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Complete characterization of polarization-maintaining fibers using distributed polarization analysis

ZhihongLi1,2,X.SteveYao1,3, Xiaojun Chen3,HongxinChen3andZhuoMeng1,2

1PolarizationResearchCenter,CollegeofPrecisionInstrument&Opto-electronicsEngineeringandKeyLaboratory

ofOpto-electronicsInformationandTechnicalScience,MinistryofEducation,TianjinUniversity,Tianjin300072,China2SuzhouOpto-ringCo.Ltd,Suzhou215123,China

3GeneralPhotonicsCorporation,5228EdisonAve,Chino,CA91710,USA

corresponding coherence length should be much less than the differential groupdelayof thePM fiber under test), to avoidmeasurement fluctuations caused by coherent addition of the two orthogonalpolarizationcomponents inside the fiber. However,such a measurement system is cumbersome to set up, and its measurement accuracy is affected by the birefringence of the lenses and connectors, as well as by misalignment of the polarization of the light input to thePM fiber.CommerciallyavailablePERmeterscanbeused todirectlymeasure thePERofaPM fiber;however, theirmeasurementaccuraciesarestilllimitedby1) thepolarizationmisalignmentof lightat the inputendof thePM fiber under test (FUT); and2) thepolarizationmisalignments of the light source and its fiber pigtail; making the measurementofhighPERfiberscumbersomeanddecreasingtherepeatability of the measured results.

One or two of the four group birefringence related parameters, aswellasPER,canbemeasuredwithdifferentimplementationsofwhite light interferometry [3,8-11], spectral interferometry[12-14], thewavelengthsweeping technique[15], the transientBrillouingrating technique [16,17],Brillouinopticalcorrelation-domainreflectometry [18],and theopticalheterodynedetectiontechnique[19].Allof thesemethodsarecomplicated tosetupand require in-depth knowledge and experience to implement. Consequently, their practical use in the industry is limited.

Optical frequency-domainreflectometry (OFDR) tomeasure thelocalbirefringenceandPERofashortPMfiber taperhasbeenreported[20];however, itsability tocharacterizea long lengthofPMfiberwithalargenumberofcrosstalkpointsisyettobeproved.

We reported previously the use of a distributed polarizationcrosstalk analyzer (DPXA) to accuratelymeasure the thermalcoefficient[4]anddispersion[21]ofPMfibers’birefringence.Inthis paper, we demonstrate methods and processes to simplify the measurements and improve measurement accuracy, and to expand themeasurementcapabilitiesof theDPXAto includeallpolarization relatedparameters, includingPER(orh-parameter),group birefringence, group birefringence uniformity, group birefringence dispersion, and group birefringence thermal coefficient. Inparticular,we introduceasimplefixtureto inducea series of polarization crosstalk peaks of equal spacing to assist in themeasurements.Toenablesuchmethodsandprocesses,wedevise amechanism inside theDPXA (General PhotonicsPXA-1000) to specifically eliminate the ghost interferencepeakscausedbyzero-and2nd-orderinterferencesoflightfrompolarizationcrosstalkpoints[22],andthereforemakeitpossibleto obtain the true locations and strengths of a large number

AbstractWepresentmethodsandprocessesofusingaghost-peak-freedistributedpolarizationcrosstalkanalyzer (DPXA) toaccuratelyobtain all polarization related parameters of polarization-maintaining(PM)fibers.WeshowthatbyfirstinducingaseriesofequidistantperiodicpolarizationcrosstalkpeaksalongaPMfiber and then measuring the positions and the widths of these peaks using the analyzer, all birefringence-related parameters of thePMfiber, includinggroupbirefringence,groupbirefringencevariation along the fiber, group birefringence dispersion, and group birefringence temperature coefficient, can be accurately obtained.We further show that theDPXAhas the ability toidentify and eliminate polarization crosstalk contributions of connectors or splices in the measurement system and therefore can be used to obtain high accuracy measurement of the polarization extinction ratio (PER) of PM fibers. Finally,wepropose a set of parameters based on the distributed polarization analysis to quantitatively evaluate the quality of PM fibers.Webelieve that themethodsandprocessesdescribed in thispaper can be widely applied in the industry for the complete characterizationofPMopticalfibers.

IndexTerms—Polarization-maintaining fiber, ghost-peak-free,equidistant periodic polarization crosstalk, group birefringence, group birefringence dispersion.

I.IntroductionPOLARIZATION-MAINTAININGoptical fibers,whichuseahighinternal birefringence that greatly exceeds perturbing birefringence effects to maintain a linear polarization along the fiber, are important to fiber optic communications and fiber optic sensors, particularly fiberopticgyroscopes.ThepolarizationmaintainingabilityofaPMfiberisgenerallycharacterizedbyitspolarizationextinctionratio(PER)orh-parameter(PERperunitlength),whilethe fundamentalparametergoverning theperformanceofaPMfiberisactuallyitsgroupbirefringence.Therefore,itisimportantformanufacturersandusersofPMfibers toknownotonly thePERof a fiber,but also itsgroupbirefringenceandall othergroup birefringence related parameters, including the variation in group birefringencewithwavelength (group birefringencedispersion[1,2]),with temperature(groupbirefringencethermalcoefficient [3,4]), and along the fiber (group birefringenceuniformity[5]).

ThePERorh-parameterofaPMfibercanbemeasuredwithapolarizationcross talkmethodspecified instandardsTIA-544-193andTIA-544-192 [6,7],where the3-dBspectralwidthofthe lightsource is required tobegreater than10nm(or the

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of polarization crosstalk points along the PM fiberwithoutambiguity. As will be shown below, the combination of the fixture and ghost-peak elimination simplifies the measurement process and reduces many potential measurement errors; it therefore assures accurate measurement results even by minimally trained personnel.Furthermore,weshowthat theDPXAcanreadilybeused to identify polarization crosstalk induced by the connectors and splices in the measurement setup, and therefore eliminate theircontributionstothetotalPERofaPMfiberundertest(FUT),resulting in more accurate measurement results without the need for careful polarization alignment of light at the input and output endsofthePMfiberundertest(FUT).Finally,weproposeasetofmeasurementparametersobtainedbyaDPXAtoquantifytheperformanceofaPM fiber,with testexamplesofdifferentPMfibers.Webelievethat themethodsandprocessesdescribed inthis paper can be widely applied in the industry for the complete characterizationofPM fibers, especially considering that theghost-peak-freeDPXA isbecomingcommerciallyavailablewiththeeffortsofsomeoftheauthors[23].

II.BasicconfigurationofDPXAFig.1illustratesabasicconfigurationforadistributedpolarizationcrosstalkanalyzer (DPXA)[4,21].Apolarizedsuperluminescentdiodesource (SLED)at1310nmwithaveryshortcoherencelength(~25µm,correspondingtoa3-dBGaussianlinewidthof30nm)iscoupledintotheslowaxisofaPMfiberundertest(FUT)(pointAofinsetinFig.1).AssumeatpointB,somepolarizationcrosstalk is induced by an external disturbance, causing some lighttobecoupledintothefastaxisofthePMfiberwithacouplingcoefficient parameter h = I1/I2 , where I1 and I2 are the light intensitiesinthefastandslowaxesofthePMfiber,respectively.Becausethepolarizedlightalignedtothefastaxistravelsfasterthan that aligned to the slow axis, at the output of the fiber, the faster light component will be ahead of the slow component by △Z＝△nZ, where △Z is an optical path length difference, △n isagroupbirefringenceof thePM fiberandZ is the fiberlengthbetweenthepointwherethecrosstalkoccurs(B)andtheoutputend(pointC).Apolarizerorientedat45°totheslowaxisof thePMFUTwasplacedat theendof the fiber.Polarizationcomponents from both slow and fast axes were projected onto the same direction - the linear polarizer axis - so as to produce an interference pattern between the two components in a scanningMichelsoninterferometer.Whentherelativeopticalpathlength is scanned, an interference peak appears when the two polarization components overlap in space but disappears when they are separated by more than the coherence length of the light source (i.e.SLED).Thegroupbirefringence△n of thePMFUTbetweenpositionsBandCcanthenbecalculatedasfollows:

△n＝△Z/Z (1)

ItisevidentfromEq.(1)thattheaccuracyof△n depends on the measurement accuracies of both △Z and Z.

NotethattheillustrationinFig.1assumesonlyonepolarizationcrosstalkpointalong the fiber. If therearemultiplepolarizationcrosstalk points, second order interference peaks will occur. Thatis,thelightinthefastaxisresultingfromthecouplingatacrosstalk point will couple back to the slow axis at subsequent crosstalkpoints furtherdown the fiber.Asshown in Fig.2a,consider a situation where there are three coupling points X1, X2,

and X3alongthePMfiber,andthelightinputtothePMfiberispolarizedalong theslowaxisof thePMfiber,withno fastaxiscomponent. At each coupling point, light is coupled not only from the polarization mode along the slow axis to the polarization mode along the fast axis, but also from the polarization mode along the fast axis to the polarization mode along the slow axis. As a result of this coupling, the resulting wave packet series outputbythePMfiber includewavepacketscausedbymultiplecouplings.AsshowninFig.2b,fourwavepackets,includingzeroorder coupling S0 (nocoupling)andsecondordercouplingsS12, S23and S13 emerging at the output are aligned to the slow axis of thePMfiber,andthreemainwavepacketsf1 , f2and f3 emerging attheoutputarealignedtothefastaxisofthePMfiber,wherethey are generated by coupling from the slow axis to the fast axis (firstordercoupling)atpointsX1 , X2 and X3, respectively.

Fig.1. Illustrationofaghost-peak-freedistributedpolarizationcrosstalk analyzer using a scanningwhite lightMichelsoninterferometer.The insetshowsthedelayrelationbetween theoriginalandcrosstalkcomponents.Lightwithashortcoherencelength travelling in the fiber is polarized along its slow axis at inputpointA.CrosstalkisinducedbyastressatpointBwherea small portion of light is coupled into the fiber’s fast axis. A relative delay at the output point C between the two polarization components is △Z.The locationZofcrosstalkpointBcanbeobtained from a measurement of △Z.FRM,MDL,PD,andDAQareFaradayrotatormirror,MotorizedDelayLine,photodetector,and data acquisition card, respectively.

After passing through the 45 degree oriented polarizer, the wave packets aligned to the slow and fast axes were projected onto the same direction - the linear polarizer axis, as shown in Fig.2c.When thismixed light is input to the interferometer,a series of interference peaks can be observed as the delay in onearmof the interferometer ischanged. In thesimplewhitelight interferometers described in [10,11,24], these secondorder couplings cause ghost crosstalk peaks which result in ambiguity.AsshowninFig.1,weuseadifferentialgroupdelay(DelayDevice) insideaDPXAtoremoveall theghostcrosstalkpeaks resulting from thesecondordercouplings [22],makingit possible to accurately identify and measure large numbers of polarizationcrosstalkpointsalongaPMfiberwithoutambiguity.Inparticular,as illustrated inFig.2d, theDelayDeviceaddsanadditionaldelayLbetweenpolarizationcomponents in theslowand fast axes.ThisdelayL in vacuumshouldbe longer than△Z,wheretheadditionaldelayLisaddedtothelightpolarizedalongtheslowaxisofthePMfiber.Thus,thetwowavepacketsequences from the fast-axis and slow-axis are separated in time (orspace)after the lightpasses through theanalyzer. Ifwe preset the same delay offset between the fixed and moving arms in the interferometer and restrict the range of the variable delay line in themovingarm, theundesiredzeroorder(S0 with S0,SijwithSij, and fi with fi)and thesecondorder (S0withSij,

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and fi with fj)interferencesignals(ghostinterferencepeaks)willnot be generated as the delay line scans. Only the desired first orderinterferencesignals(S0 with fi)andthemuchweakerthirdorderinterferencesignals(fiwithSnm)willbepresent.Notethatthethirdorderpeaksarenegligible(lessthan-75dB)ifthefirstorder coupling fiislessthan-25dB.Moredetaileddescriptionofsuchaghost-peak-freeDPXAcanbefoundin[22].

Fig.2. a) Illustrationof polarization coupling at locationsX1, X2, and X3along thePM fiber;b) thewavepacketsequencespolarizedalongtheslow(denotedbyS)andfast(denotedbyf)axesattheoutputofthePMfiber;c)Wavepocketsinthetwointerferometerarmsafterlightpassingthroughthe45°orientedanalyzer, where the wave packets aligned to the slow and fast axesaremixed together.Whenthismixed light is input to theinterferometerinFig.1,aseriesofinterferencepeaks,includingmultiple ghost peaks, will be observed as the delay in one arm of the interferometer ischanged;d)Wavepockets in the twointerferometerarmsafter theDelayDevice inFig.1 is insertedbetween thePM fiber’soutput and the45degreepolarizer’sinput.Thisdifferentialdelayaddsanadditionaldelaybetweentheslowaxisand the fastaxisof thePMfiber.Only the firstorder interferencepeaksbetweenS0 and fi and the third order interference peaks between fiandSij can be generated.

III.Measurementfixture,methodsandresults

A.MeasurementFixtureTo facilitate easy and accurate measurements of groupbirefringence related parameters, we designed a spool-like fixture to induce periodically spaced polarization crosstalk peaks alongaPMfiberundertest(FUT),asshowninFig.3a. Inourexperiment, we simply use a standard fiber spool from the fiber manufacturer and affix a piece of thin metal rod with a diameter of2mmacrossitswidth.AsinglelayerofFUToflength280miswound on the spool with a 10-gram winding tension, and each turn of the fiber is placed adjacent to the previous turn, as shown inFig.3b.Ittakesusaboutfourhourstowindsuchaspoolusinga simple spool winding machine, and the time can be reduced to less than an hour with more practice and process optimization. Re-spooling fiber is a common practice in the industry forfiber manufacturers and fiber spooling/winding machines are commerciallyavailable,forexample,fromShowmarkLLC.

Fig.3 (a) Illustrationofa lengthofPM fiberwoundona fiberspool with a thin metal rod to induce periodic transversal stressesonthePMfiberatthelocationswherethefibercrossestherod.(b)Detailedviewofthefiberwhenfiberistransitioningfromoneturntothenext.(c)Detailedviewofthefiberwhenitcrosses the metal rod.

As will be shown next, the accuracy of the length of each fiber turn on the spool is critical to the measurement accuracies of thebirefringenceparametersof thePM fiber tobemeasured.As shown in Fig. 3, the length l of each fiber turn is the circumference lc of the spool plus the additional length dl1 caused by transitioningeach turnof fiber to thenext (Fig.3b)and theadditional length dl2 causedbythepresenceofthemetalrod(Fig.3c):

l = lc +δl1 +δl2= πdc+dc ⋅ dc ⋅d1 dc − d1( )− arccos dc − d1( ) dc + d1( )( ) 2( )+2 ⋅dc ⋅ dc ⋅d2 dc − d2( )− arccos dc − d2( ) dc + d2( )( ) 2( ) (2)

The length l canbepreciselydeterminedwhen thediametersof thespool(dc ), thefiber(

d1 ),andthemetalrod( d2 )areknown. Inpractice,onemayuse lc to approximate l. Forourexperiment with dc = 0.17 m, d1 = 1.65x 10-4 m and d2 = 2 x 10-3

m, the relative length error (dl1+dl2) / lc for the approximation is about0.1%.Therelativelengtherrorcanbereducedtolessthan0.015%withametalrodofdiameterd2 = 5 x 10-4 m. Notethatthe measurement accuracy of the circumference lc isabout0.006%when a Vernier caliper is used for measuring the diameter of the spool. Incomparison, the fiber lengthmeasurementaccuracy in[4] is limitedby theaccuracyofanOTDR(optical timedomainreflectometer)oraruler,toontheorderof1%.

Asexpected, “point-like”stressesareautomaticallyapplied tothefiberatthepointswherethefibercrossesthemetalrod(Fig.3c) toproducemultipleperiodicpolarization crosstalkpoints,withaperiodicitypreciselydefinedbyEq. (2).Theseperiodiccrosstalk peaks act like embedded ruler marks on the fiber, which automatically yields precise length information essential for groupbirefringencerelatedmeasurements,asrequiredbyEq.(1).Notethatiftheghostpeakscausedbysecondordercouplingarenot eliminated, there would be many false peaks between the true periodic peaks, making it difficult to identify the positions of the true peaks.

Inpractice, suchaspool-like fixturecanbemachinedwith aprecisepredetermineddiameter (orcircumference)andwithathin slot or bump across its width to induce periodic polarization crosstalkpoints,makingtheembeddedrulermoreaccurate.Itisimportant to point out that the reasons for making such a fixture are1) topreciselydefine the lengthsbetweencrosstalkpeaks,because the accuracy of group birefringence measurement is proportionaltotheaccuracyofsuchlengths,asshowninEq.(1),and2) tocreateadistributionofcrosstalkpeaks to reflect thelocalgroupbirefringencesalong the fiber.Note that thespatialresolution of the local group birefringence is determined by the circumference of the fixture, on the order of the 0.5 m in our experiment.Itcanbeeasilyimprovedbyreducingthediameterofthefixture,consideringthatthespatialresolutionoftheDPXAisaround6cm(assumingthegroupbirefringenceof thePMfiberis(5x 10-4 ),althoughthe0.5mresolutionissufficientformostPMfibercharacterization.

B. Group birefringence and group birefringence uniformitymeasurementsFig.4a is themeasuredpolarization crosstalk curveof aPMPANDAfiberwithacorediameterof6µm, a cladding diameter of80µm,andabufferdiameterof165µm, as a function of the interferometer delay △Z,showingthepolarizationcrosstalkpoints

l = lc +δl1 +δl2= πdc+dc ⋅ dc ⋅d1 dc − d1( )− arccos dc − d1( ) dc + d1( )( ) 2( )+2 ⋅dc ⋅ dc ⋅d2 dc − d2( )− arccos dc − d2( ) dc + d2( )( ) 2( )

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inducedbytheline-pressurefromthemetalrodonthefiber.Thepeaks at the far left and right correspond to polarization crosstalk induced at the output and input connectors, respectively, due to slightmisalignmentof the lightcoupling intothefiberaxis.Fig.4b shows the detailed view of the equidistant periodic crosstalk peaks caused by transversal pressure induced whenever the fiber crosses the metal rod. As one can see, these measured crosstalk amplitudes vary from peak to peak because of the angle variation between the direction of transversal pressure and the fiber’s principal axes during the winding of the fiber onto the spooling wheel; however, such an amplitude variation does not affect the periodicity measurement, which is important to the group birefringence measurement. One can readily obtain the spacing between any two stress crosstalk points by simply multiplying the circumference of the spool by the number of stress-induced crosstalkpeaksbetween the twopoints. In addition,onecanprecisely obtain the relative delay △Zwith theencoderof themotorized delay line.

Fig.4 (a)Polarizationcrosstalk curveof280meterPM fiberwound on a spool as a function of the interferometer delay △ZinsidetheDPXA.Thepeaksatthefarrightandleftcorrespondto the crosstalk induced at the input and output connectors, respectively, from slight axis misalignment between the light polarizationand thePMfiberaxis; (b) theequidistantperiodiccrosstalk peaks are induced by the pressure of the metal rod on thePMfiber.

When Eq. (1) is used to obtain△n, the total relative error d△n/△n canbeexpressedas[4]:

δΔn Δn = (δ

ΔZ ΔZ )2 + δZ Z( )2= (δ

ΔZ Δn)2 + δZ( )2Z (3)

where d△n is the group birefringence inaccuracy, d△z is the reading error of the delay △Z of the variable delay line inside the DPXA,anddz isthemeasurementerroroflengthZ.Notethatinthepreviousreports[4,21],theabsolutelengthoftheFUTmustbe accurately measured in order to obtain an accurate group birefringence △n according toEq.(3).Any lengthmeasurementerror will proportionally contribute to the accuracy of △n. Incontrast, here we can use the relative length defined by the circumference of the fiber spool to eliminate the need for absolute lengthmeasurementanditsassociatederror,andEq.(1)canbe

rewrittenas:

△n = (δ z/Nl )(4)

where l is the fiber length corresponding to the period of the crosstalkpeaksdefined inEq. (2),N isan integer to representthe number of periods we choose in the calculation, and dz is thecorrespondingdelay in the interferometer for theNperiods.Theerror sources for△n are from both the relative location inaccuracy d△z between the polarization crosstalk peaks measured withthevariabledelaylineinsidetheDPXAandtheerrorinthemeasurement of l .Notethatthedelaylinegenerallyhasanerrorindependent of the traveling distance; we therefore choose to usemultipleperiodicities(N>>1)intheexperimenttoreducetheeffect of delay line error d△z, similar to the case of measuring the thickness of a stack of paper in order to accurately determine the thicknessofasinglesheetofpaper.WefoundinourexperimentthatwhenN≥5, the measurement uncertainty is sufficiently small. Theaverage△n obtained is △n = 4.65x10-4 whenN=5.

Fig.5(a)Measuredgroupbirefringenceasafunctionofdistancealongthe280meterfiberwithN=5,withoutapplyingdispersioncompensation, where the fiber length between any neighboring crosstalkpeaksisdefinedbyEq.2(0.535mintheexperiment)of the fiberspool.Themeasurementuncertainty isshown toincreasewith thedistance. (b)Measuredgroupbirefringenceas ina);,butwithdispersioncompensation.Themeasurementuncertaintyatlargedistancesissignificantlyreduced.The6-pointwindowed sweeping average of the group birefringence as a functionofdistanceisshownbytheredline.Inbotha)andb),thezeropositionisplacedattheFUT’soutputconnector.

Fig. 5a shows the variationof△n as a function of distance Zalong the fiber for thecaseofN=5,whereZ isobtainedbydividing △Zby theaverage△n obtained inFig.4,asdefinedin Eq. (1). The largedata fluctuations at largedistances arecaused by dispersion induced peak broadening caused by group birefringencedispersion[21],whichwillbediscussedinSectionIIIC,because thebroadening increases theuncertaintyof d△z in Eq. (4).Dispersioncompensationproceduresdescribed in

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[21]canbeused to further improve themeasurementaccuracyby multiplying the distributed crosstalk curve with a dispersion compensation function when the group birefringence dispersion oftheFUTismeasured,asdescribedinSectionIIIC.Fig.5bisthe measured group birefringence as a function of distance along the fiber, showing that the measurement uncertainties are greatly reducedwhenthedispersioncompensationprocedure in[21] isapplied.Itisalsoevidentthatthemean△n slightly varies along thefiberlengthfortheFUT.

Note that the tension applied to the fiberwhenwinding thefiber on the spool is not critical to the measurement accuracy. In a separate experiment,we foundnonoticeabledifferencesin measured birefringence using the same method when three different tension settings (5, 10, and15grams)of the fiberwinding machine were used to wind the spool.

C. Group birefringence dispersion measurementAsdiscussedin[21],theenvelope of a measured crosstalk peak (i.e. the interferencepeak) is influencedby theSLED’sspectraldistribution and by the group birefringence dispersion △D of thePMfiber. In fact, theenvelopewidth increasesquadraticallywith thedistanceZdue to theeffectof thegroupbirefringencedispersion.TherelationshipbetweenenvelopebroadeningW and group birefringence dispersion △D canbeexpressedas[21]:

W/W0=(1+(α△D)2Z2)1/2 (5)

where α =2πc(△λ/λ0)2 (6)

Intheequationsabove,cisthespeedoflightinvacuum,△λ is the3-dBspectralwidthof the lightsourcewithaGaussian lineshape, and λ0 is the center wavelength of the light source used for themeasurement, respectively.W0 is the 1/e width of the interference envelope when the dispersion △DorZequalszero.Asshown in [21],onemaysimplymeasure thewidthsofanytwopolarizationcrosstalkpeakswithaknownspacingZbetweenthem to obtain the dispersion △DusingEq. (5).However, inorder to increase measurement accuracy of △D, thewidthsofcrosstalkenvelopesatmultiple locationsalong thePMFUTaremeasured, and △Disthenobtainedbycurve-fittingtoEq.(5).

Fig.6. Envelopewidthsof crosstalkpeaks inducedbystressat various locations along the fiber. Theenvelopewidthsofpolarization cross talk peaks broaden as fiber length increases due to group birefringence dispersion. Curve-fitting determines thegroupbirefringencedispersionoftheFUTtobe△D＝0.0079 ps/(km. nm).

Fig.6showsthewidthsofthecrosstalkpeaksasafunctionoftheir locationsalong the fiber.Thedistance ismeasured fromthe first inducedcrosstalkpeakandevaluatedevery20peaks(N=20or 10.7m).Unlike in [21], inwhich the locations ofcrosstalkpeakswerecalculatedusingEq. (1),which requiresthe total fiber lengthZ tobemeasuredprecisely, for thiscase,only the relative locations are required, and they can be precisely obtained by multiplying the circumference of the fixture by the number of peaks, minimizing the error contribution of fiber distance in dispersion measurement. One may argue that the groupbirefringencedispersionmayalsobeobtainedusingEq.(5) bymeasuring thewidths of the crosstalk peaks causedby the output and input connectors; however, the error of the fiber distance measurement also contributes to the dispersion measurement. In addition, such a two-pointmeasurement issensitivetomeasurementuncertaintiesofthewidths.Themethodpresented here can effectively avoid such error sources. As canbeseen fromFig.6, thewidthsofcross-talkpeakstart toshowsignificantbroadeningatadistancelargerthan100m.Thegroup birefringence dispersion △Dof thePMfiber isaccuratelyobtainedbya least-square fitting toEq. (5) tobe△D＝0.0079 ps/(km .nm).Note thatadispersioncompensation functioncanbeobtainedonce the △D of the fiber isdetermined,asdescribed in [21].Thisdispersioncompensationfunctioncanbeusedtoremovethebroadening of the crosstalk peaks, and hence, to reduce the mea-surement uncertainties of the group birefringence along the fiber, asdescribedinSectionIIIB.

D.GroupbirefringencethermalcoefficientmeasurementAsdiscussedin[4], thePMfiber isexpectedtobesensitivetotemperature because of anisotropic strain which is caused by differential thermal expansion at different regions in the fiber cladding, and which varies linearly with temperature in the vicinityofroomtemperature.Thegroupbirefringence△n can be writtenas[4]:

△n = γ (T 0 - T ) (7)

whereT is the temperature of the FUT, T0 is the softening temperature of silica glass with dopants in the stress-inducing region of the cladding, and γ is the thermal coefficient of group birefringenceofthePMfibertobemeasured.

Asin[4],weplacethefiberspoolofFig.3aintoatemperaturechamber,with two fiberpigtailsoutsideof thechamber. Fig.7ashowstwotypicalpolarizationcrosstalkcurvesofaPMFUTasa functionof relativedelay for twodifferent temperatures:80°Cand40°C.Clearly,thepositionsofallpolarizationcrosstalkpeaksareshiftedwith the temperature,aspredicted inEq. (7).In our previous report [4],weobtain the thermal coefficientof group birefringence by measuring the position of the crosstalk peak induced by the input connector as a function of temperature.However,asdescribedin[4],therearetwomajorerror sources that affect themeasurement accuracy: 1) fiberlengthmeasurementerror, and2) the fiber lengthoutside thetemperaturechamber. Inordertomakeaccuratemeasurements,the fiber inside the chamber must be sufficiently long and the fiber pigtails must be kept sufficiently short.

In this section,we show that both the error sources canbe

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effectivelyminimized for the following reasons:1)because theperiodic polarization crosstalk peaks induced by the measurement fixture act as ruler marks along the fiber, the fiber length measurement between any two peaks can be easily obtained with ahighprecision,and2)weonlymeasure the relativepositionvariation with temperature between any two periodic crosstalk peaks on the fiber section inside the chamber, and therefore eliminate the error contribution of fiber sections outside of the chamber.Inthisexperiment,wechoosetomeasurethespacing△Zbetween the1st and 50th peaks, and to measure the group birefringence △n asafunctionoftemperature.AsshowninFig.7b,thepeakpositionsofthe48th, 49th, and 50th peaks shift to the left as temperature increases, reducing the spacing △Z.Thefactthat the spacing △Zdecreaseswith temperature indicates that△n has a negative thermal coefficient. As mentioned previously, the thermal coefficient of the group birefringence γ can be obtained by linear-fitting of △n toEq.(7)usingtheleastsquarefittingmethodateachdifferenttemperature.Notethatinordertoreduce the effect of dispersion, we choose the crosstalk peaks close to the output end of the fiber under test, although dispersioncompensationasdescribed inSection IIIBand3.3may also be used to reduce peak broadening and improve measurement accuracies for measuring peaks closer to the input connector(N>>50).

Fig. 7 (a) polarization cross talk curvesof aPM fiber as afunctionoftherelativedelayat80°C(blue)and40°C(red);(b)Theexpandedviewof thepositionsof the48st, 49th, and 50th peaksat80°C(blue)and40°C(red); (c) △n obtained at seven different temperatures by measuring the spacing between the 1st and the 50thcrosstalkpeaksatdifferenttemperaturesusingEq.(4).

Inourexperimentwemeasured△n foronePM fiber at sevendifferenttemperatures(i.e.-40°C,-20°C,0°C,20°C,40°C,60°C,80°C)andtheresultsareplottedinFig.7c.Linear-fitting△ntoEq.(7)yields a group birefringence thermal coefficient γ of4.123x10-7.

E.PERmeasurementAsmentionedintheintroduction,traditionalmethodsofPMfibercharacterizationdescribed in [6,7],ormethods thatuseaPERmeter formeasuring thePERofaPM fiber,aresusceptible to1)polarizationmisalignmentat the inputendof the fiberundertest (FUT),and2)polarizationmisalignmentbetween the lightsource and its fiber pigtail if a pigtailed light source is used. UsingaDPXA,onecanreadilyidentifythecrosstalkcontributionsfrom the polarization misalignments at the two fiber ends, as well as at the interface between the pigtail and the light source, andeliminate theircontributions to the totalPER,because thecorresponding polarization crosstalk peaks measured with a DPXAarespatiallyseparated.NotethatforthePERmeasurementdescribed in this section, we do not induce the periodic polarization crosstalk peaks as in the previous sections.

Fig.8shows themeasuredpolarizationcrosstalk curvesof aPMfiber jumperwithFC/PCconnectorsandaspoolofPMfiberof length250metersdirectly fromaPM fiber vendor, fusionsplicedwithtwoFC/PCconnectors.WhenaFUTisconnectedtotheDPXA,thepolarizationmisalignmentattheconnectionpointsinduces significant crosstalk peaks. An auto-search program can be implemented in theDPXAsoftware toautomatically identifythose peaks, because the polarization crosstalk signatures of the fibers inside theDPXAareknown,asshown inFig.8. Inaddition, the polarization crosstalk peak resulting from the light source and its pigtail is located outside the region defined by the twoconnectors,andthusisnotincludedforPERcalculation.Bydefinition,thePERofthefibercanbecalculatedas:

PER = 101og ( Ps/Pf ) (8)

where Pf is the total power coupled to the fast axis from the slow axis and can be obtained by integrating all polarization crosstalk peaks between the two connectors, and Ps is the total power remaining in the slow axis Ps = P - Pf , where P is the total received power at the fiber output.

WeimplementanalgorithmintheDPXAsoftwaretoautomaticallycalculate thePERwhileexcluding thecontributionsof the twoend connectors from the crosstalk measurement curve, as shown inFig.8a.OnemayalsousetheDPXAsoftwaretocalculatethetotalPERcontributionbetweenany twopointsalong the fiber,and therefore to further exclude the contributions from the two fusionsplicingpoints,asshown inFig.8b.Table2comparesmultiplePERmeasurement resultsof a13meter fiber jumperanda250meterPMfibercoilobtainedwithacommercialPERmeterandaDPXA. It isevident that thePERvalueobtainedbythePERmeter isseveraldBsmaller than thatobtainedwithaDPXA,duetothecontributionsofcrosstalkfromthepolarizationmisalignmentat the inputconnector. Inaddition,asanticipated,themeasurement repeatabilityof aDPXA ismuchbetter thatthatofaPERmeter.Therefore,itismucheasiertouseaDPXAtoobtainmoreaccuratePERmeasurements than touseaPERmeter.

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Note thatweusedaSLEDsourcewithaspectralwidtharound30nmwhenusingaPERmeter for thePERmeasurement, inaccordancewith the requirementof teststandardTIA-544-193[7]toavoidmeasurementfluctuationscausedbycoherenteffectsresultingfromtheuseofanarrowline-widthlaser[25].

Fig.8 (a) Polarization crosstalk curves of a 13m jumperwith two FC/PC connectors and (b) a 250mPM fiber coilsplicedwith twoFC/PCconnectors.PERmeasurementwithacommercialPERmeteralwaysincludesthecontributionsoftheinputconnectorandtwosplices,whiletheDPXAhastheabilityto identify and eliminate polarization crosstalk contributions of all connectors andsplices in themeasurement system.Notethat fiber length in the horizontal axis is obtained by dividing the fiber delay line distance △ZbytheaveragegroupbirefringenceobtainedusingtheproceduredescribedinSectionIIIB.

Table 2. Comparison of PERmeasurements of a 13m PMfiber jumper and a 250 m PM fiber coil obtained with acommercialPERmeterandaDPXA

Measurement#

PERofFiberjumper PERofFibercoil

ERM(dB)DPXA(dB)

ERM(dB)DPXA(dB)

1 22.5 34.81 25.7 30.82

2 24.9 34.27 21.8 30.81

3 23.3 35.06 25.4 30.31

4 26.8 34.64 22.5 30.90

5 25.8 35.14 23.8 31.09

Uncertainty(Max-Min)(dB)

4.3 0.87 3.9 0.78

F.PMfiberqualityevaluationUntilnow,theonlyparameteravailabletoausertocharacterize

thepolarizationperformanceofaPM fiber fromavendorhasbeenPERorh-parameter,whichmaynotbeable toreflect thetrue polarization performance of the fiber, especially considering thatPERmeasurementusingconventionalmethodsmayhavesignificant fluctuations, as discussed previously. Here,weproposetouseasetofparametersobtainedfromasingleDPXAscan to fully and unambiguously describe the fiber’s polarization performance.

Fig.9PolarizationcrosstalkcurvesofthreedifferentPMfibers.a)aPANDAPMfiberat1310nmwithabufferdiameterof250µm.Adefectpointisseenataround220m;b)aPANDAfiberat1310nmofthesamecore/claddingdiametersasina),butwithareducedbufferdiameterof169µm;c)athirdPANDAPMfiberat1310nmwithsimilarcladdingdiametersas ina),butwithanevenmore reducedbufferdiameterof136µm.Twomajordefectpointswithcrosstalkmorethan45dBareseen.

Fig.9showsDPXAscansofthreedifferentPMfibersmeasureddirectlywhile still on the fiber spool from the vendor.Wepropose to use four parameters to characterize the quality of a PMfiberwithrespectto itspolarizationrelatedperformance:1)theaveragepolarizationcrosstalk,2)themaximumcrosstalk,3)

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the number of crosstalk peaks above a certain threshold defined by themanufacturer or the user, and 4) PER. The averagecrosstalk is themajor contributor to thevalueofPERand isclosely related toh-parameter (PERperunit fiber length).Themaximumcrosstalk isan indicationofwhether thePM fiber isdegraded or damaged during manufacturing, packing or shipping ofthePMfiber,althoughasingleorafewhighcrosstalkpeakscontribute insignificantly to the totalPERof a long fiber. Forsome applications, such as fiber gyro coils, the high crosstalk sections must be removed to assure high quality fiber coil production. A large number of high crosstalk peaks present in the fiber may indicate problems in the fiber drawing or packaging processes.Italsomakesitimpracticaltosortoutonlygoodfibersections for demanding applications.

Table3. lists these fourparameters for threedifferent fibersundertest,obtainedfromFig.9.FiberIisacommercialPANDAfiberat1310nmwithabeatlengthof2.57mm,acorediameterof6µm,acladdingdiameterof125µm,andabufferdiameterof250µm.Fiber II isadifferentPANDAfiberat1310nmwiththesamecorediameterasFiberI,butwithadifferentbeatlength(2.13mm),acladdingdiameterof80µm,andabufferdiameterof169µm.Finally,Fiber III isa third typeofPMfiberat1310nmwithabeatlengthof2.6mm,acorediameterof6.4µm,acladdingdiameterof80µm,andabufferdiameterof136µm.It is evident fromFig.9a that Fiber I has the lowestaveragecrosstalk, resulting in thehighestPERof28.78dB;however,it hasadefectpointabout220m from theoutputconnector,with ahighcrosstalkpeakof -42.36dB,probably causedbymishandlingwhenwinding the fiber to thespool.SuchadefectcannotbeidentifiedwithasimplePERmeasurement.Wefindinexperiments that such a defect may be permanent, i.e. the fiber cannot recover even when the corresponding stress is released. Conversely,FiberIIIhasthehighestaveragecrosstalkof-59.22dB,correspondingtoalowPERof16.25dB.Italsohasalargenumberofhighcrosstalkpeaksabove-55dB,probablybecausethethinbufferlayer(136µm)cannoteffectivelyprotectthefiberfromexternalstresses.Therefore,allfourparameterscollectivelygivea fullpictureof thequalityorperformanceof thePMfiberunder test.

Table3.Fourparameters to fullycharacterize thequalityofthreedifferentPMfibers

Average crosstalk(dB)

Maximumcrosstalk (dB)

Numberofcrosstalk peaks above -55

(dB)

PER(dB)

FiberI -73.87 -42.36 1 28.8

FiberII -66.78 -51.88 23 23.6

FiberIII -59.22 -42.15 1711 16.5

IV.ConclusionsInsummary,wedemonstratemethodsandprocesses forusinga ghost-peak-freeDPXA to fully characterize all polarizationrelated parameters of a polarization-maintaining fiber, including group birefringence, group birefringence variation along the fiber, group birefringence dispersion, group birefringence temperature coefficient,andPER. Inparticular,wedevisea fixture to induceperiodic polarization crosstalk peaks with equal spacing and measure the locations and widths of the peaks to obtain all

groupbirefringence relatedparameters.Theperiodicitydefinedby the circumference of the fixture can be used as a built-in ruler to avoid the need for measuring the fiber length, whose measurement error causes a significant error for the group birefringencemeasurement. Inaddition,weshow thataDPXAis capable of identifying crosstalk caused by the polarization misalignments at the fiber input and output ends, as well as at the fiber pigtail of the light source, and to eliminate their contributions to thePERof the fiber,enablingeasierandmoreaccurate PERmeasurements. Finally,we propose a set ofparametersobtainedfromtheDPXAmeasurementofaPMfiberthatfullyquantifythefiber’spolarizationrelatedperformance.Webelieve that the methods and processes described in this paper can be readily applied in the industry to completely characterize PMfiberswitheaseandwithhighrepeatability.

V. AcknowledgmentsThisworkwas supported by the National Basic ResearchProgramofChina (973Program)undergrant2010CB327806,National InstrumentationProgramundergrant2013YQ03015,the InternationalScience&TechnologyCooperationProgramofChinaundergrant2009DFB10080and2010DFB13180,ChinaPostdoctoralScience Foundation under grant 20100470782,theMedical InstrumentsandNewMedicineProgramofSuzhouundergrantNo.ZXY2012026, theFoundationResearchProjectof Jiangsu Province under grant No. BK20130373 and No.BK20130374,and the InternalDevelopmentFundingofGeneralPhotonics Corporation.

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