擾，在受到這種微擾作用的波導(dǎo)中的光場(chǎng)可以展開(kāi)成各種導(dǎo)波模式的疊加，于是有每個(gè)導(dǎo)波模均滿足考慮到各導(dǎo)波模之間滿足正交條件，即前向波后向波在對(duì)m的求和中，每一個(gè)m值包含兩項(xiàng)：一個(gè)代表沿-z方向傳播的波

另一個(gè)代表沿z方向傳播的波

分別為兩個(gè)方向第s階模式波的振幅函數(shù)。

該方程就是耦合模理論的基本結(jié)果，只要把耦合問(wèn)題轉(zhuǎn)化為微擾問(wèn)題，并且能寫(xiě)出微擾的具體表達(dá)式，就可以由該方程求出問(wèn)題的具體解。導(dǎo)模之間的耦合兩個(gè)波導(dǎo)距離靠近出現(xiàn)耦合時(shí)，波場(chǎng)可以近似表示為兩個(gè)無(wú)擾動(dòng)波場(chǎng)的和：具體到此例，表達(dá)式為具有耦合的波導(dǎo)的折射率分布1.同向耦合可得耦合方程為

耦合系數(shù)為相位常數(shù)的修正項(xiàng)為修正后的總場(chǎng)可以表示為式中

相位失配因子波導(dǎo)a和b中光波所攜帶的能量分別為b端輸入能量在相位失配合情況下，最大轉(zhuǎn)換效率為假設(shè)在z=0處只有波導(dǎo)b存在單模傳輸，微擾發(fā)生在z>0區(qū)，即B(0)=B0，A(0)=0，根據(jù)能量守恒原則反向耦合式中周期性波導(dǎo)將此式代入耦合模方程得模式s與模式p之間通過(guò)

的第l個(gè)諧波的耦合，可以用下式描述

其中s階模與p階模之間的相位失配因子

耦合系數(shù)

描述模式p和模式s之間通過(guò)

的第l個(gè)諧波的耦合方程為

式中

后向波和前向波之間通過(guò)

的第l個(gè)諧波的耦合

其中耦合系數(shù)相位差

令

耦合方程變?yōu)?/p>

解為在相位匹配條件下

周期波導(dǎo)中的正向和反向傳播的電磁波之間的耦合可以利用一對(duì)耦合方程來(lái)描述。這一對(duì)耦合波方程可以推廣到任意的兩個(gè)波模a與b之間（幅值分別用A和B表示）的耦合：式中當(dāng)a、b波模傳輸方向相反時(shí)，均取上面的符號(hào)，

而當(dāng)a、b傳播方向相同時(shí)，均取下面的符號(hào)。光纖定向耦合器(Coupler)耦合器的工作原理兩光纖的纖芯很接近時(shí)，光場(chǎng)導(dǎo)致介質(zhì)極化，模場(chǎng)互相滲透，發(fā)生耦合耦合波方程組的解邊界條件:R(0)=1,S(0)=0兩參數(shù)相同光纖的耦合d=0，R2(z)=cos2(Kz) S2(z)=sin2(Kz)耦合長(zhǎng)度： L0=p/2K耦合系數(shù)：2D2Ddn2n1n2n1n2可以通過(guò)控制平行光纖的長(zhǎng)度以及兩光纖間距來(lái)控制耦合比相同波長(zhǎng)光信號(hào)耦合結(jié)論:當(dāng)耦合器的參數(shù)相同時(shí)(1)相同波長(zhǎng)間的耦合均會(huì)引入3dB(50%)損耗(2)不可能將兩個(gè)輸入端口的光功率經(jīng)過(guò)耦合器后從同一個(gè)端口輸出不同波長(zhǎng)光信號(hào)的耦合(分波)兩個(gè)波長(zhǎng)從輸入端口1輸入,分別在輸出端口1,2輸出l1l2l1l2不同波長(zhǎng)光信號(hào)的耦合(合波)兩個(gè)波長(zhǎng)從兩個(gè)輸入端口輸入,在同一個(gè)輸出端口輸出l1l2l1l2波長(zhǎng)可選擇的耦合器和分波器(1)對(duì)EDFA注入光功率（泵浦光＋信號(hào)光）(2)對(duì)簡(jiǎn)單的WDM系統(tǒng)作波長(zhǎng)分離(3)對(duì)DWDM系統(tǒng)增加管理信道性能參數(shù)制備工藝1XN耦合器星型耦合器光束耦合器棱鏡耦合器用夾具將一高折射率的棱鏡壓在平板波導(dǎo)上，棱鏡底部與薄膜波導(dǎo)的表面之間有一很窄的空氣間隙（或折射率匹配液），構(gòu)成棱鏡－波導(dǎo)耦合系統(tǒng)。

實(shí)現(xiàn)有效耦合應(yīng)滿足的條件：（1）在光波沿波導(dǎo)傳輸?shù)膠方向上，棱鏡中光波矢量的z分量應(yīng)該和波導(dǎo)中光波波矢的z分量，及波導(dǎo)導(dǎo)模的傳播常數(shù)β相等，這就是相位匹配條件。（2）為了保證耦合的效果，提高能量交換效率，必須根據(jù)耦合強(qiáng)度來(lái)調(diào)節(jié)沿耦合邊界的長(zhǎng)度。棱鏡中以角度將光束入射到棱鏡底面，該光波沿波導(dǎo)方向（z方向）的傳輸常數(shù)為由斯涅耳定理，

根據(jù)耦合模理論，棱鏡模和導(dǎo)波模之間的耦合長(zhǎng)度（沿z方向）應(yīng)滿足

相互作用長(zhǎng)度由入射光的光束有效寬度決定，即

實(shí)現(xiàn)輻射模－導(dǎo)模的100％完全耦合所需要的耦合系數(shù)為（3）為提高耦合效率，還可以在棱鏡與光波導(dǎo)之間滴入匹配液，如水（n=1.33）、甘油（n=1.47）、二碘甲烷（n=1.74）(3)由于棱鏡耦合器入射光必須高度對(duì)準(zhǔn)，很難用半導(dǎo)體激光器激勵(lì)。玻璃光柵耦合器功能與棱鏡耦合器類(lèi)似，用于實(shí)現(xiàn)自由空間和平面介質(zhì)光波導(dǎo)之間的耦合，不同的是棱鏡和間隙介質(zhì)被光柵薄膜代替。

光柵的作用:無(wú)光柵時(shí)，不可能將入射光束耦合進(jìn)波導(dǎo)而形成導(dǎo)模。加入光柵后，由于光柵的周期性，在具有周期性結(jié)構(gòu)的薄膜光波導(dǎo)（簡(jiǎn)稱(chēng)光柵波導(dǎo)）的導(dǎo)模沿z方向傳播時(shí)，每一個(gè)基本傳播模式的波場(chǎng)都受到周期的調(diào)制，或者說(shuō)光柵對(duì)導(dǎo)模產(chǎn)生了微擾，其作用相當(dāng)于改變了入射光波的相位，這種相位微擾可以通過(guò)下式表示出來(lái)，即沒(méi)有光柵覆蓋時(shí)的m階導(dǎo)波模的傳播常數(shù)光柵周期引入光柵后，可以同時(shí)滿足相位匹配條件和導(dǎo)波條件，入射光束就能被耦合進(jìn)入波導(dǎo)，并激勵(lì)起相應(yīng)的導(dǎo)模。

通過(guò)這種光柵耦合器，光束分別以傳輸角和向空氣一側(cè)或向襯底一側(cè)傾斜，且有關(guān)系

光柵耦合器的優(yōu)點(diǎn)：

1)不受光波導(dǎo)折射率大小的限制。2)可以選擇所有導(dǎo)模中的任意一種進(jìn)行激勵(lì)。3)可以與波導(dǎo)集成。震動(dòng)或外界環(huán)境的變化，不會(huì)改變耦合效率，穩(wěn)定性好，體積小，價(jià)格便宜。4)調(diào)整光束的入射位置時(shí)不需要特別嚴(yán)格的精度。5)也可以在橫向進(jìn)行同樣的耦合，因此可以激勵(lì)寬度非常大的波導(dǎo)光。光柵耦合器的缺點(diǎn)：1)由于光柵耦合與入射光角度的高度相干性，光柵耦合器不能有效地用于發(fā)散光束的耦合；2)光柵耦合器設(shè)計(jì)過(guò)程需要進(jìn)行復(fù)雜的理論計(jì)算，而且制作比較困難；3)器件的參數(shù)在制作后無(wú)法進(jìn)一步調(diào)整；4)對(duì)于條形波導(dǎo)，光束截面的匹配比較困難。光柵耦合器的主要應(yīng)用：既可用作光束輸入耦合器，也可用作光束輸出耦合器，既可以用半導(dǎo)體波導(dǎo)，也可以用其他任何薄膜波導(dǎo)，而且這種光柵既可以直接制作在波導(dǎo)表面，也可以將其他材料制成的光柵放置在波導(dǎo)表面上。發(fā)展無(wú)限的新型光纖特種光纖光子晶體光纖特種光纖保偏光纖摻稀土元素光纖雙包層光纖倏逝場(chǎng)光纖多芯光纖紅外光纖納米光纖保偏光纖幾何形狀引起高雙折射高雙折射橢圓芯保偏光纖結(jié)構(gòu)剖面示意圖保偏光纖應(yīng)力誘導(dǎo)高雙折射保偏光纖摻稀土元素光纖摻稀土元素光纖是采用某種工藝技術(shù)將釹、鉺和釔等稀土元素離子單獨(dú)或混合摻入光纖芯中而制成的。目前主要是摻雜到光纖纖芯中的，但亦有同時(shí)摻雜到光纖包層中去的。其摻雜濃度可從1PPm到0.25Wt%的寬廣范圍內(nèi)變化。纖芯中摻雜稀土元素有Er、Yb、Nd、Tm、Pr、Er/Yb、Ho等纖芯直徑～4μm，NA0.1包層直徑～125μm，形狀為圓形摻稀土元素光纖摻稀土元素光纖用這種摻雜光纖可以獲得四方面的應(yīng)用：(1)激光光纖與光纖放大器；(2)基于吸收、熒光的分布溫度傳感；(3)增大菲爾德常數(shù)；(4)提高克爾效應(yīng)及非線性光學(xué)系數(shù)。雙包層光纖雙包層光纖及其工作原理

雙包層光纖纖芯中摻雜稀土元素有：Er、Yb、Nd、Tm、Pr、Er/Yb、Ho等 單模光纖：纖芯小4μm，NA0.1纖芯結(jié)構(gòu)分類(lèi)大芯多模光纖：纖芯大（>30μm），NA大 大模面積（LMA）：纖芯大（>30μm），

NA小（<0.1）

內(nèi)包層形狀

圓形（同心、偏心）方形、矩形、、六邊形、星形和D形圓形偏心內(nèi)包層圓形同芯內(nèi)包層雙包層光纖矩形內(nèi)包層方形內(nèi)包層六邊形內(nèi)包層雙包層光纖星形內(nèi)包層D形內(nèi)包層雙包層光纖用包層泵浦的光纖激光特種光纖倏逝場(chǎng)光纖主要用途：倏逝場(chǎng)光纖生化傳感器基于電光克爾效應(yīng)的光調(diào)制器多芯光纖主要用途：

密集型光纜

光子器件用于圖像傳遞的傳像光纖紅外光纖方形中空光纖芯紅外光纖納米光纖納米光纖直徑在數(shù)百nm范圍內(nèi),所傳導(dǎo)的光場(chǎng)能量大部分以倏逝場(chǎng)的形式存在倏逝場(chǎng)計(jì)算納米光纖的傳感應(yīng)用發(fā)展無(wú)限的新型光纖特種光纖光子晶體光纖ContentsIntroduction

Whatisphotoniccrystalfiber?WorkingprincipleofPCFStructuresofphotoniccrystalfiberCharacteristicsofcrystalfiberFabricationofcrystalfiberApplicationsConclusionsIntroductionPhotoniccrystalfibers(PCFs)wasfirst

demonstratedin1996andhasgeneratedmuchattentionsincethen.PCFsareopticalfibersthatemployamicrostructuredarrangementoflow-indexmaterialinabackgroundmaterialofhigherrefractiveindex.Thebackgroundmaterialisoftenundopedsilicaandthelowindexregionistypicallyprovidedbyairvoidsrunningalongthelengthofthefiber.一維、二維和三維光子晶體示意圖光子晶體能帶結(jié)構(gòu)和態(tài)密度Whatisphotoniccrystalfiber?Photoniccrystalfibers,

alsoknownas

microstructured

Fibers,areabrandnewrangeofopticalfibersofferingsignificantnewpossibilitiesandfunctionalitywithintelecommunicationsandopticalcomponentsingeneral.

PCFsmaybedividedintotwocategories,highindexguidingfibersandlowindexguidingfibers.Similartoconventionalfibers,highindexguidingfibersareguidinglightinasolidcorebytheModifiedTotalInternalReflection(M-TIR)principle.

Thetotalinternalreflectioniscausedbythelowereffectiveindexinthemicrostructuredair-filledregion.TwocategoriesphotoniccrystalfiberWorkingprincipleofcrystalfiberLowindexguidingfibersguidelightbythephotonicbandgap(PBG)effect.ThelightisconfinedtothelowindexcoreasthePBGeffectmakespropagationinthemacrostructuredcladdingregionimpossible.ThestrongwavelengthdependencyoftheeffectiverefractiveindexandtheinherentlylargedesignflexibilityofthePCFsallowsforaholenewrangeofnovelproperties.Suchpropertiesincludeendlesslysingle-modedfibers,extremelynonlinearfibersandfiberswithanomalousdispersioninthevisiblewavelengthregion.M-TIRisanalogoustototalinternalreflectionknownfromstandardopticalfibers.Itreliesonahighindexcoreregion,typicallypuresilica,surroundedbyalowereffectiveindexprovidedbythemicrostructuredregion.Theeffectiveindexofsuchafibercan,inthesimplecase,beapproximatedbystandardastepindexfiber,withahighindexcoreandalowindexcladding.However,therefractiveindexofthemicrostructuredcladdinginPCFsexhibitsawavelengthdependencyverydifferentfrompuresilica-aneffectwhichallowsPCFstobedesignedwithacompletenewsetofpropertiesnotpossiblewithstandardtechnology.?StepindexfiberWorkingprincipleofcrystalfiber

Photoniccrystalfiber?Asanexample,thestrongwavelengthdependenceoftherefractiveindexallowdesignofendlesslysingle-modedfibers,whereonlyasinglemodeissupportedregardlessofopticalwavelength.Furthermore,itispossibletoalterthedispersionpropertiesofthefibers,therebymakingitpossibletodesignfiberswithananomalousdispersionat

visiblewavelengths.?Morecomplexindexstructurescanalsobeconstructedbyutilizingarrangementsofholesofdifferentsizeinvariousperiodicorunperiodicstructures.Inaddition,highlyasymmetriccorefiberscanbefabricatedtherebycreatingfiberswithveryhighlevelofbirefringence.WorkingprincipleofcrystalfiberWorkingprincipleofcrystalfiberPhotonicbandgapfibersarebasedonphysicalmechanismsfundamentallydifferentfromtheM-TIRguidingfibers.Thebandgapeffectcanbefoundinnature,wherethebeautifulandbrightcolorsthatareseeninbutterflywingsaretheresultofnaturallyoccurringperiodicmicrostructures.TheSEMpictureatthelowerleftshowsthemicrostructureonabutterflywing.Thestructuresizeisintheorderofafewmicrons.InaPBGfiber,thecoreiscreatedbyintroducingadefectinthePBGstructure(e.g.anextraairhole),therebycreatinganareawherethelightcanpropagate.WorkingprincipleofcrystalfiberAsthelightcanonlypropagateatthedefectregion,alowindexguidingcorehasbeencreated.Thisisnotpossibleinstandardfibers,andthelowindexguidingofPBGfibersthereforeopensawholenewsetofpossibilities.Inthisway,itispossibletoguidelightinair,vacuumoranygascompatiblewiththefibermaterial.Especiallythepossibilityforguidinginairorvacuumhasattractedmuchattention,asitmightholdthekeytotransmissionfiberswithextremelylowlosses.WorkingprincipleofcrystalfiberThedifferentguidingmechanisms.(A)Conventionaltotalinternalreflection(TIR);thisoccurswhenthewavevectorcomponentinthedirectionofpropagationliesintherangekn2<β<kn1.(B)PBGguidancewhenthelightisevanescentintheairregions;thiscanonlyoccurwhenliesinthesamerangeasin(A);theprocessisoneoffrustratedtunneling,thatis,thecladdingresonatorsareoutofresonancewiththecorewaveguideandhencetunnelingisprevented.Workingprincipleofcrystalfiber(C)PBGguidancewhenthelightispropagatinginallsubregionsofthefiber;thiscanonlyoccurwhenliesintherangeβ<kn2,theunderlyingMechanismbeingaBraggPBG.PBGPCFVectoranalysisofPCFfiberStructuresofcrystalfiberTypicalHoneycombbasedPCFstructureAir-guidingPCFLowbendloss:unnoticeable@3mmradiusLowFresnelreflection:<10-4ReducednonlinearitiesPotentialultra-lowlosstransmissionStructuresofcrystalfiberStructuresofcrystalfiber1.7μmCoreHighlyNonlinearFiberFEATURES: -Smallmodefieldarea -Zerodispersioninthe visiblewavelengthrange -BendinginsensitiveAPPLICATIONS:?-Continuum generation -Four-wavemixing -Ramanamplification15μmCoreLargeModeAreaFiberFEATURES:Handlesveryhighpowerlevelswithoutnonlinearities-LowfiberlossAPPLICATIONS:-HighpowerdeliveryHighNumericalAperturePCFHighnumericalaperture(NA):upto0.7LargecoreareaLownonliearitiesDoubleCladdingPCFExtremelyhighNAforthepumpcore/innercladding.Largemodeareaforsignalmodesignal:highpowerdelivery,lownonlinearity,andagoodoverlapbetweenpumpingandsignalarea(highpumpefficiency)HighlyNonlinearPolarizationMaintainingFiberFEATURES:-PolarizationMaintaining -Smallmodefieldarea -Zerodispersioninthe visiblewavelengthrange -Bendinginsensitive -Continuumgeneration-Four-wavemixing-RamanamplificationAPPLICATIONS:EndlesslySingle-ModeFiberEndlesslysingle-modelargemodeareaPCFcanhandleupto20timesmorepowerthanconventionalfiberandismadeentirelyfromun-dopedsilicaglass.EndlesslySingle-ModeFiber(a)(b)ActualunitcellinthephotoniccrystalwithItscircularapproximation

VariationofVeffwithΛ/λforvariousrelativeholediametersd/Λ.ThedashedlinemarksVeff=2.405,thecutoffVvalueforastep-ndexfiberChromaticDispersionAnomalousdispersionSupercontinuumGenerationSupercontinuumgenerationina75cmlengthofPCF.Thefiberispumpedwith100fs,680nmpulse.Thepulseenergyis~1nJ.Lossproperties3.2dB/kmat1550nm7.1dB/kmat850nm2kmlengthfiberΛ=2.26μmd=1.51μmd/Λ=0.67Macro-bendinglosspropertiesHighlybirefringentpropertiesBeatlength=0.4mmAtwavelength1540nmFabricationofcrystalfiberFabricationofPCF,likeinconventionalfiberfabrication,startswithafiberpreform.PCFpreformsareformedbystackinganumberofcapillarysilicatubesandrodstoformthedesiredair/silicastructure.FabricationofcrystalfiberThiswayofcreatingthepreformallowsahighlevelofdesignflexibilityasboththecoresizeandshapeaswellastheindexprothecladdingregioncanbecontrolled.Thisisveryusefulforfabricationofe.g.polarizationmaintainingfiberswithhighlyasymmetriccoreregions,wheremultipleofthecapillarytubesisreplacedwithsolidsilicarods.FabricationofcrystalfiberWhenthedesiredpreformisconstructed,itisdrawntoafiberinaconventionalhigh-temperaturedrawingtowerandhair-thinphotoniccrystalfibersarereadilyproducedinkilometerlengths.Throughcarefulprocesscontrol,theairholesretaintheirarrangementallthroughthedrawingprocessandevenfiberswithverycomplexdesignsandhighairfillingfractioncanbeproduced.FabricationofPCFFabricationofcrystalfiber?Finally,thefibersarecoatedtoprovideaprotectivestandardjacketthatallowsrobusthandlingofthefibers.Thefinalfibersarecomparabletostandardfiberinbothrobustnessandsizeandcanbebothstripedandcleavedusingstandardtools.

ApplicationsofPCF

1.

Fiberdeliveryofveryhigh-powerlight,single-modefromUVtoinfrared;2.

Dispersioncompensation;3.

Whitelight(supercontinuum)sources;4.

Wavelengthconverters;5.

Hollowtransmissionfibers;6.

Multi-corefibercouplers;7.Pulseshapers;ApplicationsofPCF8.

Chemicalsensorswithlonginteractionlengths;9.

Temperature-insensitivePMpigtails