IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 8, APRIL 15, 2014 797

Pump-Power-Independent Double Slope-AssistedDistributed and Fast Brillouin Fiber-Optic Sensor

Avi Motil, Orr Danon, Yair Peled, and Moshe Tur

Abstract— A small modification of the fast and distrib-uted slope-assisted Brillouin time domain analysis (SA-BOTDA)method allows it to easily implement pump-power independentmeasurements of strain and/or temperature, using the ratiobetween readings taken on both slopes of the Brillouin gainspectrum. Employing this new double SA-BOTDA measurementtechnique, fast (∼100 Hz at ∼1-kHz effective sampling rate)strain measurements are shown to be immune to pump pulsepower variations as large as 6 dB. At the expense of halving thesampling rate, this technique still maintains all the benefits ofits SA-BOTDA predecessor. In particular, its ability to handle(Brillouin) longitudinally inhomogeneous fibers is demonstrated.

Index Terms— Optical fiber sensors, nonlinear optics, Brillouinscattering.

I. INTRODUCTION

D ISTRIBUTED Brillouin sensing, employing the classi-cal Brillouin Optical Time Domain Analysis (BOTDA)

technique [1], [2], is used today not only for long rangesensing [3], but also for dynamic [4]–[12] and high res-olution sensing [2] over short fibers. One of the fastestfully distributed BOTDA-based techniques, the Slope-AssistedBOTDA method [8], [11], [12], uses a tailored probe wavewhose frequency, while at distance z into the fiber, is tunedto the middle of the linear section of either the rising orfalling slopes of the Brillouin Gain Spectrum (BGS) at z [7].Dynamic strain variations spectrally shift the local BGS tolower or higher frequencies, depending on the sign of theapplied strain, resulting in a change of the local Brillouingain of the probe. Strain information is then deduced fromthe measured gain variations using a calibrating conversionfactor. With a sampling rate, limited only by the round triptime of flight in the fiber and optional time averaging, strainvariations of up to hundreds of Hertz have been measured ona 100m of Brillouin longitudinally-inhomogeneous fiber witha dynamic range of a few hundred microstrains and a spatialresolution down to 10cm [8], [12]. A practical problem withthe SA-BOTDA implementation of [7], [8] is the dependenceof the conversion factor on variations in the pump power.A recently introduced interesting implementation, workingon the slope of the phase of the BGS [10], rather than on

Manuscript received November 4, 2013; revised January 3, 2014; acceptedJanuary 14, 2014. Date of publication January 27, 2014; date of current versionMarch 25, 2014. This work was supported by the Israel Science Foundationunder Grant 1380/12.

The authors are with the School of Electrical Engineering, Tel AvivUniversity, Ramat Aviv 69978, Israel (e-mail: avimotil1@gmail.com;orrdanon@yahoo.com; yairpeled@gmail.com; tur@post.tau.ac.il).

Color versions of one or more of the figures in this letter are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/LPT.2014.2302833

its magnitude, successfully removed the pump-dependencevulnerability, and simultaneously extended the dynamic rangefor strain/temperature measurements at the expense of mea-surement complexity. In Ref. [13], two pumps and two probeswere used to simultaneously monitor both slopes of the BGS.In their architecture, strain/temperature was inferred from thepump-independent ratio of the two gains, as demonstrated in[13] for a static measurement. Both methods, [10] and [13],may require extra means to handle practical situations wherethe Brillouin Frequency shift (BFS) varies along the fiber bymore than the ∼width of the BGS. In this letter we presenta cost-free (hardware-wise) modification of the originalSA-BOTDA technique [8], which periodically probes bothslopes of the BGS in order to achieve immunity to pump powervariations, called here the Double-Slope-Assisted BrillouinBOTDA (DSA-BOTDA). This technique maintains the ben-efits of SA-BOTDA of [8] in its ability to handle (Brillouin)longitudinally inhomogeneous fibers, at the expense of halvingthe sampling speed. Fast vibrations of tens of Hz were simulta-neously measured over a fiber length comprising segments ofdifferent BFS, demonstrating immunity to a few dB of pumpvariations and a potential dynamic range of the order of theeffective Brillouin linewidth (which was broadened due to theuse of short pump pulses).

II. METHOD

The logarithmic Brillouin-induced gain of the probe (i.e.,the natural logarithm of the ratio of amplified probe intensityto the probe intensity with no pump power) at distance z intothe fiber is given by [2]:

G B(z, ν, νB(z), P(z)) = K · P(z) · S([ν − νB(z)]/�νB),(1)

where P(z) is the pump power at z, S(ν) is a normalizedversion of the BGS, ν is the optical frequency of the probe,measured with respect to that of the pump, νB(z) is the BFS,denoting the strain/temperature sensitive frequency at whichthe BGS attains its maximum at location z, and �νB is theFull-Width-Half-Maximum (FWHM) of the BGS, assumed tobe strain/temperature insensitive, albeit dependent on the pumppulse width [2]. K is determined by material constants but alsodepends on the relative polarizations of the pump and probewaves at z. This latter dependence is practically removed bypolarization scrambling so that K will be treated from nowon as a constant. For an optical fiber in a dynamic strainenvironment, the BFS, νB , as a function of both time andlocation along the fiber, can be described by:

νB(t, z) = ν̄B(z) + δνB(t, z), (2)

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798 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 8, APRIL 15, 2014

Fig. 1. A logarithmic plot of RB of (4) as a function of BFS deviationsδνB (t, z) for various of �ν = ν+(z)-ν−(z), ranging from 30 to 90MHz.Inset: The normalized BGS, calculated for a pump pulse width of 15ns.

where δνB(t, z) and ν̄B(z), respectively denote its dynamicand static (or averaged) components. In the SA-BOTDA of[8], [11], [12], the probe frequency is set at either:

ν+(z)= ν̄B(z) − γ+�νB/2 or ν−(z) = ν̄B(z) + γ−�νB/2

(3)

ν+(z) (ν−(z)) are frequencies residing within the approxi-mately linear regions of the opposite positive and negativeslopes of the BGS at z, where the strain/temperature-to-frequency sensitivity is positive for ν+ and negative for ν−.γ± are positive numbers (of the order of unity), which are notnecessarily equal. In order to track the z variation of ν+(z)(or ν−(z)) along a fiber having an arbitrary Brillouin profile,the SA-BOTDA hardware, [8], [9], has the means to fast tunethe probe optical frequency. In this letter the same hardwareis used to overcome the pump sensitivity of the technique byreplacing the simultaneous two-slopes probing of Ref. [13],which had used two different lasers, by a periodical probingof both ν+(z) and ν−(z) with a single laser. For a known BGSand ν̄B(z) (i.e., the static or average BFS) along the fiber, wechoose ν+(z) and ν−(z) to reside on the slopes of the BGSand we form the ratio [13]

RB(δνB, z, ν+, ν−) = G B(z, ν+(z), ν̄B(z) + δνB, P(z))

G B(z, ν−(z), ν̄B(z) + δνB, P(z))

= S([ν+(z) − ν̄B(z) − δνB(t, z)]/�νB)

S([ν−(z) − ν̄B(z) − δνB(t, z)]/�νB),

(4)

which is a function of δνB(t, z) but is independent of thepump power, P(z). For δνB(t, z) = 0 this ratio is unity ifboth ν+(z) and ν−(z) experience the same Brillouin gain.For a given shape of the BGS, which strongly depends onthe shape of the pump pulse for pulse widths shorter than∼50ns [2], a logarithmic plot of RB(δνB , z, ν+, ν−) againstδνB(t, z) produces a family of calibration curves that dependon the frequency difference �ν = ν+(z)-ν−(z). Fig. 1 showsthese curves for a pump pulse width of 15ns (as used in ourexperiments below), as calculated by the perturbation methodof [14]. While small values of �ν give rise to shallow curves,the large �ν ones provide higher sensitivity but are more proneto noise, since either ν+ or ν− experiences a relatively lowBrillouin gain [13].

Fig. 2. (a) Experimental setup: DFB-LD: A narrow linewidth (<10kHz)laser diode. AWG: arbitrary waveform generator, VSG: vector signal gen-erator, EOM: electro-optic modulator, EDFA: Erbium-doped fiber amplifier,CIR: circulator, FBG: fiber Bragg grating filter, PS: polarization scrambler,PC: polarization controller, Pol.: in-line polarizer, IS: isolator, ATT: attenuator,PD: photodiode, FUT: fiber under test. (b) The FUT layout: Two segments,out of the 50m long optical fiber, were attached to two audio speakers.

While it is preferred to choose ν+(z) and ν−(z) to haveequal gains, failure to do so only shifts the zero point forlog(RB(δνB, z, ν+, ν−)) as a function of δνB(t, z). It is alsoseen that quite a wide dynamic range is available, of the orderof the width of the BGS and only slightly lower than thatof [10]. Thus, once the BGS shape is known, sequentiallyprobing it at two judiciously chosen frequencies on its twoslopes is enough to produce an estimate of δνB(t, z), whichis independent of P(z) at no additional hardware cost but atthe expense of halving the available sampling rate.

III. EXPERIMENTAL SETUP AND RESULT

The basic SA-BOTDA setup of [8], Fig. 2(a), was used inthis experiment, where the optical frequency of the pump pulseis fixed while that of the probe can be continuously (∼fewns) tuned using the Arbitrary Waveform Generator (AWG).Clearly, this setup is capable of repeatedly switching theprobe frequency from one slope (ν+(z)) to the other (ν−(z)).Moreover, the same setup can scan the whole BGS of the fiberto determine its shape, as well as the longitudinal distributionof its static BFS, ν̄B(z), as in the Fast BOTDA technique [9].The fiber arrangement of Fig. 2(b) was used to demonstrate theimmunity of the proposed method to variations in the pumppower. In the first two experiments attention was focused onthe 2m segment. First it was stretched to ν̄B = 10.925GHz,which is 65MHz away from that of the rest of the fiber,and then vibrated by an attached speaker at a frequencyof 55Hz. The inset of Fig. 3 shows the BGS of the 2mfiber section, measured with the setup of Fig. 2(a), using itsFast-BOTDA characteristics [9], with a pump pulse width of15ns (providing ∼1.5m of spatial resolution). The observed70MHz FWHM of the BGS is in line with the width ofthe short pump pulse [2]. The experimentally obtained shapeof the BGS was then used to calculate a family of RB

curves as a function of BFS deviations, δνB , for differentvalues of �ν = ν+-ν−. For the dynamic measurement, the�ν = 70MHz (γ± = 1), solid curve in Fig. 3, was chosen as

MOTIL et al.: PUMP-POWER-INDEPENDENT DSA 799

Fig. 3. A logarithmic plot of the gain ratio, RB (calculated from the measuredand normalized BGS, inset), as a function of BFS deviations for various valuesof �ν = ν+-ν−, ranging from 50 to 70MHz. Pump pulse width was 15ns.

Fig. 4. Two SA-BOTDA (natural logarithmic) gain measurements inducedby the 55Hz strain vibrations, taken at opposite slopes of the BGS (withBGS(ν+)≈BGS(ν−)) for a continues manual change of the pump pulse powerby more than 6dB (from (1) the gain is proportional to the pump power).

a compromise between sensitivity (the slope of the RB curve),the dynamic range and the measurement SNR, which is higherfor lower values of �ν [13]. The pump was pulsed at the rateof 1MHz. The Brillouin-amplified probe intensity, as measuredby the photo-detector, was sampled at 250MSamples/s by areal time oscilloscope with deep memory and divided by theno-pump probe values to determine the linear and then thenatural logarithmic gains. The interlaced results from alter-nating the probe frequencies between ν+ and ν− were time-demultiplexed and individually averaged over 500 realizationsof the polarization scrambler, resulting in an effective samplingrate of 1kHz {=1MHz/(500 averages)/(2 slopes)}. RB wasthen calculated as a function of time and was later translatedinto frequency deviations using the �ν = 70MHz curve ofFig. 3.

The frequency deviations were converted to strain valuesusing a previously obtained factor of 1000με/50MHz. Finally,the immunity of the DSA-BOTDA method to pump powerchanges was verified by manually varying the latter usinga polarization controller followed by an in-line polarizer,Fig. 2(a). Fig. 4 shows two conventional SA-BOTDA dataseries, experimentally obtained from the two probing frequen-cies. As expected, the results from the two slopes are out ofphase and their magnitudes, while almost equal, significantlydepend on the pump power, which spanned a range in excessof 6dB, as inferred from the ordinate values which are pro-portional to P(z). In contrast, the DSA-BOTDA results ofFig. 5 confirm the immunity of the technique to pump powervariations, as the measured strain variations amplitude remainsconstant while the pump power is not.

Fig. 5. The extracted 55Hz strain variations in the presence of >6dB changein the pump power, see Fig. 4.

Fig. 6. RB (deduced from the measured BGS, inset) with �ν = 70MHz andthe three selected working points: −10MHz, center (0MHz) and +10MHz.The inset also shows the locations of the probe frequencies, ν+ and ν−, onthe BGS for each working point.

Fig. 7. The three SA-BOTDA vibration (110Hz) data series for the threeworking points: −10MHz, center (0MHz) and 10MHz, for pump pulse powervariations of 3dB. Here, ν̄B of the 2m segment was 10.88GHz.

We next show that the DSA-BOTDA method works wellalso when γ± �=1 (i.e., when ν+ and ν− are not centeredaround the gain peak). Here, vibrations of 110Hz, with aslightly lower magnitude were applied to the 2m section andmeasured for three different combinations of {ν+, ν−}, subjectto �ν = ν+-ν− = 70MHz. These three choices of γ±are represented in Fig. 6 as three working points along the�ν = 70MHz ratio curve. Their frequency deviations fromthe center were: −10MHz (γ+≈1.285, γ−≈0.714), 0MHz(γ± = 1) and +10MHz (γ+≈0.714, γ−≈1.285). During eachmeasurement the pump pulse power was manually varied by3dB. In Fig. 7 the three SA-BOTDA data series are presentedfor the three working points. The extracted 110Hz strainvibrations are presented in Fig. 8. The strains measured aroundthe −10MHz, center (0MHz) and +10MHz working points are46±1με, 47.7±1με and 47.5±1με (rms), respectively. Again,the measured values appear to be independent of both thevariations in the pump pulse power and the chosen workingpoint along the RB slope.

800 IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 26, NO. 8, APRIL 15, 2014

Fig. 8. The extracted 110Hz strain variations. The strains measured aroundthe −10MHz, center (0MHz) and +10MHz working points were 46±1με,47.7±1με and 47.5±1με (rms), respectively.

Fig. 9. The three SA-BOTDA data series for the three measured segmentsas was measured using a 12ns pump pulse.

Fig. 10. The measured strain, which is clearly independent of pumpamplitude changes, measured at the 2m segment, 1.5m segment and the non-vibrating segment is 81±1.5με, 28±1με and 3.2±0.7με (rms) respectively.

Finally, the method’s ability to handle a Brillouinlongitudinally-inhomogeneous fiber was demonstrated. Toemulate such a fiber, the 2m and 1.5m fiber segmentsof Fig. 2(b) were stretched to two different BFS values of10.918GHz and 10.864GHz, respectively, while the BFS ofthe middle (non-vibrating) 13m fiber was 10.861GHz. The2m (1.5m) segment was vibrated at 100Hz (60Hz). As perthe protocol of [8] and based on the different BFS values ofthe fiber segments, two complex probe waves were generated,such that one of them followed the variation of ν+(z) whilethe other followed the ν−(z) profile. The measured gains atthe middle of the three fiber sections for each slope are shown

in Fig. 9, taken while the pump power was varied by ∼3dB.Fig. 10 depicts the calculated strain, obtained from Eq. (4),using the appropriate conversion factors. The results for thethree segments are clearly independent of the pump power.

IV. DISCUSSION AND CONCLUSION

We have successfully demonstrated the immunity of thedouble slope BOTDA method to significant pump powervariations. The technique employs the same hardware usedby the tailored-probe SA-BOTDA of [8], and maintainsall of its advantages. In particular, it can handle Brillouinlongitudinally-inhomogeneous fibers [8], where now the valuesof both ν− and ν+ = ν− + �ν should be tailored totrack their corresponding points on the z-dependent BGS.The sampling rate, though, is compromised by a factor of 2.Yet, very high sampling rates can be achieved, satisfyingmany practical dynamic applications. Here we demonstratedan effective sampling rate of ∼1kHz, mainly limited by theneed to average over the random polarization states generatedby the polarization scrambler. The spatial resolution of theDSA-BOTDA can be also greatly improved by employing oneof the available spatial resolution enhancement methods [2].

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