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Stress in optical waveguides. 2: FibersP. K. Bachmann, W. Hermann, H. Wehr, and D. U. Wiechert

The stress properties of GeO2-and F-doped optical fibers drawn in different conditionshave beeninvestigat-ed. The results are in excellent agreement with calculated data based on a generalized theoretical model.For constant drawing forces the influence on the stress profiles was found to be independent of drawing speedand temperature. The total observedstress is the sum of preform stress and drawing-induced stress.

I. IntroductionIn the first part of this work we investigated thestress distribution in optical fiber preforms which wereprepared by the low-pressure PCVD process.' EitherGeO2-doped or F-doped quartz glass was used as thematerial system. It was found that the axial stressprofile and the thermal expansivity of the individualdoping regions are strongly correlated.In this paper we consider residual stress in opticalfibers which were drawn from the preforms. The de-pendence of stress on the drawing force and drawingtemperature is investigated systematically for the dop-ing systems SiO2/GeO2 and SiO2/F. The experimentaldata are discussed on the basis of a generalized modeldescribing mechanically induced stress in fibers witharbitrary refractive-index profiles. Comparison be-tween theory and experiment provides additional in-formation on the elastic and viscous properties ofPCVD glasses. The material parameters deducedfrom the experiments allow one to calculate the axialstress profile for any SiO2/GeO2 or SiO2/F glass fiber asa function of the drawing conditions.II. Theoretical BackgroundDuring the manufacturing process for optical fibers,the quartz material undergoes several high tempera-ture cycles. With and without external forces, stressdevelops in the fibers during coolingto room tempera-ture. Three major stress-enforcing mechanisms,which will be briefly explained in the following can beseparated. We restrict our discussion to the axial

The authors are with Philips GmbH Aachen Research Laborato-ries, P.O. Box 1980, D-5100 Aachen, Federal Republic of Germany.Received 20 November 1986.0003-6935/87/071175-08$02.00/0. 1987 Optical Society of America.

stress component a because the relationship betweenthe principal components of stress in cylindricallyshaped samples is well known for elastic stress andexplained elsewhere. 2A. Thermal StressThermal stress isgenerated due to a mismatch ofthethermal expansion coefficients in a fiber consisting ofseveral different radially symmetric material compo-nents. The axial stress component azth can be ex-pressed by3

zTh E(T)U rooT.. 1 - v(T) [a(r, ) - c(T)]dT, (1)where cRc(T) = . a(r,T)rdr. (la)In Eq. (1), T* is a virtual temperature well above roomtemperature where stress starts to develop on coolingto room temperature Troom. T* is approximated bythe setting point temperature of the softest materialcomponent present in the fiber. c(r,T) is the thermalexpansion coefficient at radial position r and tempera-ture T, E(r,T) and (r,T) are Young's modulus andPoisson's ratio, respectively. For the small dopingconcentrations used in optical fiber preparation thecompositional and temperature dependences ofE(r,T)and (r,T) were neglected. Furthermore, weassumedfor E and v the values given for pure silica,4 i.e., E = 7.7X 105 kg/cm 2 and v = 0.164.B. Hydrostatic PressureStress can alsobe generated in temperature regions,where certain material components behave elasticallybut others are still fluid.5 If, for example, the fibercladding solidifies at a temperature T higher thanthe setting temperature T 0 of the fiber core, the fluidcore, which has no free surfaces, exerts a hydrostatictension to the cladding on cooling.

1 April 1987 / Vol. 26, No. 7 / APPLIEDOPTICS 1175

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This additional axial stress in the cladding can beexpressed by5 Eqs. (5) and (6)for the final and the initial states.Hooke's law:a2 = K[aCl - aco] (T~ci T*.) (2)

The constant K of Eq. (2) depends on the geometricalshape and the elastic properties of fiber core and clad-ding. a and a denote the thermal expansion coeffi-cients of the fluid core and of the solidified cladding,respectively.C. Mechanically Induced StressMechanically induced stress is built up during thefiber drawing process due to a radial variation of theviscoelastic properties of the fiber.6 For simplicity, weconsider again a two-component system and assumethat during drawing the fiber core shows a much lowerviscosity than the cladding. In this case most of thedrawing tension is taken up by the cladding. Whenthe fiber core behaves more and more elastically oncooling, t tends to fix the stress in the cladding materi-al. Consequently, stress is frozen in the fiber afterremoval of the drawing tension. Modern fiber designslike depressed cladding or multiple cladding indexprofiles are based on several differently doped radiallysymmetric regions. Consequently the resulting stressdistribution is more complicated than in the case oftwo-component systems such as simple step-index fi-bers. We therefore extend in the following he analy-sis of mechanical stress, which was presented by Paeket al.6 for a two-component system, to the more generalcase with n differently doped regions in the fiber.The basic equations for the axial stress componentsare

- = const,Ili ?Inrj -f = e' -en = const,

nE'Aj , = .j=inE A, r = F.J=i

(3)(4)(5)

Ejk = i,f,1

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pin hole

translation cylinstage lens

Fig. 1. Experimental setup for determiningstressprofiles in fibers.

400 um, he theoretical resolution of our setup is +1.2,gm. Experimentally the resolution was slightly poor-er (1.5 Mm)because of the unavoidable depth offocus.The accuracyin the determination ofthe axial stressalsodepends on the angular resolution ofthe analyzer,on the length of the optical path in the sample, and onthe accuracy of the Abel transformation. The erroralso varies with the radial position in the sample.With an angular resolution better than 0.050,the reso-lution limit for glass fibers with 140 -Amdiameter was-0.3-0.4 kg/mm2 . Wechecked the overallexperimen-tal accuracy with the expression$crdr= I=rdr (12)which has to vanish within the accuracy of measure-ment1 ; Paztot was well below 0.05 in all the experi-ments.We assumed the value C = 3.4 X 10-5 mm 2/kg for thestress-optical coefficient in all the calculations. Thisvalue was obtained from measurements of purequartz-glass fibers and is in good agreement with theresult published in Ref. 8.

B. Fiber PreparationThe investigations were made on fibers prepared bythe low-pressure plasma-induced chemical vapor de-position (PCVD) process.9-11 The deposited SiO2 lay-ers were either undoped or doped with GeO2 or fluo-rine. Both Heraeus and General Electric waveguideSiO2 tubes wereused as substrate materials. After thedeposition step, the collapsing of the internally coatedtubes wasdone by means of an oxyhydrogenburner ata temperature of 2200C. The fibers were drawnfrom the preforms which were investigated in Ref. 1.The drawing temperature and the drawing speedwere varied from 19000C to 21000C and 5 to 60 m/min,respectively, whichresulted in a drawing force rangingfrom 0.05 to 1 N. This force acted exclusively on theglass material because the fibers used in our experi-

ments remained uncoated. In our study a wide varietyof different refractive-index profiles was investigated.The refractive-index profiles were measured with theRNF method and agree very well with the index pro-files measured on the preforms.IV. Experimental ResultsA. GeneralFigure 2(a) showsaseries of stress profilesmeasuredon fibers which were drawn with different drawingforces from the same preform. The correspondingindex profile of the multiple-step preform is depictedin Fig.3, where the doping-induced relative-index dif-ference

A = ndoped WGnWG

is plotted vs the preform radius. In each separateindex step the PCVD quartz is homogeneouslydopedwith different concentrations of GeO2 . The slightlyincreased index of the undoped PCVD quartz resultsfrom chlorine incorporated in the PCVD depositionstep.For comparison, the stress profile measured on thepreform is shown in the upper part of Fig. 2 afterscalingdownto match the radial extension of the fiber.Obviously,before fiber drawing the difference in axialstress Au,between GeO2-doped SiO2 and quartz-glass(WG quartz of Heraeus, for example) is positive, andthe stress difference between undoped PCVD quartzand WG quartz is negative (see Ref. 1 for details).When the drawingforce is increased the radial varia-tion of the stress changes [Figs. 2(a)-(d)]. Stress inthe outer cladding region,whichconsists ofthe materi-al ofthe WGsubstrate tube, changes from compressiveto tensile stress. The tensile stress in the GeO2-dopedregions decreases and partially changes to compressivestress with increasing drawingforce. The stress in theWG quartz and the undoped PCVD quartz regionsalsochanges significantly. This seems to indicate that thedrawing force is essentially taken up by the substratematerial at a temperature where the deposited PCVD

1 April 1987 / Vol. 26, No. 7 / APPLIEDOPTICS 1177

detectorprojection lens

choppersample

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12108

,86420

refractive ndex profilepreform1)202 substrate

I SiO

I undoped/ PCVDSiO2_ Irage . .. . ..l '... ... . ..0 1 2 3 4 5 6

radius (mm)Fig. 3. Refractive-index profile of the preform shown in Fig. 2.

+3

6E

E

'al2i

0 10 20 30 40 50 60 70 80radius r [pm]

Fig. 2. Axial stress profile of fibers, drawn with increasing drawingforce (a)-(d); (a) is the downscaled stress profile of the correspond-ing preform.

+2+ 1

0- 1

materials are still viscous. (Later we will verify themodel discussed in Sec. II by means of the experimen-tal results.) Figure 2 also illustrates that fiber regionswhich are homogeneously doped, i.e., in which therefractive index has a constant value, have a radiallyindependent constant stress level.B. Linear Variation of Stress with Drawing ForceIn Fig. 4 the measured axial stress in the outer clad-ding of two fibers having different GeO2 doping pro-files is plotted vs the drawing force which ranges from0.05 to 0.85 N. (Curve 1 in Fig. 4 corresponds to themultiple-step fiber already shown in Fig. 3.) Obvious-ly the experimental stress data of the twofibers fall onstraight lines. The extrapolation to zero external loadresults in a perfect agreement with the data obtainedfrom preform measurements (circles). Of course, dueto the different GeO2 concentrations in the inner de-posited layers of the two fibers, the a,(F = 0) value andthe slope of the straight lines in Fig. 4 differ.Alldopant concentrations studied so far showedthislinear relationship. Hence the difference in axialstress between the doped PCVD layers and the WGmaterial, which is used as a reference, should also varylinearly with the drawing tension. Two examples areshown in Fig. 5 for the material systems PCVD SiO2 /WG SiO2 and PCVD SiO 2-GeO 2 /WG SiO2 . Againextrapolation to F = 0 gives the value measured in thepreform. So far the results confirm the assumption ofa linear superposition of two stress generating mecha-

Fig. 4. Measur

WE

caE

0 .4 .8F [N]

ed axial stress of the WG material of two differentfiber sets vs drawing force.

0 -- undopedPCVD-SiO

-5 - s 7[ ]

04 -

EE- 0-CD

-4 -0

.5GeO- doped PCVD-SiO

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nisms-thermal stress and mechanically inducedstress. The slope of the function is different for thetwo material systems.C. Drawing TemperatureIn addition to the drawing tension the drawingtem-perature is alsoan important parameter. The drawingspeed can be increased, for example, by increasing thetemperature while keepingthe external forceconstant.Usually quartz glass fibers are drawn at a temperatureof -2000'C which is well above the setting point tem-perature. Moderate variations of the temperatureshould therefore have negligible effects on the stressprofile.Two sets of fibers were drawn from the same pre-form; the first set with constant drawing temperatureof 20650C while varying the drawing velocity VD be-tween 15m/min < VD < 60 m/min. The second set wasdrawn with a constant drawing velocity of 19.6m/minand different drawing temperatures ranging from19600C to 20800C. This resulted in drawing forcevariations between 0.15and -0.8 N forboth sets. Theresulting stress differences between undoped PCVDSiO2 and WG SiO2 are plotted vs the drawing force fordifferent drawing temperatures (Fig. 6). Again a lin-ear dependence of the stress on the drawing force isfound. Regardless of the drawing temperature all themeasurement points fall on the same line. Hence theresults are virtually independent of the drawing tem-perature. The experimental observations are in goodagreement with the theoretical considerations in Sec.II.

D. Quantitative Analysis of the MeasurementsTo calculate the mechanically induced residualstress by means of the model described in Sec. II, thematerial specific parameters, i.e., the viscosity andYoung's modulus, have to be known. On the otherhand, these parameters can be deduced from the slopeof the axial stress vs drawing force plot according toEq. (10). Unfortunately this sloperepresents a differ-ence between a viscosity and an elasticity term. Spe-cial efforts have therefore been taken to separate thetwo terms experimentally.From the preform shown in Fig. 3 a second fiber setwas drawn. However we modified the WG cross-sec-tional area by means of overcladding the preform withadditional WG tubes. With the two fiber sets oneobtains two independent slope values and two slopeequations for each material component in the fibers.For the fiber drawn from the original unsleeved pre-form the slope is given by Eq. (9):Zl(WG) 1 1

F 71' E ' (13)with

I nIwhr Ani; E'= ae tbwhere index n indicates the WG substrate tube materi-

6 -2-_ -4a|~ -6-D -8 -U3

20152065 a19

2065\1960-2065

0 .5 1.0 F[N]drawing force [N]

Fig. 6. Axial stress difference of undoped PCVD SiO2 and naturalquartz vs drawing force for different temperatures.

Ea

U

2

0

.

-1

Fig. 7. Axial stress level of the WG SiO2 vs drawing force for (a) theoriginalfiberset correspondingto Fig. 2 and (b)the fiber setafter theRIT experiment.

al component.Applying additional overcladding by means of therod-in-tube technique (RIT) the slope is given byRIT

FwG) (14)with

ARIT ITAorig

where Aorig is the cross-sectional area (CSA) of theoriginal fiber,ARIT is the CSA of the fiber drawn from theovercladded preform, andAWG is the CSAofthe overcladded tube in themodified fiber.The axial stress in natural quartz for (a) the originalfiber and (b) the RIT fiber is shown in Fig. 7 vs thedrawing force. With the slopes denoted in the figure,the scaling factor (p= 0.686, and

ARIT= 5.8 X 10 -3 mm2,one obtains

E' = 17.5 X 10-3 mm2, Arig= 17.6 X 10-3 mm2 ,11 10.9 X 10-3 mm2 AW = 10.4 X 10- mm2 .1 April 1987 / Vol. 26, No. 7 / APPLIEDOPTICS 1179

l . . . . . .

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These results show that E' Arig, ' AWG:(a) The elasticity of GeO2 -doped PCVD quartz isessentially the same as that of natural quartz glass.(b) During fiber drawing the viscosity of the wholefiber is clearly dominated by the viscosity of the sub-strate tube material.Hence we can introduce the following assumption:EiE and s

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A [%O]-12 -10 -8 -6 -4 -2 -0I- - II I I Iy =a0 -=1323 *. - -~

43 *63 \"\ \ /

F - dopedPCVD - SiO2

-12y = 13

232-4E-6 NID

-10A [%M]

-8 -6l l

63

- 8- -10

Fig. 10. Axial stress difference of F-doped PCVD SiO 2 and WGquartz vs relative-index difference for different drawing tensions Y= F/AWG.The solid line corresponds to preform data; the dashedline corresponds to extrapolated data with -y = 0.

-4 -2 0I - I I

2 NE_____.___-~~~~ p-4 m~

. ___, , .0E ,

-8

Fig. 11. Mechanically induced residual stress difference in F-doped PCVD quartz vs relative-index difference as a function ofdrawing stress. The dashed lines are calculated data using E(A) =const.

inadequate to describe the SiO2/GeO2 binary system.Therefore the solid line in Fig. 9 (right-hand side) mayonly be used as an estimate.The viscosity reduction of -70% typically for PCVDquartz is found to be not correlated with the chlorineconcentration in the deposit. It may be caused by aslightly modified microstructure of the deposit com-pared to WG material.It is known that the viscosity of synthetic quartzdepends very sensitively on the thermal history andincorporation in the network, the small scatter of thePCVD data obtained here is an indication of the repro-ducibility of the PCVD process and the natural quartzused. Nevertheless, additional investigation is neces-sary to explain the viscosity reduction.2. F-DopedPCVDSilicaThe A - A relationship of fluorine-doped silica isshown in Fig. 10 for various A values. The measure-ments were performed onfour differently doped fibersindicated by four different symbols. A systematicvariation of A, with both A and yis observed. Simi-lar to GeO2 -doped silica, the Ac(A) curve (which isstrongly nonlinear for SiO2/F) is shifted to lowervalueswhen the drawing force is increased. However, sincethe A, values of the preform are negative for values ofA usually used in optical fiber technology (2%oo A

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Analysis of the AOlech data of F-doped SiO 2 resultsin the plot [(A)/flWG] vs A given in Fig. 9 (left-handside). Obviouslythe viscosity decreases stronger withthe F-induced index depression than with the GeO2-induced index increase (right-hand side of Fig. 9).For fluorine-doped silica the published data arerather scarce. The upper solid line on the left-handside corresponds to a simple connection of the datapoints published in Ref. 13 (open ellipse) with thestarting point A = 0%o. (Without any fluorine theviscosity ratio has to be 1.) This assumption is basedon a Fulcher behavior of the viscosity of fluorine-doped silica shown in Ref. 13 (linear interpolation ofthe constants analogous to oxyd glasses).In addition to the data collected on PCVD fibers weperformed stress measurements with different ten-sions on SiO2/F fibers drawn from a Fluorosil preformprepared by means of POD15 (Heraeus GmbH,Hanau). The preform consists of deposited F-dopedSiO2 as outer cladding and a core of pure SiO2. Therelative refractive index of the cladding is -7.6%o re-ferred to the core. The value for [?1(-7.6%o)/flWG]e-duced from the experiment is given by the solid squarewith the error bars in Fig. 9. One observes an apparentagreement between this result and the value deducedfrom Ref. 13 and a systematic deviation from thePCVD data as it was also observed in the SiO2/GeO 2system. The reason for the parallel shift of the datafor F-doped PCVD glass is not yet clear but might bethe same as for GeO2 -doped PCVD glass.V. Summary

We investigated in detail the stress properties ofoptical fibers prepared by means of PCVD using anexperimental setup with a spatial resolution of +1.5gtm. The measured stress profiles were compared withcalculated data. A generalized model for the predic-tion of stress properties offibers with n different mate-rials was used for the calculation and the agreementbetween experiment and theory is excellent. Our re-sults show that homogeneously doped fiber regionsexhibit constant stress values. The stress differencesbetween undoped PCVD SiO2 an substrate silica werefound to linearly increase with increasing drawingforce. At constant drawing force the measured stressprofiles were found to be independent of the drawingtemperature and the drawing speed. The total ob-served stress in fibers is simply the sum of the stressobserved in preforms and the mechanically inducedstress during fiber drawing. For highly F-dopedPCVD SiO2 a small additional stress component can be

found, the origin of which is not yet clarified.With the model and the measured stress profiles theviscosity and the elastic behavior of GeO2-doped andF-doped PCVD quartz were deduced over the wholedoping range usuallyused for optical fibers (-12%o A< 10%o). Young's modulus seems to be unchangedexcept for fluorine doping levels corresponding to A