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3Light propagation with ultralarge modal areas in optical fibers

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June15,2006/Vol.31,No.12/OPTICSLETTERS1797
Lightpropagationwithultralargemodalareasin
opticalfibers
S.Ramachandran,J.W.Nicholson,S.Ghalmi,M.F.Yan,P.Wisk,E.Monberg,andF.V.Dimarcello
OFSLaboratories,25SchoolhouseRoad,Somerset,NewJersey08873
ReceivedJanuary26,2006;revisedMarch6,2006;acceptedMarch23,2006;postedMarch31,2006(Doc.ID67485Wedemonstraterobustsingle-transverse-modelightpropagationinhigher-ordermodesofafiber,withef-fectiveareaAeffrangingfrom2100to3200␮m2.Thesemodesareaccessedusinglong-periodfibergratingsthatenablehigher-order-modeexcitationoverabandwidthof94mmwithgreaterthan99%ofthelightinthedesiredmode.Thefiberisdesignedsuchthattheeffectiveindexseparationbetweenmodesisalwayslarge,henceminimizingin-fibermodemixingandenablinglightpropagationoverlengthsaslargeas12m,withbendsdownto4.5cmradii.Themodalstabilityincreaseswithmodeorder,suggestingthatAeffofthisplatformissubstantiallyscalable.©2006OpticalSocietyofAmericaOCIScodes:060.2280,060.2400,140.3510.
Recentinterestinhigh-powerfiberlasersandampli-fiershasdriventhequesttoachievelarge-mode-area(LMAopticalfibersthatofferrobustsingle-modeop-eration.ThestraightforwardandconventionalmeanstoachieveLMAfibersistoscalethefiberdimensions,butextendingsuchanapproachpasteffectiveareas͑Aeff͒ofϳ800␮m2yieldsmultimodefibers1thataresusceptibletolossandnoiseduetomodecoupling.2Hole-assisted,photoniccrystalfibers(PCFsoffersomeadditionaldesignflexibilitybyselectivelyleak-inghigher-ordermodes(HOMs,3butthisapproachsuffersfromthesamelimitationsasconventionalfi-bers,andachievableAeffiscurrentlylimitedtoϳ1400␮m2.AvariantofPCFs,arigidglassrod,hasgainedmuchrecentattention,sinceastraightlightguidecanclearlyaffordonescalingofAeffwithlowsusceptibilitytomodecoupling.4However,suchstructuresnegatemanyadvantagesofflexiblefibers,rangingfromlong-lengthdevicesthatenablehigh-dispersionpulsestretchers/compressorstoeaseofpackaging.Air-guidedphotonicbandgapfibersmaybeapromisingalternative,5sincethesignaltravelsinairwithnegligiblenonlinearities,butairguidancenegatesthepossibilityofconstructingadistributedamplifierbyincorporatingrare-earthdopants.
Here,wedemonstrateanovelplatform,usinganintentionallymultimodefiberwherethesignalisse-lectivelyexcitedinasinglehigher-orderspatialmode,toshowthatrobust(negligiblemodemixingandloss,bend-resistantsignalpropagationcanbeachievedinrecordlargemodeareas.Ourresultsin-dicatethatsignalscanbepropagatedwithveryhighspatialcoherenceeveninhighlymultimodestruc-tures,andthisliftsthefundamentalrestrictiononscalingfiberstoguidelightinincreasinglylargeAeff.WeillustratethiswithafiberdevicewithAeffrang-ingfrom2100to3200␮m2thatisrobusttobendingdowntoradiiofcurvatureof4.5cm.
FortheextremeAeffvaluesdesiredforhigh-powerfiberlasers,conventionalfibersareslightlymulti-modeeventhoughtheyaredesignedforsignalpropa-gationinthelowest-orderfundamentalmode(theso-calledLP01mode.ThisisbecauseincreasingthecoresizetoachieveAeffϾ400␮m2necessarilyleadstoamultimodefiber.ThestabilityoftheseLMAfibersis
0146-9592/06/121797-3/$15.00
governedbytheextenttowhichrandom,distributed,resonantmodemixingbetweenthedesiredmodeanditsnearestantisymmetricmode(LP1mmode,wheremistheradialmode-ordercanbesuppressed.2Thissuppressionincreaseswiththepurityoflaunchintothedesiredmodeaswellasthedifferencebetweentheeffectiveindices͑neff͒ofthetwomodes.Theblacklineintheplot(Fig.1illustratesthetrade-offbe-tweenstability(denotedbyn0m−n1mandAefffortheLP01modeofconventionalfibers.ConventionalLMAfibersarelimitedtoAeffϳ800␮m2,becauselargerAeffyieldlowenoughn01−n11valuesthatmodecou-plingbecomesprohibitivelyhigh.Thedashedlinesintheplotdepictthisdemarcation:whileactualvaluesforn01−n11maydiffersomewhat,basedonexperi-mentalconditions,wemayusethislineasaproxyfordistinguishingdesignsthatarerobusttomodecou-plingfromdesignsthataresusceptibletoit.AlsoshownisadatapointdenotedPCF,whichillustratesthelargestAeff͑ϳ1400␮m2͒reportedinPCFs.WhilethedifferenceinneffversusAefftrade-offissimilartotheconventionalcase,PCFscanbedesignedwithlargedifferentialmodallosses.Thisenablesradiat-
Fig.1.Effectiveindexdifferencebetweennearestneigh-bors(stabilityproxyversusAeff.Modestabilityincreaseswithmodalorder.Top,near-fieldimagesafterϾ2mpropa-gationwith7cmbendsofLPG-excitedHOMswithAeffrangingfrom2100to3200␮m2.©2006OpticalSocietyofAmerica

1798OPTICSLETTERS/Vol.31,No.12/June15,2006
Fig.2.(ColoronlineCharacteristicsofHOMfiber.Thehorizontalandverticalscalesoftheimagesandthehori-zontalscalesoftheplotsareidentical.(aNear-fieldimageofafiberfacet,showing86␮minnercladding.(bRefractive-indexprofileoftheHOMfiber,withacoresimi-lartoSMFand86␮minnercladdingfollowedbyadown-dopedoutertrench.(cNear-fieldimageoftheLPafter12mpropagationwith4.5cm07modeat1600nmradiusbends.(dIntensitylinescanof(candtheoreticalprofile:Aeffϳ2100␮m2.
ingouttheLPattheoutput.Hence11mode,yieldinghighermodalpuritythesefibersrelaxtheconstraintonconventionalfibersandcanofferstableoperationforcaseswithsignificantlylowernNevertheless,itisevidentthatconventional01−n11values.orpho-toniccrystalLMAfibersareinherentlylimitedbythetrade-offbetweenstabilityandAIncontrast,operatingintheeff.
HOMpresentsauniquedesignspacetoscaleAeff.ThecoloredcurvesinFig.1showthestability͑ndifferentLP0m−n1denoting1m͒versusHOMsAeffforfour0mmodes(mϾinaspeciallydesigned,intentionallymultimodefiber[indexprofileshowninFig.2(b].WhiletheyexhibitastabilityversusALPefftrade-offasdotheconventional01modes,theydramaticallydifferontwoaccounts.First,then0m−n1mvaluesforHOMsareanorderofmagnitudehigherthanthosefortheLPdicatingtheabilitytoobtainstable,mode-mixing-01mode,in-freesignalpropagationwithsignificantlylargerAimportant,theneff.More0m−n1mvaluesincreasewithmodalorderm,indicatingthatthisconceptissub-stantiallyscalable.Thisisahighlycounterintuitiveresultthatchallengestheconventionalwisdomthatfibersmustbesinglemodeforrobustsignalpropaga-tion.However,theresultsinthisplot,combinedwithanin-fibergratingdesignedtoselectivelycoupletoonlythedesiredmode,dramaticallyopenupthisde-signspace.ThemodeimagesshowninFig.1areex-perimentallyrecordednear-fieldimagesofthegrating-excitedLPaHOM04,LPfiber,05,LPwith06,andLPA07modes,re-spectively,intheLPeffrangingfromϳ2100␮m2(formode.Themode07modetoϳ3200␮m2(fortheLP04imageswereobtainedaf-terpropagationthroughmorethan2moffiber,withbendswitharadiusofcurvatureofatleast7cm.The
modeprofilesclearlyillustrateHOMpropagationwithveryhighmodalpurityandrepresentwhatwebelievetobethelargestdemonstratedAeffinfibersthatarebendresistant.
Figure2showsthedetailsofourfiberandoneoftheHOMs(theLP07mode.Thenear-fieldimageofthefiberfacet[Fig.2(a]andthecorrespondingre-fractiveindexoftheprofile[Fig.2(b]showthatthedesigncomprisesacoresimilartothoseofsingle-modefibers(SMFs,followedbyaninner-cladregionof86␮mdiameterandadowndopedprotectivetrench.Figure2(cshowstherecordednear-fieldim-ageofthegrating-excitedLP07modeafterϳ12mofpropagationat1600nm,andFig.1(dcomparesacorrespondingintensitylinescanwiththetheoreti-callypredictedmodeprofile.Themode-intensitypro-filesareusedtocalculateA/͐I2dA,yieldingeffofthemode,givenbyAeff=͑͐IdA͒22140␮m2forthesimu-lationand2075␮m2fortheexperiment.Theexcel-lentmatchbetweenexperimentandtheoryvalidatesthesimulationsshowninFig.1,onthebasisofwhichweclaimthatthisplatformisscalableinAwavelength-eff.Anat-tractivefeatureofthisplatformisitsagnosticnature.Simulationsrevealthatfor␭=1050nmAeffis1980␮m,whichisonly6%smallerthanthevalueat1600nm.Thisisbecause,unliketheLP01modeinaLMAcore,theHOMhasanegli-gibleevanescenttailpastitswaveguidingboundary—theinner-clad-to-trenchboundary.
Acriticalcomponentofthisdeviceisalong-periodfibergrating(LPG,whichexcitesthedesiredHOM,asshown-intheschematicinFig.3(a.ThesignalisfirstcoupledintotheSMF-likecoreoftheHOMfiber[seethefiberprofileinFig.2(b],suchcouplingcanbeachievedwithveryhighmodalpurityandlowlossusingconventionalsplices.Thereafter,thesignalisconvertedtothedesiredLP07modewitha2cmLPGwhoseconversionefficiency␩isshowninFig.3(b(␩Ͼ99%overa94nmbandwidth,withpeakϳwidths99.93%.␩areTheenabledextremebytheefficienciesdispersiveanddesignbroadofband-theLP07mode.6,7Theresonantnatureofthiscoupleren-suresthattheincomingsignaliscoupledonlytothedesiredLP07mode.Sincegratingsarereciprocalde-vices,anoutputLPGwouldconvertthesignalbacktoaGaussianshape.
Fig.3.(Coloronline(aDeviceschematic:lightiscoupledintoandoutofHOMwithLPGswhoseconversioneffi-ciencyisshownin(b.LPG,broadbandcouplingwitheffi-ciency␩Ͼ99%over94nm,withpeakcouplingashighas99.93%.(cAlternativeschematicforcharacterizingHOMfiber:thecleaveservestofoldthedevicepropagationpathsothatthesingleLPGactsasbothinputandoutputLPGs.X,splice;OSA,opticalspectrumanalyzer.

June15,2006/Vol.31,No.12/OPTICSLETTERS1799
Fig.4.(ColoronlineHOMpropagationcharacterizationin3mlongfiberasshowninFig.3(c.(aExcessbendloss(topandmode-mixingefficiency(bottomversusbendra-dius.(bNear-fieldimagesforbendradiiRforRϾ1=7cm,R=4.5cm,R7cm;there2aredistortions3=3.8cm.ThereisnochangeforRϽ4cm.ModaloutputisstabledowntoRϳ4.5cm.
WhilethedesiredoperationofthisdevicewouldutilizetheschematicinFig.3(a,characterizingtheperformanceofthedeviceisfacilitatedbyhavingac-cesstotheHOM;hence,formeasuringloss,modemixing,andmodaldistortions(describedbelow,weusetheequivalentschematicshowninFig.3(c.Thecleaveservestobackreflectthesignalthroughthede-vice,whichisreconvertedbytheinputLPGintotheLP01mode.Thisbackreflectedlightisthenroutedthroughthecirculatorforspectralandlossmeasure-ments.
Figure4(aisaplotoftheexcessbendloss(topandmode-mixinglevel(bottom;themode-mixinglevelshownindBindicatesthefractionoflightinun-wantedmodes,asafunctionofbendradius,mea-suredona3msegmentoftheHOMfiber.Themode-mixinglevelwasmeasuredbyrecordingtheamplitudeoffluctuationsinthetransmittedinten-sity;sincemodemixingleadstosimultaneouspropa-gationofseveralmodes,spectralinterferenceattheoutputenablesaccuratedeterminationoftheratioofpowerindifferentmodes.8ForbendradiiϾ7cmthesignalexperiencesimmeasurablylowbendlosses,andmode-mixinglevelsremainbelow−30dB(0.1%,consistentwiththefactthattheLPGhadϳ99.93%conversionefficiency.Thereafter,downtoabendra-diusofϳ4cm,thebendlossesaswellasmode-mixingamplitudesincreaseslowly,indicatingtheon-setofsmallamountsofloss/modecoupling.ForbendradiiϽ4cm,thelossesaswellasthemodecouplingincreaserapidly.Thisisconsistentwithnear-fieldimagesofthemodaloutputrecordedinthebentfiber.Figure4(bshowssuchimagesforbendsof7,4.5,and3.8cm,respectively.Whilemodalimagesforbendradiidownto4.5cmyieldapureLPfiberbenttoR07output,thatofthe3=3.8cmshowsdistortions,presumablyduetounwantedcouplingtootherHOMs.Thetotalinsertionlossofthisfibersche-matic,includinginputsplice,LPG,andpropagationintheHOMfiber,wasϽ0.2dB.
Onepotentialdrawbackofthisplatformisthatthesignaltravelsforashortdistanceinthe(smallerALPmode,whichispotentiallysusceptibletononlin-effearities.01Weexpectthisissuetoberesolvableforsev-eralreasons.First,totallength-scalesoverwhichthesignalresidesintheLP01modecanbesubcentimeter,sinceLPGswithlengthsasshortas0.5cmcaneasilyberealized(shortLPGswillyieldtheadditionalben-efitofgreaterbandwidth.Second,coreswithverylargeAefffortheLP01canbedesignedinthisfiber;thiscorecanbesubstantiallylargerthanthoseofconventionalLMAfibers,becauseonlycentimeterormillimeterpropagationlengthsarerequiredintheLP01mode.ThecombinationoflargeAtimeterlengthsfortheLPeffandsubcen-01modeshouldsubstan-tiallyminimizeanynonlinearitiesduetothem.Inaddition,foroutputpowerlevelsthatwillnotevenwithstandtheaforementionedcores,onecouldsim-plyoutputthemodeintheHOMandusefree-spacephaseplatestoconvertthemtoanydesiredoutputshape(includingGaussian;seeRef.9foranexampleofsuchdevices.ThisisfeasiblebecausetheHOMisstrictlyspatiallycoherent,andhencecanberelayedthroughlensesorspatiallytransformedwithdiffractive-opticelements,infreespace.
Insummary,wehaveshownthatthehigher-ordermodesinafiberofferorders-of-magnitudehigherde-signflexibilityforobtainingsignalpropagationinul-tralargemodalareasinafiber.Ourdemonstrationofstable,bend-resistant,long-lengthsignalpropaga-tioninmodalareasrangingfrom2100to3200␮m2representsanimprovementbyafactorof2to4overAeffofalternativefibersthatalsoofferrobustbend-resistantlightpropagation.Moreimportantly,thisconceptappearstooffersubstantialscalabilityinachievableAincreaseswitheff,becausethemodestabilityactuallymodeorder.
ThisworkwasperformedunderthesupportoftheU.S.DepartmentofCommerce,NationalInstituteofStandardsandTechnology,AdvancedTechnologyProgram,CooperativeAgreementNumber70NANB4H3035.S.Ramachandran’se-mailaddressissidr@ieee.org.References
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4.J.Limpert,N.Deguil-Robin,I.Manek-Hönninger,F.Salin,F.Röser,A.Liem,T.Schreiber,S.Nolte,H.Zellmer,A.Tünnermann,J.Broeng,A.Petersson,andC.Jakobsen,Opt.Express13,1055(2005.
5.J.Limpert,T.Schreiber,S.Nolte,H.Zellmer,andA.Tünnermann,Opt.Express11,3332(2003.
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