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Research on highly nonlinear photonic bandgap fibers

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Research on highly nonlinear photonic bandgap fibers

    Research on highly nonlinear photonic

    bandgap fibers

    OPTOELECTRONICSLETTERSVoI.

    2No.6.15Nov2006

    Researchonhighlynonlinearphotonicbandgapfibers

    FANGHong,LOUShu-qin,GUOTie-ying,LIHong-lei,YAOLei,andJIANShui.sheng Instituteoflightwavetechnology,Bei#ngJiaotongUniversity,Be0ing100044,China (Received30August2006)

    AnewtypeofhighlynonlinearphotonicbandgapfiberwithmodifiedhoneycombIatticeisbroughtforward.

    Basedol3fuII-vectorplane-wavemethod,thestructureofbandgapsandthedistributionsoftundamentaI

    modefieldareanalyzed.Thenitsnonlinearcoefficientiscalculated.andtheeffectofeachstructuraIpa.

    rameteronthenonlinearcoefficientisdiscussed.AtIast,consideringmanyfactorssynthetically,wemake

    someoptimizationdesignofthestructuraIparameters.Itcanbeconcludedthatthisnewtypeofphotonic

    bandgapfibercangainthenonIinearcoefficientof30Wkm_..

    CLCnumber:TN818Documentcode:AArticleID:1673.1905(2006)06.0412.04 Sincethefirstphotoniccrystalfiber(PCF)wasfabri.

    catedbyKnightJCandhiscolleaguesat1996,this

    typeoffibers,consistingofacentraldefectregionsur

    roundedbymultipleairholesrunningalongitslength,

    hasbeenthesubjectofmuchinterestbecauseofitsu

    niquepropertieswhicharenotrealizedinconventional

    opticalfibers[.

Forthedifferentapplications,thecoredefectofPBG

    FscanbeintroducedindifferentforlILForexample.the hollow-corePBGFshavethepotentialofprovidinglow- lOSSandlow-nonlinearwaveguidanceinai.whichcan beusedasthefibersfortransmittingveryhighpower light.However,thiskindoffibershassomedifficulties infabricationandsplicingwiththeconventionalfibers. Inaddition.forthePBGFswithhoneycombstructurein theircladding,acentralperiodicity-breakingairholecan beintroducedasthedefect[,,here,themostoflight poweristransmittedintheringsolidcore.anditiscon

    firmedthatthisfibercanbedesignedtohaveveryhigh nonlinearcoefficientandnoveldispersivecharacter.But theringforrnoffundamentaImodefieldbringssome obstaclefortheapplicationsofthisfiber.

    Inthisletter,anewtypeofhighlynonlinearphotonic bandgapfiberisbroughtforward.Basedonfull-vector plane-wavemethod,thestructureofbandgaps,thedis

    tributionsoffundamentalmodefieldandtheeffectof eachstructuralparameteronthenonlinearcoefficientare analyzedanddiscussed.Furthermore,consideringmany factorssynthetically,wemakesomeoptimizationdesign ofthestructuralparameters.

    Thefull-vectorplane-wavemethodisoneofthemost usefulmethodforanalyzingthecharactersofPCFs,as

    peciallyforPBGFs.anditshighdegreeofaccuracyand efficiencyhasbeenconfirmedinseveralpapersL. SupportedbytheNational863ProjectofChina(2004AA31G 200).

    E-mail:macrofang@263.net

Basedonbasicdeftnition,thenonlinearcoefficient7

    canbeexpressed[:

    y()2(,2)dzdy

    ((,2)dzdy)

    (1)

    where2isfreespacewavelength,Sistheareaofthefi

    ber'scrosssection,2(z,)isthedistributionofrefrac

    tiveindex,I(x,Y,)isnormalizedintensity.Thenonlin

    earrefractiveindex2isonlyrelatedtothematerial[10]:

    2.9×10(z,)?air

    2.76(z,)?SiOz

    2.76+0.0974X(mol)

    (z,)?Si02+Ge()2

    (2)

    whereXisthegermaniaconcentration.

    ThenormalizedintensityI(z,y,)isgivenbythe

    definitionofthePoyntingvectorasfollows:

    I(z,,)1_FE

    XH"

    where

    P一』

    s

    %L

    

    ?

    ]一沈[

    (3)

    ?

    ;:]dxdy=II~eVs]J

    (4)

    Andthen.themagneticfieldHandtheelectricfieldE canbecalculatedwiththefull-vectorplane-wavemethod mentionedpreviously.

    ThecrosssectionoftheproposedPBGFwithmodi- fiedhoneycomblatticeiSdepictedinFig.1,wherethe lightgrayandwhitecirclesexpressSi02andairholes, respectively.Andthedarkgraycirclesandblackcircles allexpresstheareawithdopedgermania,buttheger

    maniaconcentrationoftheblackcirclesincladdingis higherthanthatofthedarkgraycirclesinthecore.All /??????/,????l

    

    ,,

    W

    /

    2

    m

    ?

    

    O

    l

    ,

    ,,

    z

    ,

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     structuralparametersareshowninFig.1.andtheger

    maniaconcentrationoftheblackcirclesis1,thatofthe

darkgraycirclesis2,sol>2.Therefore,theeffec

    tiverefractiveindexofcladdingisbiggerthanthatof core,whichshowsthatthelight-confinementmechanism inthisfibermustbePBGeffect.

    :S,i02A/'pere.l

    隧】_1q?1

    ——

    啊】?L

    

    A

    ??_1一一一霜圈LJ?一J1lLJ

    _??J1

    H一】???lSl

    r1曩?—r一?一—??LL

    _

    d

    _Ir?lr

    _?圈[A

    .酮圈瞬L一瞬—?

    ,

    2

    1Schenmticdesignofhighlynonlinearphotonicbandgap fiher

    Akeyoffull-vectorplane-wavemethodischoosing therangeofsupercell,whichhasveryseriouseffecton thecalculationspeedandtheaccuracyofresults.Inthe stepofcalculatingPBGofcladding.thesmallestbasic cellofthecladdingstructureischosenastheSupercell1 inFig.1,whichisenoughtorecoverwholecladding structurewhenitisperiodicallyextended.However,in

    thestepofcalculatingdefectmode,muchlargerrange includingthecoreneedstobechosenastheSupercell2 inFig.1.Smallrangeofthesupercellmayinducethe modefielddisturbancebetweenthetwoneighbouring cores.

    Ontheassumptionthatgermaniaconcentrationofthe blackcircles1209/6,theeffectofotherstructuralpa

    rametersofcladdingonPBGiscalculatedandanalyzed. Therefractiveindexofgermaniadopedareacanbecal

    culatedbySellmeierformulac.

    Firstly,fixingd/A0.5anddd/A1,Fig.2(a)

    showstherelationshipbetweentheeffectiverefractive indexoftwobandgapsandnormalizedwavelengthfor differentvalueofA.Asseenfromthefigure,thethree curvesforA1.5btm,2.5btm,3.5btmareidentical, whichconfirmthatthedifferentvalueofAjustchange thewavelengthpositionofthePBG,ratherthanits shape.Thischaracterimpliesthatwecanadjustrelative dimensionofthefibertotunethepointofwidestP13G atanywavelengthaccordingtoourexpectation.Inaddi

    tion,wecanalsoseefromthefigure,thatthesecond PBGdisappearswhenthenormalizedwavelengthislar

    gerthan1.1,thatistosay,thefiberissingle-modeop

    erationinthisrange.becausethereareonlyfundamental modesnsidethefundamentalPBGasarule.

    Optooloctroo.Lett.Vol2No6?0413?

    Secondly,fixingA2.5tim,Fig.2(b)showsthe

    changeofthePBGswiththechangeofrelativediame

    tersofdopedcirclesinthecladdingdd7Aandairholes d/A.Asseenfromthefigure,whenthevalueofdd/A

    increases,theeffectiverefractiveindexofPBGsslightly increaseswiththesamestructuralshapes.Ontheother hand,whenthevalueofd/Aincreases.thePBGsiswid

    enedobviously,theeffectiverefractiveindexofPBGs decreases,andthewavelengthwherethesecondPBG disappearsmovestolongerwavelength.Therefore,when needingawiderPBG,wewoulddesignthestructuraI parameterswithlargerrelativediameterofairholes.but thecostmaybegivingupthecharacterofsingle-mode operation.

    ^/A

    ^/.4

    ?2Effectiveindexofphotonicbandgapedgesvel'SllSnot-. malizedwavelength(a)fordifferentpitchA,(b)fbdngpitch A,fordifferenta/Aand/A

    Thenwewillanalyzethedefectfundamentalmodesin thisfiber.ThestructuralparametersareA2.5ttm,/

    A0.5,dd/A1,d/A0.4,120mol,2

    15mo1.Fig.3showstheelectricalfielddistribution andeffectiverefractiveindexoftwodefectmodesinside thefundamentaIPIG,atthewavelengthof1.55

    ThedifferencebetweenthesetwovaluesofneffiStheor

    derof10.whichcanbeconsideredascomputinger

    ror.Moreover,asseenfromtheirdistributionofvector field.thesetwomodesareverysimilartotheHE11mode intheconventionalstep-indexfibers.So,wecanconsider

?

    0414?

    thesetwomodesastwopolarizationsofthefundamental

    modes.Inaddition,thedistributionofthesemodefieldis closetoGaussformastheconventionalstep-indexfi

    bers.Therefore,itispossibletoachievethemodefield matchwiti1alowsplicinglOSSwhensplicingthisPBGF withconventionalstep-indexfiber.

    Fig.3Electdcalfielddistributionof(a)x-polarizedfunda. mentalmodeand(b)y-polar/zedfundamentalmode Duetothestructurewithgermaniadopedsolidcore, theproposedPBGFshaveveryhighnonlinearcoeffi

    cient.Andasweknow,themodefieldareaisanimpor

    tantfactorthateffectsonnonlinearcoefficient,i.e.we candecreasethedimensionofPBGFsproportionally. whichcanbegainedbydecreasingthevalueofA,inor

    dertoenhancenonlinearcoefficient.Thisisthecommon characterinallfibers,andinthisletter,wefocusonthe effectofdopedareaandconcentrationinthecoreonthe nonlinearcoefficient.

    Fixingthestructuralparametersofcladding.A2.5

    ttm,d/A=O.5,dd/A=1,ml20mol,Fig.4(a)and

    (b)showtheeffectiverefractiveindexofPBGedges, fundamentalspacemode(FSM)andfundamentaldefect modeversuswavelength,withdifferentvaluesofd/A andm2.respectively.AsseenfromFig.4(a),effective refractiveindexofdefectmodeincreaseswiththein

    creaseofthed/A,andthecurvemovesclosetothe FSM-linegradually.Thereasonisthatthedifferencebe

    tweenthedefectcoreandperiodicstructureincladding 0ptoelectron.Lett.Vo1.2No6

    isreducedasthed/Aclosetothevalueofdd/A=1.As

thesamereason,whenincreasingthegermaniaconcen

    trationofdopedareainthecore2closetothatof dopedareainthecladdingm120%mol,thecurves

    moveupslightlyasseenfromFig.4(b).

    (um

    (um)

    Fig.4Effectiveindexofphotonicband~pedges,fundamental defectmodeandFSMw21"sllswavelength.(a)fixingm2=15% mol,fordifferent/a,(b)fixing/a=0.4,fordifferent Ge-dopedconcentrationinthecoleJ,l2

    Fig.5(a)and(b)showtheeffectofdopedareaand concentrationinthecoreonnonlinearcoefficientyand effectivemodefieldareaAH.Thesefiguresshowthat thenonlinearcoefficientincreaseswiththeincreaseof dopedareaandconcentration,andtheeffectivemode fieldareadecreaseswiththeincreaseofdopedareaand concentration.However,thechangingextentinducedby dopedconcentrationismuchsmallerthanthatbythe otherfactor.Thereasonisthatthechangeofrefractive indexinthecoreinducedbyincreasinggermaniaconcen

    trationisrathersinailrelativetotherefractiveindexin puresilicon.

    So,inordertoenhancethenonlinearcoefficientofthis PBGF,wehavethreemethods:first,decreasingthedi

    mensionofthefiberproportionally;second,increasing therelativedimensionofthedopedareainthecore; third,increasingthegermaniaconcentrationofthedoped areainthecore.Foreachmethod,therearesomeadvan- iill

电譬

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    dcfA

    

    %toolGe

    ?5(a)t~dngm2=15%moi,nonlinearcoefficientandef- fectivemodefieldareaversusdc/A,(b)ngddA=0.4, nonlinearcoefficientandeffectivemodefieldEweaversusGe- dopedconcentrationinthecotem2

    tagesanddisadvantagesforpractica1applications,sowe needtoconsiderallofthefactorssyntheticallywhende

    signingthestructureoffiber.Forthefirstmethod,the nonlinearcoefficientcanbelinearlytunedeasily.How

    ever,asweknowfromthepracticalexperience,drawing themicrostructurefiberwithverysmallpitchandhole sizeismuchmoredifficultthanthatwithrelativelarge pitchandholesize[.Ontheotherhand,thePBGF-S withverysmallcorehavesomedifficultiesinmodefield matchingwiththeconventionalfibers.Forthesecond andthirdmethods,thenonlinearcoefficientcanbetuned Optoelectron.Lett.Vo1.2No.6?0415?

    whilekeepingthestructuralparametersinvariable. However.ifthedopedareaandgermaniaconcentration inthecoreareclosetothatinthecladding,thecurvesof effectiverefractiveindexmoveuptotheFSM-lineas seenfromFig.4,i.e.theyareclosetotheedgeofPBG, leadingtoanincreaseofleakagelossofPBGFs.whichis verybadforpracticalapplications.Andaspreviousanal

    ysis,theeffectofdopedareainthecoreonthenonlinear

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