[doc格式] 基于稀释波导的InP衬底上高耦合效率、低偏振敏感度1．55μm波长光纤一波导耦合器

[doc格式] 基于稀释波导的InP衬底上高耦合效率、低偏振敏感度1．55μm波长光纤一波导耦合器 基于稀释波导的InP衬底上高耦合效率、低 偏振敏感度1(55μm波长光纤一波导耦合 器 第29卷第1期 2008年1月 半导体 JOURNALOFSEMICoNDUCToRS Vo1.29No.1 Jan.,2008 AHigh--EfficiencyFiber-to?WaveguideCouplerwithLowPolarization DependenceUsingaDilutedWaveguideinInPSubstrate witha1.55mWavelength ZhangYun,Zu0Yuhua+,Gu0Jianchuan,DingWuchang,ChengBuwen, YuJinzh0ng,andWangQiming (StateKeyLaboratoryofIntegratedOptoelectronics,InstituteofSemiconductors,ChineseAcademyofSciences,Beifing100083,China) Abstract..Weproposeafiber—to—waveguidecouplerforside—illuminate dP-i-nphotodiodestoobtainhighresponsivityand lowpolarizationdependencethatisgrownonInPsubstrateandissuitableforsurfacehybridintegrationinlowcostmod- ules.Thefiber.to.waveguidecouplerisbasedonadilutedwaveguide,whichiscomposedoftenperiodsofundoped120nm InP/80nmInGaAsP(1.05”mbandgap)multiplelayers.Usingthesemi-vecto rialthreedimensionalbeampropagation method(BPM)withthecentraldifferencescheme,thecouplingefficiencyoffiber.to.waveguideunderdifferentcondi— tionsissimulatedandstudied.andtheoptimizedconditioasforfiber.to.waveguidecouplingareobtained.ForTE—likeand TM.1ikemodes,thecalculatedmaximumcouplingefficiencyishigherthan94%and92%,respectively.Thecalculatedpo- larizationdependenceislessthan0.1dB,showinggoodpolarizationindeDendence. Keywords:dilutedwaveguide;BPM;fiber-to—waveguide;waveguidephot odiode PACC:4281MEEACC:4130 CLCnumber:0472.3Documentcode:AArticleID:0253.4177(2008)01.0055—08 1Introduction Comparedwiththesurface..illuminatedphotodi.. odes,side.illuminatedphotodiodeshaveaspecialad. vantage:thereisnotradeoffbetweenquantumeffi. ciencyandbandwidth.Thismeansthattheycanover. comethetradeofflimitationwiththeside.illuminated photodiodestoobtainhighresponsivityandhigh bandwidthatthesametime.Waveguidephotodiodes withanexternalquantumefficiencyofgreaterthan 80%and3dBbandwidthofgreaterthan50GHz. whichissideilluminated.havebeenreportedCl1. The mainproblemofsuchdetectorsiscouplingthelight fromafibertothedetectorswithhighefficiencyand lowpolarizationdependenceL.Agreatdealofstruc. tureshavebeenproposedandfabricatedsuchasta. pers3_andgratingcouplers[.Usingtheseapproa— ches,theside—illuminatedphotodiodesmaygainhigh responsivity,butattheexpenseofcomplicatingfabri— cationL5j.Dilutedwaveguideswithdifferentepitaxial layershavebeenadoptedasthefiber..to..waveguide couplerintheevanescentlycoupledside.illuminated photodiodesandwaveguidep—i—nphotodiodes[1『5,... Adilutedwaveguidecoupler,composedoftenperiods ofundoped100nm/80nmInP/InGaAsP(Q1.1/.tm), withacouplingefficiencyofmorethan82%andpo. 1arizationdependenceoflessthan0.5dBhasbeenre. alized[引.Recently.acouplingefficiencyofhigher than90%foradilutedwaveguidecouplercomposed ofsevenInGaAsP(Q1.07~tm)layerswith50,80,110, 140,170,200,and580nmthicknesses,interspersedbe. tweenthe150nm.thickInPlayer,withapolarization dependencelessthan0.8dBhasbeendemonstra— ted.Ourapproachusestenperiodsofundoped 120nm/80nmInP/InGaAsP(Q1.05~,m)planardilu— tedwaveguideasthefiber.to.waveguidecoupler.In thispaper,thesimulationandoptimizationofthe coupleraredescribedindetail.notonlyforthedilu— tedwaveguide.butalsoforthelensedfiber.TheBPM algorithmisintroduced,andmathematicalformula— tionsforthefullandsemivectorBPMareestablished anddiscussed.Themainequationsforthesemi.vector BPMintheformofstandardalternatingdirection method(ADI)basedonCrank.Nicholsonschemeare derived.Weexplaintheoreticallywhyadiluted waveguideischosenasthefiber.to..waveguideCOU-. pier.Usingtheimaginarydistancesemi—vectorBPM, thewholemodesofdilutedwaveguidewithdifferent widthsarecalculated.Thecouplingefficiencyoffi— ber..to..waveguideatdifferentconditionsissimulated andtheoptimizedconditionsforfiber..to-.waveguide couplingareobtained. *ProjectsupportedbytheNationalHighTechnologyResearch&Devel opmentProgramofChina tCorrespondingauthor.Email:yhzuo@red.semi.ac.en Received9July2007,revisedmanuscriptreceived21August2007 (No.2006CB302802) ?2008ChineseInstituteofElectronics 56半导体第29卷 2TheBPMalgorithm torwaveequationsinuniformstructures[11]: j鲁?(1) j..--.2-r=yyEy+AE E={0l1×(nE)]+ 等E+(HH} E={8l1×旦3y(nE)]+ AEy E 竺E+(nzdx’ H:)kE 1 2k{旦3x[去×旦oynoo\LH. 1 2k {立Oy[嘉×旦3xnooILHnEy)I- nE)I— J 爵) 静} (2) k0isthewavenumberinfreespaceandtz0isacon— AE一{ stant,chosenasareferencerefractiveindex. Equation(1)showsthatthetransverseelectric fieldcomponentsarepolarization?dependentandCOU— piedwitheachother.InEq.(2),theoperatorsA andAwaccountforpolarizationdependencedueto differentboundaryconditionsatinterfaces,andde— scribesucheffectsasdifferentpropagationconstants, fielddistribution,etc.forTEandTMmode.Theoff- diagonaltermsAyandA”accountforpolarization couplingandhybridmodesduetogeometriceffects, suchasthoseirregulargeometricshapesinthecross- sectionalstructure,andthematerialanisotropy.The epitaxialstructureofthedilutedwaveguidepresented hereisaregularshapeforisotropymaterials,thusthe couplingsbetweenthetwopolarizationsarequite weakinpropagation.Theoff-diagonaltermsAand Acanbeneglected,transformingEq.(1)into: 尝=,鲁:(3) Thisisthesemi.vectorBPMandispreciseenoughfor thedilutedwaveguide. Withthefinite-differenceapproachbasedonthe centraldifferencescheme,alsothewell—known Crank.Nicholsonscheme.xmA,Y=nAyandz lAz.Equation(3)canbediscretizedinthefollowing fOrms[12l: 丁+1.E(m+1,n)一E2一R+l.二垦竺=!13墨!丝?三竺:!!墨二! (Ax) )二丝+En2(m,)一2.2m}(?v)一…J + whereTandRarethetransmissionandreflectioncoefficientsacrosstheindexi nterfacesbetweenmAxand m+?’whcharedefined . as : . }__,尺.:.一一万一 Ey=一jJ 2,lokol T.+lEy(m,n+二E二墨竺!:二垦竺!!=]墨!?!竺!=墨!竺二 (?y) E(+1,n)一2E(m,n)+Ey(m一1, (Ax)+En2(m,n,,)一n.2J.2E(m,n)j + andsoweobtainthefollowingequation: , (1+jAzaA)E=[1一jAz(1一a)A]E,, (1+j?ZaA)E=E1一jAZ(1一a)A]E whereparameter口isintroducedtocontroltheschemesforsolvingthefinitedifferenceequations.T hediscrete formulaforthemagneticfieldcomponentshavebeenderivedandcanbealsofo undinRef.E11].Thesystemof equationsbasedontheCrank.Nicholsonapproachisnottridiagonal,andrequi resO(?.N;))operationsto solve.ThehelDofalternationdirectionimplicit(ADDmethodc.]allowsthe3 Dproblemtobesolvedwithopti- mal0(N?N)efficiencyE 引.TheequationsofthestandardADIschemeareasfollows: where 一 {+1.E(m+1,n)一[2一R+1.一尺一1(Ax)]E(rn,n)+=.墨二: (5) 第1期ZhangYuneta1.:AHigh?EfficiencyFiber—to—WaveguideCouplerwithLo wPolarizationDependence…57 AE +m,)一]kE(,)I E(m,/-/+1)一2E(m,/-/)+E(m,/-/一1) ByE一{ BxE1jJ 2/-/ojCo\ (Ay). 丁,+lE(m,/-/+1)一[2一R +[z(m,,f)一.2J,c.zE(,)} 二!!:!璺?三竺,!=墨!竺二 (Ay). +[z(m,,f)一o2,(.Ey(,)} . E .... y.... (.... m ......... + ........ 1 ..... , .... n ...... )...... - ........ 2.——,. E....... y.——, (..... m ——— , — n — )— + —— Ey(m-1,n) (Ax). addinghigherorderterms(等).Aand BBinEq.(5),wefind: (譬)× (一等A)(一等A)E” = (1+)(1+等A)? (一等B)(一等B)E州 :/1+, ?z 2 Then,weobtaintwotridi standardADIform: + 等B)E agonalequationsofthe f(一譬A)E{=(+A,)E l(一等A)E州:(+等)吉… f1一等B)E=(+等曰,)E l(一等A)E=(+等A)E{ Employingfulltransparentboundarycoil【ditions (TBC)asdescribedinRefs.[15,16],wewillgetthe numerica】resultsofthedilutedwaveguide. 3Waveguidestructureandmodesimula— tion Thedilutedwaveguide,alsocalledafiber—to— waveguidecoupler,isakindofwaveguidecomposed ofmultipleInP/InGaAsP/InPwaveguideswithweak opticalconfinement,aspresentedinFig.1.Theelec- tromagneticfieldsinthedilutedwaveguideare(E, H,H:)and(H,E,E:)forTEandTMmode, Fig.1Schematicofcrosssectionforwaveguidestructureofthe dilutedwaveguide,grownonasemi?insulatingInPsubstrate,with aperiodofNd1andd2standforthethicknessofInGaAsP andInPrespectively. +f)一]kE(,)} respectively.Indexdistributionisquitedifferentalong thex.directionandthey-direction.Inthex-direc- tion.indexdistributionisuniformandinthey-direc- tion,indexdistributionisperiodica1.InasingleInP/ InGaAsP/InPplanewaveguide,theboundarycondi- tionsfortheelectricfieldcomponentsofTEandTM modeinthe.Yplanearesodifferentthattheoptical fieldsdistributions(electriccomponent)aresignifi- cantlydifferent.Thecouplingefficiencyoffiber—to- waveguideisdecidedbytheoverlapintegralbetween thenormalizedopticalfieldofasinglemodefiber (x,Y)andthenormalizedopticalfieldofwaveguide 玎(,y): I,I2 = ?…(,y)(,y)dxdyl(8) whereiandfaretheordersofmodesinwaveguidein thex.andy-directions,respectively.Asaresult,the polarizationdependencephenomenonoffiber--to-- waveguidecouplingappears.But,inadiluted waveguide,whichiscomposedofmultipleInP/In— GaAsP/InPwaveguides,theguidemodesareformed bystrongcouplingbetweentheopticalfieldsinindi— vidua1waveguides.ForTEmode,althoughtheelectric fieldcomponentisalongthex.directionwithuniform indexdistribution,duetothethinInPseparatelayers, therearestrongevanescentfieldsoftheEcompo— nentinthey—direction.Therefore,thecouplingbe— tweentheEcomponentfieldoccursandformsthe TEmodeofthedilutedwaveguide.ForTMmode,the electricfieldcomponent,whichisperpendicularto theepitaxialgrowthdirection,isalongthey-direction withastep.1ikerefractiveindexdistribution.and thereforetheevanescentfieldcouplingismuchstron- gerthaninTEmode. Theoptica1fieldsoftheguidemodesinthedilu— tedwaveguidewerecalculatedwiththeimaginarydis- tanceBPM(ID.BPM)[17--i9].Weignoredtheimagi. narypartoftherefractiveindicesandsetthemtobe 3.146forInPand3.28forIn088Ga012As026P074 (Q1.05)[2oatthewavelengthof1.55um.Wecan chooseasetofGaussianfunctions(x,Y)El7]asthe eigenfunctiOnstoexpandthemodesofthediluted waveguidesasfollows,gti(,Y,o)c(,y), 58半导体第29卷 VerticaldirectionY/um Verticaldirectiony/pan 卷 言 量 Fig.2DistributionofTEfundamentalmodefield(a)andTM fundamentalmodefield(b)inthedilutedwaveguidewithten periodsof120nm/80nmInGaAsP(Q1.05/~m)/InP where(,Y,0)istheincidentfieldtoexciteguide modes.Thepropagationcanbeexpressedas(,Y, z):,asthenameimplies,the longitudinalcoordinatezisreplacedbyImziz,and sothepropagationalongtheimaginaryaxisshould follow(,Y,Imz)=c(,),).Since thefundamentalmodehasthehighestpropagation constantbydefinition,thefundamentalmodealways dominatesafterasufficientlylongpropagation,and thefundamentalmodepropagationconstantcanbe obtainedbythevariationaltypeexpression= — Ig— r* — [k— 2 o — n2 — (x— , — y)gr+— 3 — gr— /3— x — + — 3g — r/— 3y — ]d— xdy . Theca1.Jgrd xdY……, culationresultsoftheopticalfielddistributionofTE andTMfundamenta1modesbasedontheID—BPMare showninFig.2.Theyareofsimilarenvelopedespite smallvariationsduetoevanescentfieldcoupling. Thesesmallvariationshavelittleeffectonthecou. piingefficiencyandcanbeneglected.Thus,thefiber— to-?waveguidecouplerisoflowpolarizationdepend-? ence.Inaddition,the1/eopticalfieldisconfinedin thedilutedwaveguidewithtenperiodsofInP/In? GaAsP.UsinganorthogonalizationprocedureL2,we canobtainahigherordermodespropagationconstant andthenfindalltheguidedmodesofthediluted waveguide,asshowninFig.3.Thedilutedwaveguide hasathicknessofonly2/_tm,thusthereisonlyafun damenta1modeinthey-direction.Therefore,in ordersofTEmode OrdersofTMmode OrdersofTEmode Orde~ofTMmode Fig.3Calculatedopticalfieldsdistributionalong?direction withawidthof5Iim(a),(b)andlO,um(c),(d)forTEandTM modesrespectively Eq.(8),they-directionmode rection,thecalculatedoptical order=0.Inthe—di— fieldswithdifferentor. dersofmodesarepresentedinFig.3.Therearethree modeswhenthedilutedwaveguideisof5/_tmwidth forbothTEandTMmodes[Figs.3(a),3(b)],while withadilutedwaveguidewidthof10um,therearesix modesforTEandfiveforTMmodes[Figs.3(c),3(d)] respectivionYllxm Modesizeoffiber:Diameter/p~m Incidentpositionx/ixm IncidentpositionY/p~m Fig.4Calculatedfiber-to-waveguidecouplingefficiencieswithadilutedwaveguidewidthof5ttm(a),(b)Thecouplingefficiency varieswiththefibermodesizeD,withthecenterofincidentlightpositionbeing(0,1);(c),(d)Thecouplingefficiencyvarieswith theincidentpositioninthe-direction,withthecenterofincidentlightpositionbeing(,1),D:4;(e),(f)Thecouplingefficiency varieswiththeincidentpositioninthey-directionwhilethecenterofincidentlightpositionis(0,),D=4,forTEandTMmodes, respectivelyComparingthecouplingefficiencyofTEmodewithTMmode,thepolarizationdependenceissmallerthan0.1dB. greatinfluenceonfiber?-to?-waveguidecouplinginthe nextsection. 4Fiber-to-waveguidecoupling Inordertosimulatethecouplingofsinglemode fiber.to.waveguide,wechooseanopticalfieldwith 2 theGaussiandistribution,(,Y)e一(D/2)2e,as theinputsinglemodefibermodefieldtocalculatethe overlapintegralwiththemodesofdilutedwaveguide fromEq.(8),whereDisthemodesizeoftheoutput lightfromasinglemodefiber.Wecalculatethefiber— to:waveguidecouplingefficiencies,whichvarywith thediametersDandtheincidentpositioninthe. andy-direction,respectively,atthewidthsof5”m andlOumwithoutconsideringthereflectionofthe incidentfacet.Theresultsarerepresentedasfollows. Thedilutedwaveguidewithawidthof5umrea. chesthehighestcouplingefficiency(>94%)withthe modesizeof2.9umforTEmodeand3umforT’M mode,asshowninFigs.4(a)and4(b).Theodd modeshavenocontributiontothecouplingefficien. cy.becausetheopticalfieldoftheoddmodeiszeroin they-zplaneat:0.showninFig.3.Thecoupling efficiencyismainlydecidedbythefundamental mode.DHetothemultimodeinthe.direction.the couplingefficienciesofhigherordermodesvaryperi— odicallywiththeincidentposition.showninFigs.4 (c)and4(d),andthetotalcouplingefficiency,the summationoftheindividualmode’S,isquiteflatand 08【.!_普比?I【dIlou 口Q【.疆Q普云Il0u 0II910强比IIIIA0U II【.疆比IIII口Il0U A.口Q 【aveguidecouplingefficiencieswithadilutedwaveguidewidthof10um(a),(b)Thecouplingefficiency varieswiththefibermodesizeD,centeroftheincidentposition(0,1);(c),(d)Thecouplingefficiencyvarieswiththeincidentposi- tionin.direction,centeroftheincidentposition(,1),D4;(e),(f)Thecouplingefficiencyvarieswiththeincidentpositionin y-directioncenterofincidentposition(0,y),D4,forTEandTMmodes,respectivelyComparingthecouplingefficiencyofTE modewithTMmode,thepolarizationdependenceissmallerthan0.1dB. hasgoodincidenttoleranceinthex.direction.Inthe y-direction,thedilutedwaveguideisnotsymmetric andtheopticalfieldexpandstotheInPsubstrateto someextent,andthecenterpositionofthemodeisa. roundY0.8(seeFig.2).Thus?theoptimalpositionfor incidentisnotY=1butv=0.9forTEmodeandv=0.8 forTMmode,asshowninFigs.4(e)and4(f). Forthecouplingefficiencycurvesversusthefi— bermodesizeD,thecenterpositionofincident1ight xandYwhenthedilutedwaveguidewidthis10”m aresimilartothecurveswhenthewidthis5um.Be— causetherearemoremodesthanthewaveguidewith 5”mwidth,aspresentedinFig.3,thecouplingeffi- ciencyvaryingwithisnearlyconstantandtheCOU. piingefficienci