spatial and temporal power transfer measurements on a low-loss optical waveguide

Spatial and Temporal Power Transfer Measurements on aLow-Loss Optical Waveguide

Donald B. Keck

Experimental measurements of the spatial and temporal transfer of power of a 225-m length of low-losgoptical waveguide have been made. In particular, measurement of the angular attenuation showed sub-stantial loss of the high order modes, which reflected itself in an -8.2 nsec/km decrease in measured dis-persion. Additionally there was a reduction of the effective numerical aperture from 0.15 to 0.12. Negli-gible mode coupling was observed in this particular waveguide, which allowed a phenomenological calcu-lation of temporal output for an assumed uniform excitation of all modes. This agreed well with experi-mental measurements. Calculation of this output from knowledge of the index profile is presently not inagreement, and some possible reasons are indicated.

Introduction

With the attenuation problem in glass opticalwaveguides for communications better understood,'and with recent progress such that it now is possibleto attain values in the vicinity of 2 dB/km in thenear infrared, a greater effort is being spent world-wide on trying to characterize the waveguide for itsuse in communications systems. Much of this workcenters on defining the dispersion or informationcarrying capacity of these devices, which, for certainapplications and types of waveguide, could ultimate-ly provide the transmission distance limitation.

One can separate this dispersion problem intothree parts: material dispersion, intramodal disper-sion, and intermodal dispersion. It has beenshown3 ' 4 in the case of certain single-mode wave-guides that material dispersion dominates intram-odal dispersion in the 600-1000-nm spectral region.More generally, these two coupled with sourcebandwidth will define the limit of information carry-ing capacity. In this respect fused silica is one of thebetter glass choices4 for minimizing dispersion, giv-ing rise to pulse spreading of a few tenths of a nano-second/kilometer for a GaAs laser input. On theother hand, intermodal dispersion within a multi-mode guide having a step refractive index profile,can be very much larger than this, having values ofseveral tens of nanoseconds/kilometer for typicallow-loss waveguides. There are several methods forreducing the effect of intermodal dispersion with dis-tance. Probably the best known is by use of a near-

The author is with Corning Glass Works, Corning, New York14830.

Received 10 January 1974.

ly parabolic index profile, which tends to equalizethe group velocities of the propagating modes.5' 6

An example of this type of waveguide is the SEL-FOC waveguide, which indeed has exhibited ex-tremely small intermodal dispersion. Another ef-fect that tends to reduce pulse spreading with dis-tance is intermodal coupling. It has been calculatedthat for random coupling between modes, thespreading should follow a square root of length rath-er than a linear dependence of length. 8 This effecthas also been observed in present optical wave-guides.9 Lastly there are techniques for decreasingdispersion at the expense of increased attenuation,obviously making them less attractive. These in-clude selective mode attenuation, selective mode ex-citation (in the absence of mode coupling), and se-lective mode detection.

This work measures the magnitude of some of theabove factors governing dispersion for a specific mul-timode waveguide and correlates them with actualpulse transmission measurements. In particular, thefactors included are mode coupling, preferentialmode attenuation, and the effect of the refractiveindex profile. A desirable goal would be to predictthe output pulse shape from the known input pulseshape and various waveguide parameters such as ra-dial index profile, for example. This is not possibleat the present time, and a phenomenological modelwas chosen; that is, the measurement of the transferfunction for a given piece of waveguide can predictfairly well the waveguide output for an arbitrarysource input.

Experimental Technique

The sample that was measured was a high silica,multimode waveguide approximately 220 m long,with an attenuation of 4 dB/km at 1.05 m. Its

1882 APPLIED OPTICS / Vol. 13, No. 8 / August 1974

NCIA

0

w0zwU-

a:

X

z

0.1

O 0.1 0.2 0.3 04 0.5 0.6NORMALIZED RADIUS

0.7 0.8 0.9 1.0

Fig. 1. Plot of radial index difference between core and claddingfor experimental waveguide.

spectral response is typical of that previously re-ported.' The radial index distribution for thisguide, shown in Fig. 1, was obtained from an elec-tron microprobe scan of the entire end with a subse-quent radial averaging to produce the profile shown.Although it is substantially a step profile, the depar-ture from a step will be shown to have a pronouncedeffect on the dispersion. The equivalent step wave-guide numerical aperture is 0.15 with a core diame-ter of 75 im, giving rise to approximately 1540 pro-pagating modes. For all measurements the fiber waswrapped on a 16.5-cm radius of curvature drum.

Measurements were made of both the spatial andtemporal transfer characteristics of the waveguideutilizing very similar equipment. That used for thetemporal transfer is shown schematically in Fig. 2.In both cases a plane wave input from a lasersource was made incident on the waveguide as afunction of angle. The intent was to have a uniformareal excitation and, through a scan of the inputangle in a plane containing the fiber axis, to allowfor excitation of all possible fiber modes.

Go A.

Loer

Optional Collecting

In the case of the spatial measurements a He-Nelaser beam with a diameter of 800 ym and a diver-gence of 1.1 mrad was used. The intensity distribu-tion over the end face of the fiber was measured tobe constant to 3%. Appropriate mode strippingwas employed near the input end to remove claddinglight. At the fiber output end, measurements ofboth the total transmitted power as well as its angu-lar distribution were obtained for the various inputangles and for two different fiber lengths. The ob-vious far-field scan of a pinhole to obtain the angulardistribution produced unusable intensity fluctua-tions due to the coherent input beam and the result-ing modal interference pattern. This was avoided inlarge part by an averaging technique. A lens wasused to Fourier transform the angular into a radialdistribution. An iris diaphram was then smoothlydriven in the lens focal plane and the transmitted in-tensity measured with a large area silicon solar cell.The data was digitally punched on paper tape, andthe computer obtained derivative of this data gavethe desired angular distribution.

For the temporal measurement the source was anRCA SG 2001 laser diode emitting at 905 nm drivenin a self-pulsing mode by discharging a 15-cm, 50-4coaxial line through a Hg reed relay. The techniqueis very similar to that described by Gloge et al.10The light was collimated with a 10x microscopeobjective and allowed to fall on the fiber input.Again uniform areal excitation was achieved withsmall angular divergence. Detection was accom-plished by a TIXL 55 Si avalanche photodiode anddisplayed on a sampling oscilloscope having a 25-psec rise time. Figure 3(a) shows a typical pulsethrough zero fiber length for this system. The ob-served -400-psec FWHM pulse is presently photo-diode limited.

Observations

Spatial Transfer MeasurementsFigure 4 shows a semilog plot of the measured rel-

ative transmitted power as a function of the inputplane wave angle for fiber lengths of 228 m and 2 m.

,X. Photodiod.

Fig. 2. Schematic of experimental apparatus.

August 1974 / Vol. 13, No. 8 / APPLIED OPTICS 1883

I I I I I I I I I

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

(a)

(b)

Fig. 3. Observed temporal output for the (a) direct input laserpulse and (b) the transmitted pulse through 225 m of waveguide

with 20X input lens. Time scale is 500 psec/div for bothmeasurements.

Several things can be obtained from the data. Fair-ly obviously, as shown in this plot, the proper man-ner to specify waveguide transmission is by the inputmodal coupling efficiency, as given by the shortlength transmission and the attenuation per unitlength of each mode as determined from their ratioof long and short length transmissions. For this par-ticular guide the normalized coupling efficiency, as afunction of angle, is essentially unity for input anglesof less than -7°. Beyond -8° the efficiency dropsat a rate of 0.36 dB/deg. This interesting observa-tion is not presently explained by any skew ray anal-ysis of the step index profile and cannot be attrib-uted to the angular attenuation.

The attenuation per unit length as a function ofinput angle for the guide was calculated from thesedata and is shown in Fig. 5. The high order modesare strongly attenuated. This plot points up a diffi-culty in specifying the attenuation of a waveguidemerely by the ratio of two transmitted intensities atdifferent lengths. Quite clearly, one could measuretwo very different attenuation values of predomi-nantly high order modes are excited or if predomi-nantly low order modes are excited. This conditionwould occur if, for example, an LED were used inone measurement and a weakly focused laser beamin the second measurement. For extremely low at-tenuation such as 2 dB/km, accurate specification ofthe attenuation will have very important ramifica-tions regarding applications, and a proper methodmust be found in light of the above discussion.

Finally, these data may be used to specify an ef-fective numerical aperture for the waveguide. Thenumerical aperture for this guide taken from the

index data of Fig. 1 is about 0.15, giving an accep-tance angle of approximately 8.5°. In view of thestrong attenuation of the high angle modes, this isan overestimate. A more realistic value might beobtained, for example, from the -3 dB transmissionpoint for the entire waveguide length. Using thisdefinition one obtains an effective numerical aper-ture for this waveguide of 0.12 and a correspondingacceptance angle of about 7°.

Attention is next turned to the output angular dis-tribution. For a plane wave excitation in a perfectstep guide one would expect the output to form acylindrically symmetric distribution. The outputangle should equal the input angle, and the angularwidth will be governed by the input width, diffrac-tion effects, and mode coupling both at input andduring propagation. It is the latter that is of presentconcern. Figure 6 shows the waveguide far field nor-malized radiant intensity for three representativeinput angles, 0, 4, 7 and for the two lengths, -2m and 228 m. Although not shown in this one-di-mensional plot, the output distribution is indeed az-imuthally symmetric and falls at the input angle towithin experimental accuracy. Mode couplingshould manifest itself as a spreading of the angulardistribution with length. While there may be somecoupling to lower order modes as shown by compar-ing the 4 and 7 data for the two lengths, theamount of power coupled is a small fraction of thatin the excited modes. Whatever mode distribution

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L-2m

7IIIIIIIII

L= 228 IIIII

I

I I I I I I l- 4 6 8 10

INPUT ANGLE (DEGREES)2 12 14

Fig. 4. Relative transmitted power for fiberlengths of 228 m (solid) and 2 m (dashed) as a

function of input plane wave angle.


I I I I I

- I I

III I

11 I

N I

- I I

D. 10171 -0- -0- -0 - 0- -X

Fig. 5. Measured angular attenuation of waveguideas a function of input plane wave angle at 632.8 nm.

0 1 2 3 4 5 6 7 8

is excited by the plane wave input is essentially pre-served over this 228-m length. One concludes fromthese dta that coupling should have a negligible ef-fect in determining the temporal transfer character-istics of this waveguide. This observation is consist-ant with that on a similar waveguide where a char-acteristic mode coupling length was found to be ap-proximately 550 m.9 The FWHM of the output an-gular distribution is seen to be -70 mrad, 30 mrad,and 20 mrad for the above input angles, respectively.In all cases this is larger than either the angularwidth of the input beam (-1 mrad) or would be pre-dicted by diffraction (-10 mrad). The remainingincrease must be attributed to excitation of adjacentmodes at the waveguide input due to the index pro-file of the waveguide.

Temporal Transfer MeasurementTwo measurements were made on the waveguide.

First, the output temporal spread was measuredwhile attempting to excite all modes uniformly bysharply focusing the GaAs laser output onto the fiberwith a 20X microscope objective. The oscilloscopetrace of this is shown in Fig. 3(b). It is noted thatthe total pulse width (10% points) is -4 nsec. Sec-ond, the relative arrival time and pulse shape wererecorded for plane wave excitation as a function ofinput ankle. This progression of arrivals is shown inFig. 7. The observed pulse spreading at higher an-gles must include the excitation of adjacent modesmentioned earlier because the spreading is greaterthan that expected from input beam divergence.Nothing here would indicate any strong mode cou-pling, which is in agreement with the spatial mea-surements. Even without mode coupling, pulses ap-proximately 0.1 nsec broader than the short lengthpulse are obtained in the vicinity of 00. This shouldbe due largely to material dispersion. A material

dispersion limit of -0.16 nsec/km is calculated forthe present GaAs source, in reasonable agreementwith the observation. Using this selective excitationtechnique, Gambling et al.1" have pointed out thatvery high bit rates should be achievable in multi-mode waveguides. Additionally, the observationshere show the possibility of angularly multiplexingseveral beams onto a single multimode waveguide.

For a straight waveguide with a step index profile,the relative arrival time between a pulse making in-ternal angles of 0 and 00 with the waveguide axis isgiven by

At = (NL/c),[sec8 -1],

L-(nzwz

za

-JW>r

(1)

180 200OUTPUT ANGLE (mrads)

Fig. 6. Normalized transmitted radiant intensity for input an-gles of O, 40, and 7° for waveguide lengths of 2 m (solid) and 228

m (dashed).


101

I NPUTANGLE

…- ~~~0

-_-\= 3

6

7

Fig. 7. Progression of pulse arrivals as a function of plane waveinput angle. Time scale, 500 psec/div.

where N1 is the core group index, L the guide length,and c the velocity of light. Figure 8 shows both themeasured data points for the waveguide and calcu-lated (dashed curve) relative propagation delay of anassumed step index profile. The measured arrivalsare depressed by approximately 0.5-0.7 nsec beyond40 from those calculated for the step waveguide.

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The greatest dispersion measured was only 12.7nsec/km rather than the calculated 25.5 nsec/km.A portion of this difference is easily explained bythe angular attenuation data in Fig. 5. The atten-uation beyond 7.5° precludes observation of thehigh order, late arriving modes, giving rise to a pulsedispersion of 17.3 nsec/km, 8.2 nsec/km less thancalculated for a step index profile.

Discussion

With uniform excitation over the entire waveguideinput end, the data in Fig. 8 can be used to generatea matrix of transmitted power values as a function ofboth output arrival time and input angle. With thismatrix it should be possible to predict the outputpulse for an arbitrary input excitation. This wasdone for the 20X microscope objective excitation as-suming that all angles were equally excited. The fo-cused spot did not encompass the entire end face,but the calculation was made assuming that it did.The convolution integral of the assumed input dis-tribution and the measured fiber function were eval-uated for each point in time, and the resulting pulseshape is shown in Fig. 9 along with the measuredpulse output from Fig. 3(b) normalized to the peakintensities. The pulse shape agreement gives confi-dence in this phenomenological model for predictingthe temporal output from an arbitrary input distri-bution.

One would like to perform the above calculationknowing only certain waveguide parameters such asthe radial index distribution and the degree of modecoupling. For this waveguide the latter may be ne-glected. In a recent work, Gloge and Marcatili1 2 ob-tain solutions to the cylindrical waveguide problemfor a radially graded index profile of the form:

n(r) = n[1 - 2A(r/a)all/2 , (2)

where no is the axial index, A is the fractional index

Fig. 8. Relative delay as a function of input angle.Shown here are the measured data points for thiswaveguide and the calculated delay for two values ofthe parameter a. The value a = corresponds to a

step index profile.

I I II 2 3 4 5

INPUT ANGLE (DEGREES)


6 7 8

I ' T

Fig. 9. Comparison of measured (solid) and calcu-lated (dashed) temporal outputs from a 225-m opti-cal waveguide for assumed uniform excitation of all

modes.

difference between core and cladding, and a is thecore radius. They show that for a not too near 2,the delay for any mode is simply

t . L [ + ( - )b + (3aY 2 )6 + .*, ]'

where = 2[1-f2/ko2] and a is the axial propaga-tion constant of the mode, with ko = 2rno/X theaxial wavenumber. One sees from this that forsmall (max = A) to a first approximation the delayrelative to the corresponding step guide (a = o)mode is reduced by the factor (a-2)/(a+2). In thestep index profile waveguide a uniform plane waleincident at a given angle does excite a single mode.In the graded case, however, a spectrum of modes isexcited, each of whose relative arrival is diminishedby the factor (a-2)/(a+2) relative to that of thestep index. Therefore the resulting pulse shape isdifficult to predict. If the profile is not too near a =2, each plane wave input angle can be assumed toexcite a narrow spectrum of modes in the vicinity ofthe corresponding step index mode. The relativearrival of this group is then simply assumed to bediminished by the (a -2)/(a +2) factor. A best fit tothe data in Fig. 1 gives approximately a value a = 6.From the theory this would predict a decrease in therelative step index arrival time as a function of inputangle of 0.5. This curve is also shown in Fig. 8.While there is crude agreement, it is not sufficientlygood to allow accurate pulse shape predictions.This is probably due to a combination of the as-sumption that a given angle corresponds to a givenmode for the graded case and to uncertainties in themeasurement of the refractive index profile of thewaveguide. Present techniques for measuring theindex profile of a waveguide' 3 suffer resolution prob-lems in the regions of rapidly changing index.

Another complication that can enter is the factthat the waveguide was wrapped with a 16.5-cm ra-dius of curvature for all these measurements. Gam-bling et al. 1 have directly measured the resultingarrival time depression with decreasing bend radiusfor a liquid core waveguide. After accounting for the

obvious refractive index differences between our twowaveguides, their measurements indicate that bend-ing alone could more than account for the observeddata. They also, however, observe a spread in theangular output distribution for a given curvaturethat is not observed in our measurements. Possibledifferences in method of excitation could account fortheir observation of a much larger effect. In thepresent experiments the input angle was scanned ina plane perpendicular to that of the curved wave-guide. Meridional rays would not be affected bycurvature in this case, and therefore a reduced effectmight be expected. In short the degree to whichbending is affecting the measurements is not known,and the fiber transfer function can only be approxi-mately predicted from fundamental waveguide pa-rameters.

Conclusion

Although a complete theoretical explanation of thetransmission characteristics of multimode opticalwaveguides is still not at hand, a number of guideproperties have been measured and correlated withtheir effect on the transfer functions. Attenuation ofhigher order modes for this low-loss waveguide de-creased the specific dispersion by 8.2 nsec/km andreduced the effective numerical aperture. Both spa-tial and temporal measurements indicate that negli-gible mode coupling exists in -228 m of this wave-guide, and therefore the possibility of angular multi-plexing exists. The departure of the refractive indexprofile of this guide from the perfect step is believedto be primarily responsible for the decrease in theobserved pulse spreading from that of the step pro-file. Because present theory does not accuratelypredict the temporal pulse shape, a phenomenologi-cal method was used successfully. It should be re-membered that extrapolating these measured disper-sion results to very long lengths will predict a pulsespread that is always larger than that which occurs ifmode coupling begins to play a role.


5

4

0RELATIVE ARRIVAL TIME nsec)

The author wishes to thank his colleagues at Cor-ning, R. D. Maurer, J. D. Crow, and R. Olshansky,and members of the Bell Laboratories technical staff,E. A. J. Marcatili and D. Gloge, for many illuminat-ing discussions. He also acknowledges the help of T.A. Cook in obtaining the experimental data. Thecomments of the reviewer concerning the mode-anglecorrespondence in a graded profile waveguide wereappreciated and incorporated into the text.

This work was supported under Contract N00014-73-C-0293 fromthe U. S. Office of Naval Research.

References1. D. B. Keck, R. D. Maurer, and P. C. Schultz, App. Phys.

Lett. 22, 307 (1973).

2. P. C. Schultz, Paper 30-6-73, 75th Meeting American CeramicSociety, Apr. 29-May 3, Cincinnati, Ohio.

3. F. P. Kapron and D. B. Keck, Appl. Opt. 10, 1519 (1971).4. D. Gloge, Appl. Opt. 10, 2442 (1971).5. S. E. Miller, Bell Syst. Tech. J. 44, 2017 (1965).6. S. Kawakami and J. Nishizawa, IEEE Trans. Microwave

Theory Tech. MTT-16, 814 (1968).7. D. Gloge et al., Electron. Lett. 8, 526 (1972).8. S. D. Personick, Bell Syst. Tech. J. 50, 843 (1971).9. E. L. Chinnock et al., Proc. IEEE 61, 1499 (1973).

10. D. Gloge, E. L. Chinnock, and T. P. Lee, IEEE J. QuantumElectron. QE-8, 844 (1972).

11. W. A. Gambling et al. Electron. Lett. 8, 568 (1972).12. D. Gloge and E. A. J. Marcatili, Bell Syst. Tech. J. 52, 1563

(1973).13. C. A. Burrus et al. Proc IEEE 61, 1498 (1973).

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spatial and temporal power transfer measurements on a low-loss optical waveguide

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