15 September 1999

Ž .Optics Communications 168 1999 393–398www.elsevier.comrlocateroptcom

Pulse width dependance of the Brillouin loss spectrum

J. Smith a,), A. Brown a, M. DeMerchant b, X. Bao a

a Physics Department, UniÕersity of New Brunswick, PO Box 4400, Fredericton, NB, E3B 5A3, Canadab Department of CiÕil Engineering, UniÕersity of New Brunswick, PO Box 4400, Fredericton, NB, E3B 5A3, Canada

Received 17 May 1999; received in revised form 1 July 1999; accepted 7 July 1999

Abstract

Stimulated Brillouin scattering in optical fibers can be used to measure strain and temperature in a distributed manner. Toimprove the spatial resolution of these measurements, shorter pulses must be used, resulting in reduced signal strengthscausing a degradation of strain and temperature resolution. This paper studies the dependance of the Brillouin loss spectrumon the pump pulse width. Theoretical and experimental results display the nonlinear variations in the Brillouin peak powerand linewidth over a range of pulse widths from 10 to 4000 ns. q 1999 Elsevier Science B.V. All rights reserved.

PACS: 42.65.EsKeywords: Brillouin scattering; Pulse width; Brillouin spectrum; Distributed sensing

1. Introduction

Brillouin scattering based distributed fiber opticsensing allows for determination of either strain ortemperature through measurement of the Brillouin

w xspectrum of a fiber 1,2 . The distributed nature ofthe measurement arises through optical time domainreflectometry. The position at which the measuredstrains and temperatures are located along the lengthof the fiber is determined by the time of flight for apulse to propagate down and back through the fiber.

ŽThe accuracy in determining the exact location spa-

) Corresponding author. Fax: q1-506-453-4581; e-mail:j3m6@unb.ca

.tial resolution is thus determined by the width of thepulse.

For many civil engineering and aerospace applica-tions, spatial resolutions of the order of 1 m, corre-sponding to a 10 ns pulse width, are required for truerepresentation of the strain distribution on the struc-ture. As the pulse width is reduced there is a de-crease in the strength of the signal. Due to thenonlinear nature of the Brillouin scattering process,the change in signal power with pump pulse width isalso nonlinear. However, it will be shown that at

Ž .short pulse widths -150 nsf15 m the relation-ship between the signal power and pulse width isapproximately linear when using the Brillouin lossmechanism.

Ž .The linewidth FWHM of the Brillouin loss spec-trum has also been found to be dependant upon the

0030-4018r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0030-4018 99 00366-1

( )J. Smith et al.rOptics Communications 168 1999 393–398394

Ž .pulse width. For longer pulse widths )150 ns atfixed operating laser powers, the linewidth narrows

Ž .until the spontaneous Brillouin linewidth f35 MHzhas been reached as the pulse width is reduced. Frompulse widths of approximately 50–150 ns thelinewidth remains constant and as the pulse width is

Ž .reduced further -50 ns , the linewidth broadensw x Ž .3,4 . However, for very short pulses -5 ns thebroadening stops and the linewidth begins to narrow

w xagain 5 .In this paper, the quasi-steady state coupled wave

model is used to study the dependance of the Bril-louin loss spectrum on the pump pulse width. Thismodel assumes that the pulse width is much greater

Ž w x.than the phonon lifetime f10 ns 6 . Experimentalresults will be presented that show very good agree-ment with the model when the pulse width is muchgreater than the phonon lifetime. As the pulse widthsapproach the phonon lifetime, the experimentallymeasured linewidths are narrower than those pre-dicted by the steady state theory, due to transienteffects of the phonon field.

2. Theory

Brillouin scattering in optical fibers can be stimu-lated through the use of two counter-propagatinglasers. For the case of the Brillouin loss mechanismŽ .probe frequency)pump frequency , there is an am-plification of the pump when the frequency differ-ence between the pump and probe is around theBrillouin frequency of the fiber. The interaction be-tween the pump and probe lasers under steady-state

w xconditions is governed by 7

d P z gŽ .P Bsq P z P z yaP z ,Ž . Ž . Ž .P CW Pd z Aeff

1aŽ .

d P z gŽ .CW Bsq P z P z qaP z ,Ž . Ž . Ž .P CW CWd z Aeff

1bŽ .

Ž . Ž .where P z and P z are the pump and probeP CW

powers, z is the position along the fiber and a is thelinear fiber attenuation coefficient. Due to the expo-nential decay of the acoustic waves in the fiber core,

Ž .the Brillouin gain g has a Lorentzian spectralBw xprofile given by 6

gB0g n s , 2Ž . Ž .B 2

2 nynŽ .B1q ž /Dn B

where n is the Brillouin frequency, Dn is theB B

spontaneous Brillouin linewidth, and g isB0

4pn7p212

g s , 3Ž .B0 23cl rV DnA B

where n is the refractive index of the fiber core, p12

is the longitudinal elasto-optic coefficient, r is thematerial density, l is the pump wavelength, and VA

is the acoustic velocity.Ž . Ž .Eq. 1a and Eq. 1b can be solved analytically

by neglecting any increase in the pump power result-ing from Brillouin amplification. This assumptionwill be valid provided the laser powers are below theBrillouin threshold. The Brillouin signal is defined asthe amount of power lost in the CW probe. TheBrillouin spectrum is thus

Leffya LP n sP e 1yexp yg P , 4Ž . Ž .CW B Pž /Aeff

where P is the input CW laser power, P is theCW P

input pulse power, L is the total fiber length, A iseff

the effective area of the fiber core and the effectiveŽ .length of the fiber L is equal toeff

1ya LL s 1ye . 5Ž . Ž .eff

a

As the width of the pump pulse is reduced it willbe necessary to make modifications to the steady-state

Ž .theory. A reduction in the pulse width T reducesP

the length of fiber over which an interaction betweenthe two lasers can occur. The effective length will

w xtherefore be reduced to 8cTP

L s , 6Ž .eff 2nwhere attenuation has now been neglected. The spec-tral width of the pulse will also increase as the pulsewidth is reduced, and can therefore no longer beneglected. Assuming a perfectly rectangular pulse,

Ž .the spectral profile of the pulse, S n , is given byPT r2 PP yi 2 pn tS n s P e d ts sin pn T . 7Ž . Ž . Ž .H P PpnyT r2P

( )J. Smith et al.rOptics Communications 168 1999 393–398 395

As the pulse spectral width becomes comparableto the spontaneous Brillouin linewidth, one expects a

w xreduction in Brillouin gain 9 . The resultant gainwill be a convolution of the pulse spectrum with the

w xoriginal gain 10 yielding the following spectrum.

Leffya LP n sP e 1yexp yg PŽ . CW B P Aeff�=

X` sin p n yn TŽ .o P Xdn .H 2Xy` 2 nynŽ . 0X

p n yn 1qŽ .o ž /ž /Dn B

8Ž .

3. Experimental configuration

The experimental arrangement used for the auto-mated measurement of the Brillouin spectrum isshown in Fig. 1. It is based upon the method pro-

w xposed by Bao et al. 11 . Both the pump and probelasers are Nd:YAG lasers operating at approximately1319 nm. A portion of the power from each is routedto a frequency counter for measurement and controlof the frequency difference between the two lasers.The pump is pulsed using an electro-optic modulatorand a small portion is then removed and detectedwith a photoreceiver for pulse power and width

Fig. 1. Distributed fiber optic strain sensing system based on theBrillouin loss mechanism.

monitoring. The remainder of the pump and probecounter-propagate in the 400 m long sensing fiber.The time domain signal is measured at the digitizingoscilloscope. The frequency domain spectrum is re-constructed from the time domain signals acquiredby the digitizing oscilloscope as the frequency differ-ence between the two lasers is varied.

4. Long pulse width results

For pulse widths in the range of 200–4000 ns, thepeak to peak input pulse power was 30.9 mW andthe input CW probe power was found to be 1.8 mW.To provide a comparison for the experimental re-sults, theoretical Brillouin spectra were generated. It

Ž . Ž .was possible to use Eq. 4 rather than Eq. 8 toproduce the spectra, over this range of pulse widths,as the pulse spectral width was very small in com-parison to the spontaneous Brillouin linewidth. Thepeak power and linewidth of both the experimentaland theoretical spectra were then determined usingthe Marquardt–Levenburg nonlinear least squaresfitting algorithm. Figs. 2 and 3 display comparisonsof the theoretical and experimental powers andlinewidths as a function of pulse width.

The peak power undergoes an exponential in-crease to a maximum value due to nonlinear Bril-louin amplification as the pulse width is increased.The maximum value corresponds to complete trans-fer of the power in the CW probe to the pulse. Theslight deviations between the theoretical and experi-mental powers can be attributed to fluctuations inboth the input pump and probe laser powers. Thesefluctuations are commonly of the order of "0.2mW. As the CW input power is less than 2 mW, thedeviation in the signal power could be greater than10%.

The linewidth is seen to increase approximatelylinearly as the pulse width is increased. This increaseis due to the saturation of the peak powers at longpulse widths. At large pulse widths, Brillouin ampli-fication has been increased significantly, resulting inan increased transferring ratio from the CW probe tothe pump. Around the Brillouin frequency, the CWis depleted completely and the Brillouin signal powersaturates. As the pulse width is increased, a greater

( )J. Smith et al.rOptics Communications 168 1999 393–398396

Fig. 2. Variation in the Brillouin loss signal power as a function ofthe pump pulse width for long pulse widths.

range of frequencies about the Brillouin frequencyexperience saturation effects. The net result is aflattening of the peak of the spectrum, which ulti-mately results in the FWHM of the spectrum beingincreased. Fig. 4 displays normalized spectra forpulse widths of 200 and 3500 ns to illustrate thespectral broadening due to the saturation effect.

For distributed measurement of strain and temper-ature, the accuracy in determining either the strain ortemperature is determined by the precision in deter-mining the Brillouin frequency. The best resolutionsare obtained when the Brillouin spectrum is narrow

w xand the Brillouin power is large 12 . Clearly, thereis a trade-off between the Brillouin power and

Ž .Fig. 3. Variation in the Brillouin loss linewidth FWHM as afunction of the pump pulse width for long pulse widths.

Fig. 4. Normalized Brillouin spectra for pulse widths of 220 and3500 ns. A broadening of the spectrum at 3500 ns has occurreddue to depletion of the probe power about the spectrum’s centerfrequency.

linewidth. Thus, to optimize the system, the pulsepower should be selected to minimize the uncertaintyin the fitting of the spectrum.

5. Short pulse width results

For pulse widths in the range from 10 to 160 ns,the peak to peak input pulse power was reduced to avalue of 23.5 mW, due to the efficiency of themodulator, and the CW input probe power was 1.9mW. Theoretical spectra were generated numerically

Ž . Žusing Eq. 8 pulse spectral width was significant in.comparison to the spontaneous Brillouin linewidth

Fig. 5. Variation in the Brillouin loss signal power as a function ofthe pump pulse width for short pulse widths.

( )J. Smith et al.rOptics Communications 168 1999 393–398 397

Ž .Fig. 6. Variation in the Brillouin loss linewidth FWHM as afunction of the pump pulse width for short widths. Transienteffects cause the measured linewidths to be less than the linewidthspredicted considering only spectral broadening of the pulse.

and fit in the same manner as described in theprevious section. The experimentally obtained pow-ers were initially found to be less than predictedtheoretically. This was due to the extinction ratio ofthe modulator being non-zero, causing a frequencydependant depletion of the CW power as scatteringoccurred outside of the pulse. This depletion wasmeasured to determine a frequency dependant factorŽratio of the input CW power to the depleted CW

.power that the experimental results were then scaledby to account for the reduction in CW power. Figs. 5and 6 display the corrected peak power and linewidthas a function of the pulse width.

Over this range of pulse widths, the decrease inBrillouin power with decreasing pulse width is ap-proximately linear. This is in contrast to systemsbased on Brillouin gain in which an exponentialdecrease in signal power is observed as the pulse

w xwidth is decreased 4 . Slight non-linearity in thesignal power at short pulse widths results from thebroadening of the laser spectral profile.

There is considerable disagreement between thelinewidths obtained experimentally and those pre-

Ž .dicted by Eq. 8 for pulse widths less than approxi-mately 35 ns. At these short pulse widths, the pulse

Žwidth is on the order of the phonon lifetime f10.ns and transient effects can not be neglected. To

account for transient effects, the time dependantcoupled wave equations including the dynamics of

w xthe acoustic phonons must be solved 13 . The solu-

tion of these equations is out of the scope of thispaper but transient effects should account for theexperimentally measured Brillouin linewidths beingless than those predicted using the steady state the-

w xory 5 .

6. Conclusions

The pulse width dependance of the Brillouin lossspectrum in terms of the signal power and linewidthhave been studied both experimentally and theoreti-cally over a range of pulse widths from 10 to 4000

Ž .ns 1–400 m spatial resolution . The signal was seenŽto increase nonlinearly at long pulse widths )200

.ns and approximately linearly for shorter pulseŽ .widths 10–160 ns . As the pulse width increased,

the Brillouin linewidth decreased nonlinearly in therange from 10 to 160 ns and increased approximatelylinearly at pulse widths greater than 200 ns. Theexperimental and theoretical results using the steadystate coupled wave equations agreed very well forlonger pulse widths, but showed some deviation asthe pulse width approached the phonon lifetime. Inthis range, the time dependant coupled wave equa-tions accounting for transient effects must be consid-ered.

Acknowledgements

The authors would like to acknowledge the contri-butions of NBTel, the Natural Sciences and Engi-neering Research Council of Canada and ISIS Canadato this work.

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