High spatial resolution distributed sensing in optical fibers by Brillouin gain-profile tracing

Transcription

1 High satial resolution distributed sensing in otical fibers by Brillouin gain-rofile tracing Tom Serber, 1,* Avishay Eyal, 1 Moshe Tur, 1 and Luc Thévenaz 2 1 School of Electrical Engineering, Faculty of Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel 2 Ecole Polytechnique Fédérale de Lausanne, Institute of Electrical Engineering, STI-GR-SCI Station 11, CH-1015 Lausanne, Switzerland *tomserb@ost.tau.ac.il Abstract: A novel BOTDA technique for distributed sensing of the Brillouin frequency in otical fibers with cm-order satial resolution is roosed. The technique is based uon a simle modulation scheme, requiring only a single long um ulse for acoustic excitation, and no subsequent interrogating ulse. Instead, the desired satial maing of the Brillouin resonse is extracted by taking the derivative of the robe signal. As a result, the satial resolution is limited by the fall-time of the um modulation, and the henomena of secondary echo signals, tyically aearing in BOTDA sensing methods based uon re-excitation, is mitigated. Exerimental demonstration of the detection of a Brillouin frequency variation significantly smaller than the natural Brillouin linewidth, with a 2cm satial resolution, is resented Otical Society of America OCIS codes: ( ) Fiber otics sensors; ( ) Scattering, stimulated Brillouin; ( ) Resolution. References and links 1. L. Zou, X. Bao, Y. Wan, and L. Chen, Coherent robe-um-based Brillouin sensor for centimeter-crack detection, Ot. Lett. 30(4), (2005). 2. A. W. Brown, B. G. Colitts, and K. Brown, Dark-ulse Brillouin otical time-domain sensor with 20-mm satial resolution, J. Lightwave Technol. 25(1), (2007). 3. Y. Koyamada, Y. Sakairi, N. Takeuchi, and S. Adachi, Novel technique to imrove satial resolution in Brillouin otical time-domain reflectometry, IEEE Photon. Technol. Lett. 19(23), (2007). 4. L. Thévenaz, and S. F. Mafang, Distributed fiber sensing using Brillouin echoes, Proc. SPIE 7004, 1 4 (2008). 5. W. Li, X. Bao, Y. Li, and L. Chen, Differential ulse-width air BOTDA for high satial resolution sensing, Ot. Exress 16, (2008). 6. V. Lecoeuche, D. J. Webb, C. N. Pannell, and D. A. Jackson, Transient resonse in high-resolution Brillouinbased distributed sensing using robe ulses shorter than the acoustic relaxation time, Ot. Lett. 25(3), (2000). 7. H. Naruse, and M. Tateda, Trade-off between the satial and the frequency resolutions in measuring the ower sectrum of the Brillouin backscattered light in an otical fiber, Al. Ot. 38(31), (1999). 8. R. W. Boyd, Nonlinear Otics, 2 nd. ed.(academic Press, 2003), Cha M. Nikles, L. Thévenaz, and P. A. Robert, Brillouin gain sectrum characterization in single-mode otical fibers, J. Lightwave Technol. 15(10), (1997). 1. Introduction Distributed strain and temerature sensing in otical fibers using Stimulated Brillouin Scattering (SBS) has been develoing recently in various beneficial asects. Particularly, much attention has been drawn to the objective of imroving the sensors' satial resolution, and several researchers have roosed and investigated novel techniques which bring this resolution into the single-centimeter range [1 5]. The common working rincile shared by all the novel techniques is the otically-induced re-excitation of an acoustic wave in the sensing medium, rior to the actual measurement rocess. This eliminates the roblem which limits the conventional Brillouin Otical Time-Domain Analysis (BOTDA) scheme's resolution, namely - the broadening and lowering of the Brillouin gain sectrum as the temoral duration of the uming ulse is reduced to values comarable with the acoustic (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8671

2 relaxation time [6]. Since the conventional scheme emloys the um ulse as both the generator of the SBS gain rocess and as the instrument used to sense it, the attemt to imrove satial resolution by shortening the um ulse diminishes the strength and the sectral selectiveness of the acoustic resonse, thus degrading the frequency resolution and the SNR of the sensor [7]. Contrastingly, the novel high-resolution techniques detach the role of writing the information from that of reading it, by emloying a re-um as the builder of SBS resonse, and then interrogating the resonse searately. This removes any constraints relating the duration of the interrogating ulse to the acoustic lifetime. The BOTDA sensing method roosed in this aer relies on re-excitation of the acoustic field in the fiber, much like the techniques mentioned above, but differs in the way the measurement itself is erformed and interreted. The method can be briefly described in the following manner: First, steady-state continuous-wave (CW) Brillouin gain is generated throughout the sensing fiber, and then, following the abrut shut-down of the um, the robe ower is monitored in the time domain. As shall be corroborated in this aer both theoretically and exerimentally, the derivative of the signal thus obtained directly reresents the satial rofile of the Brillouin gain along the fiber. 2. Working Princile of Method During the re-excitation hase, robe light roagating through the fiber exeriences SBS amlification at any oint characterized by a tuned local Brillouin frequency, i.e., one that matches the um-robe frequency difference. The way the robe's ower evolves along its ath (this we shall from here on refer to as the gain rofile ) is unknown to us, for we detect only its integral result uon the robe ower at the fiber end. Suosing, however, we were to nullify the gain occurring over the last centimeter of the fiber, while leaving the situation everywhere else as is; The difference between the ower detected in this state and the ower detected reviously, would reresent the gain contributed only by the last cm (as visualized in Fig. 1). By reeating this differential rocess from fiber end to beginning, we could reveal the comlete gain rofile of the robe. This measurement rocess is easily realized by raidly switching off the um ower: The falling edge function for the uming field traverses the fiber from its end to its beginning, and the Brillouin gain gradually vanishes with it. Fig. 1. Schematic illustration of the SBS gain rofiles exerienced by the robe light, for: (a) um ower exists along the entire length of the fiber, and (b) um ower dros to zero in the last section of fiber only. The gain which occurred along this section in situation (a) is detected in situation (b) as the difference dp. The essential idea behind this aroach is that once re-excitation SBS has been induced, no need arises for an interrogation ulse which actually backscatters uon the acoustic waves. Instead, one can simly extinguish the um, trace the gain rofile the robe has undergone during the re-uming, and deduce the desired information through elementary signal rocessing. This technique shall be from here on identified as Gain-Profile Tracing (GPT). 3. Theory We formulate the Brillouin interaction between the uming laser beam, and the counterroagating Stokes light, through these scalar couled wave equations [8]: (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8672

3 E 1 E γ eω = j Es ρ α E z v t 4ρ nc g Es 1 Es γ eωs + = j E ρ * α E z v t 4ρ nc g ρ ΓB γ Ω + j( Ω ω + ω ) ρ = j E E * t e B B s 2 s π va s (1) (2) (3) Here E, E, ρ stand for the comlex amlitudes of the um field, the Stokes field, and the s acoustic wave, resectively. ω, ω are the otical frequencies of the um and Stokes lightwaves, Ω B is the Brillouin frequency, s Γ B is the Brillouin natural linewidth, v a is the n, v, ρ, α are the acoustic velocity in the fiber, γ e is the electrostrictive constant, and lastly g 0 refractive index, otical grou velocity, density, and attenuation coefficient of the fiber. We make two aroximations common in the literature: First, considering the case of a weak Stokes light (comared to the ower of the uming beam), we assume the latter remains nondeleted throughout the fiber. Second, we omit the constant fiber loss, which is negligible over the rather short roagation distances tyical to the working regime of high-resolution sensing. Now, if the two counter-roagating lightwaves are launched into the fiber as CWs, after a time sufficiently long for the SBS rocess to reach steady-state amlification, the build-u of the ower of the Stokes light along the Brillouin interaction length is described by the following differential equation [8]: dp ( z) γ ω ( Γ 2) s e s B = GI Ps ( z) where G( z, ω ωs ) = dz nc vaρ0γ B ( ΩB ω + ωs ) + ( ΓB 2) (4) Here P s reresents the robe (Stokes) ower. The Brillouin gain is roortional to the intensity of the um light, denoted I, and the Brillouin gain coefficient G( z, ω ), which has dimensions of m/w. For fixed um and robe otical frequencies, G becomes a function of location only, and Eq. (4) is readily solved thus: z Ps ( z) = Ps 0 ex I G( z ') dz ' (5) 0 Here P s0 is the robe ower initially injected into the fiber at z= 0. We are interested in the Stokes ower observed by the hotodetector laced at the end of the interaction length, namely at z= L. Now we assume the um ower is switched off at the fiber end at some moment t= 0, and consider the dynamics immediately following. The um field in the fiber can be viewed as ste-function with its falling edge roagating towards z= 0. At any oint where E = 0, the source terms in both Eq. (2) and Eq. (3) are nullified, and the SBS rocess instantaneously vanishes regardless of the slow relaxation time of the acoustic honons. Hence, for any later moment t> 0, the Stokes wave front currently assing the um ulse s falling edge (at L v t ), will incur significant amlification only along the interval g 0 z L vgt. Provided that any effect of the remaining acoustic field on the robe light is negligible (an assumtion to be later justified by numerical simulation), we theorize that Eq. (5) can be generalized to reresent the ower arriving at the detector at any moment t> 0 by substituting the constant boundary of integration, with a time-deendent term: (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8673

4 detected 0 s0 L ( vgt / 2) P ( t > t ) = P ex[ I G( z ') dz '] (6) The 1/2 factor aearing in the variable term accounts for the round-tri time inherent to any scheme in which the um and robe counter-roagate. Intuitively, one can see that the monotonously-decreasing Stokes ower detected at the time eriod succeeding the um light shut-down, given in Eq. (6), is none other than a backwards trace of the satial rofile of amlification the robe has been undergoing under the CW-like um, rior to its extinction. Accordingly, the local sloe at any oint along this traced rofile directly describes the local Brillouin gain existing at that oint. Stated more rigorously - by taking the derivative, and after some rearrangement of terms, we arrive at: d[ln( Pdetected )] vg I vg vg = G( L t) G( L t) dt Hence, the derivative of the logarithm of the robe signal is linearly roortional to the Brillouin gain along the fiber, maed through the standard round-tri time relation. The satial resolution exected by this treatment is hyothetically infinite, because it assumes an ideal modulation scheme which shuts down the um ower instantaneously. In ractice, the um wave will have a finite fall-time, hence its falling edge - which serves as the fundamental interrogation element of the sensor - has a finite satial width. Therefore, the limiting arameter for the satial resolution achievable with the GPT technique is the fall-time of the um modulation (which we shall denote t fall ), through the relation: resolvable ( g 2) 0 fall (7) z = v t (8) Lastly, we recall the maing rocedure illustrated above takes lace at some secific difference of the um and robe otical frequencies, i.e., at a fixed ΩB ω + ωs value. Comlete knowledge of the Brillouin frequency at each sensing oint is obtained by discretely sweeing (referably the robe) frequency and reiterating the measurement rocess for every frequency oint, in order to reconstruct a good reresentation of the Brillouin gain sectrum. 4. Numerical Simulation Validation of the roosed method was sought by straight-forward numerical integration in the time domain of the fundamental SBS Eq. (1)-(3). The results indeed verified the redictions given by the theoretical discussion. A demonstration for a secific case of a sensing fiber 10m long, with a 20cm section distinguished from the background by having a Brillouin frequency offset of 30MHz located exactly at its middle, is given in Fig. 2 as a maing of the Brillouin gain vs. location and frequency. The demonstration also simulated an imlementation of the Dark Pulse technique of [2] uon the same test fiber. The fall-time of the GPT ulse was modeled to be 100s, and the dark ulse was simulated as a square ulse with a 100s width. This is a more than fair comarison, since in ractice, the um modulation scheme that would be able to roduce the modeled GPT ulse (i.e., one having a rise/fall time of 100s), could not roduce a square ulse of identical width, but only wider square ulses. The natural Brillouin linewidth was modeled as 30MHz. At the to of Fig. 2 are the results obtained using the roosed GPT method. Clearly, the sharness of details in the maing indicates high satial resolution, in agreement with the rediction of Eq. (8), which for the 0.1ns fall-time corresonds to 1cm. Furthermore, the 30MHz frequency difference at the offset section is correctly recovered, because the sectral rofile of the Brillouin resonse faithfully reresents the local natural Brillouin gain sectrum, both at the background fiber and at the offset fiber section. At the bottom of Fig. 2, the results of the dark ulse can be seen to exhibit similarly shar details with cm-order satial resolution, but the sectral behavior of the resonse at the offset section greatly deviates from the desired curve that should be (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8674

5 centered around the detuning value of 30MHz. This is due to the effect of the secondary echo which arises in the dark ulse scheme as an acoustic resonse to the event of the um ower's re-aearance, occurring at the end of the ulse. During the time the ulse asses a certain oint, the re-excited acoustic field there exeriences some relaxation. The recovery from this relaxation begins once the ulse has dearted that certain location, therefore it is manifested in the detected signal as a hantom Brillouin resonse emanating from adjacent oints in the fiber. Thus, the resonse aearing at the offset section for detuning values around zero can be seen to reresent not the true local Brillouin gain, but rather undesired contributions made by the neighboring sections, those belonging to the background fiber. In the GPT scheme, contrastingly, once the um ower vanishes from a certain oint it does not re-aear there, hence the slow relaxation of the acoustic field bears no effect uon the robe signal, and no secondary echoes exist. Fig. 2. Simulated Brillouin Gain maing, vs. location and frequency, for: (to) the roosed GPT method, (bottom) the referenced dark ulse method. The frequency axis is lotted relative to the background fiber, so that at zero frequency detuning, the SBS resonse of the background fiber is maximum. On the left side full maings are illustrated, indicated by color axis (in arbitrary units). On the right are cross-sections of these maings taken at two exemlary locations one at the offset fiber section, and one located outside this section. The dotted lines at the to right figure show the Brillouin resonse obtained by the GPT method at the same locations with a um modulation having a finite extinction ratio of 15dB. We conclude the numerical section by addressing the issue of the finite extinction ratio (ER) the um modulation would exhibit in any real-world imlementation of the roosed method. It can be exected that leakage of um light through the modulator after the switchoff would give rise to some undesired effects uon the sensing, since ideally, we would refer to have the SBS interaction cease comletely after the shut-down event. The feature of a finite (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8675

6 ER was added to the modeled um, and simulations were run for several scenarios with varying ER values. The results confirmed that for realistic values of the ER (over 10dB), deviations from the idealized theory resented earlier are very small. Such results, obtained for a simulated um-ulse of 15dB extinction ratio (commonly, even better values of db are achieved in ractice), are shown at the to right of Fig. 2 by the dotted lines. As can be seen, the deviation from the results obtained for an idealized um-ulse of infinite extinction (indicated by the solid lines) is minor, and the frequency at which the sectral resonse curve attains its maximum remains ractically the same. 5. Exeriment and Discussion The distributed Brillouin sensor configuration of Fig. 3 was used for exerimental validation. A samle fiber was reared by inserting (i.e., slicing) short segments of fiber with a Brillouin frequency of GHz, into a 4m long fiber differing by 13MHz (i.e., with Brillouin frequency of GHz). The light of the laser source, at 1550nm, was slit into two branches, serving as um and robe waves. The um wave was modulated by a squarewave signal featuring a long on time of 0.5µ s (long enough for the re-excitation of the SBS amlification in the fiber to reach a steady state), and a markedly short fall-time of 100s. The ulse reetition eriod was set to 2µ s (hence a 25% duty-cycle). The um light was amlified to 30dBm before being launched into the samle under test. The CW robe light, with an otical frequency smaller than that of the uming light by roughly the Brillouin frequency, was generated through intensity modulation (see [9] for examle) followed by suression of the carrier and the undesired sideband, erformed by the FBG. The robe light was then launched into the sensing fiber, with an initial otical ower of 6dBm, and detected at the other end (after exeriencing SBS gain) by a high-seed hoto-receiver. The role of the FBG located just before the receiver was to filter out some of the otical noise sources, such as the Rayleigh backscatter of the um light. A high bandwidth oscilloscoe monitored the detected ower, averaging each fiber trace 1000 times. The robe frequency was ste-swet across the relevant sectral range of 10.84GHz to 10.89GHz. Fig. 3. Exerimental setu. Both MZMs (Mach-Zehnder Modulators) are amlitude modulators. PC stands for Polarization Controller, EDFA for Erbium-Doed Fiber Amlifier, FBG for Fiber Bragg Grating. Results are given firstly for the case of a samle fiber with an inserted offset segment of 5cm length, roviding a reliminary demonstration of the sensing method's validity. Figure 4 illustrates the various stages of data acquisition and analysis erformed in order to obtain the results. At the to left are shown two exemlary fiber traces (i.e., time-domain robe signals detected immediately after the um shut-down event), as catured by the oscilloscoe. The dislay of these originally time-domain signals as functions of location is based uon the (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8676

7 g standard round-tri time relation z= v t 2. One trace was detected at a frequency shift intune with the Brillouin frequency of the background fiber, and the other was detected at the shift tuned to the Brillouin frequency of the offset segment. The sloes of the signals, which - according to the redictions of the theoretical discussion - reresent local Brillouin gain, can be seen to be large only at those locations where the fiber is tuned to the frequency shift. Fig. 4. Processed exerimental data for the case of a 5cm offset segment. To left fiber traces as acquired by the oscilloscoe, rior to any rocessing. The dashed lines mark the offset segment in the fiber. To right Brillouin gain maing obtained by trace differentiation, indicated by color axis (in arbitrary units). The frequency shift ste size is 0.5MHz. Bottom left sectral gain curves obtained by taking cross-sections of the gain maing at exemlary locations. Bottom right - final results, obtained by estimating er each location oint the center of the sectral gain-curve. Each oint reresents 0.5cm of fiber. Next, each trace was rocessed according to Eq. (7) in order to resolve the absolute Brillouin gain along the fiber, and by lacing the data from all the samled frequencies side by side, the maing of the Brillouin gain vs. both location and frequency shift was roduced - shown at to right. We note that the achievable satial resolution was limited by the given um-modulation scheme to 1cm (as dictated by Eq. (8) for a um fall-time of 100s), while the robe signals were acquired with a samling frequency considerably higher, secifically 14 oints/cm. Consequentially, had the signal differentiation of Eq. (7) been realized by straight-forward derivation, the results would reresent data samled with excessive bandwidth, and heavily burdened by noise (because the difference between any two adjacent samled oints would yield information at a satial frequency well over the maximal frequency we can hoe to resolve). Therefore, the differentiation was realized by erforming linear fits to the trace with a moving 2cm window, meaning that the local derivative at any location oint was taken to be the sloe of a linear fit done on a 2cm-long interval of the trace centered on that oint. Obviously, such rocessing is a form of smoothening, which overcomes noise at the exense of reducing satial resolution; the width of the moving (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8677

8 window reresents the smallest feature still resolvable in the rocessed data, but as this width is increased, noise is satially averaged over a longer interval, and is thus diminished. Data rocessing was attemted with different window sizes, eventually the 2cm window width was chosen as the otimal achievable comromise between the intent of maximizing the satial resolution, and the necessity of smoothening the data to allow the resentation of intelligible results. Moving on to the bottom left of Fig. 4, the rocess of evaluating the Brillouin frequency at any given location in the fiber is demonstrated. Two exemlary sectral crosssections of the gain maing are lotted, one taken at a oint located in the background fiber, the other taken at a oint within the offset segment. Clearly, the cross-sections give a good reroduction of the exected Brillouin Gain Sectrum at each location, in agreement with the simulation redictions shown in Fig. 2. Lastly, by fitting the sectral gain curve er each location oint to the desired bell-shaed model of Eq. (4), and identifying the central frequency of the fit as the local Brillouin frequency, the fiber's satial Brillouin frequency rofile was evaluated illustrated at bottom right. The next exeriment was conducted using the same set-u, and a samle fiber with a shorter inserted offset segment, of 2cm length, serving as a test-case for gauging the method's achievable satial resolution. The results are given in Fig. 5 in the same manner of Fig. 4, with the two demonstrative left-side lots omitted, since the methods of rocessing and analyzing the data have not changed and their exlanation need not be reeated. As visible in the gain maing on the left, the offset segment can still be clearly distinguished from the background fiber. In the Brillouin frequency rofile (right side of the figure) the 2cm offset is seen to be detected with, aroximately, the correct satial length, but the outline is quite smoothened at the borders (the transition between the two frequencies is gradual). This suggests that the lower bound of the satial resolution has been reached in the measurement. As mentioned earlier, the theoretical lower bound for the satial resolution is, for the emloyed um ulsing, lower about 1cm; however, further aroach of this bound would require some reduction of the detected noise ower, so as to allow data-rocessing using a smaller satial window. Such mitigation of measured noise can ossibly be achieved by further otimization of the otical filtering, or by lengthening the averaging erformed for each acquired trace. We further note that the mean error of the final Brillouin frequency measurement is 1-2MHz, as seen, in the satial rofile lotted on the right, as discreancies between the measured data and the re-known rofile. This error can robably be lowered by increasing the number of samled frequency oints, thus imroving the accuracy with which the sectral gain curves are obtained and analyzed rovided longer acquisition times can be tolerated. Fig. 5. Processed exerimental data for the case of a 2cm offset segment. Left - Brillouin gain maing obtained by trace differentiation, indicated by color axis (in arbitrary units). The frequency shift ste size is 2.5MHz. Right - final results, obtained by estimating er each location oint the center of the sectral gain-curve. Each oint reresents 0.5cm of fiber. (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8678

9 6. Conclusion In this aer we have roosed and demonstrated a novel BOTDA distributed sensor exhibiting cm-order resolution, based on a direct gain-rofile tracing scheme. The sensor utilizes the common re-excitation aroach, but is unique in the fact that no interrogating ulse which hysically interacts with the acoustic waves is launched. This allows the modulation of the um to be simlified to a single-transition shut-down, therefore bringing the lower bound for theoretically achievable satial resolution to the tyical fall-time of the modulating system. It should be noted, that the total sensing distance over which the roosed technique is alicable (although this subject has yet to be fully investigated in future work) can be redicted to be limited, since the need to generate Brillouin gain under CW-like conditions along the entire fiber gives rise to several undesired henomena, such as um deletion and sontaneous Brillouin scattering. On the other hand, this limiting feature is shared by most other sensing techniques based uon re-excitation of the acoustic field in the fiber, and can be overcome only by imlementing a ulse-air technique, where each fiber trace is roduced by subtracting two searate measured signals taken at the same frequency shift (see [4,5]). The advantage, therefore, featured by the roosed Gain-Profile Tracing technique, for the alicable range of sensing lengths, is the ability to measure the desired Brillouin resonse with just one trace taken er frequency oint. To the best of our knowledge, the results reorted above, where a Brillouin-frequency difference of 13MHz was resolved with a satial resolution of 2cm, demonstrate the best satial resolution reorted so far for a sensing scenario in which the resolved frequency searation is smaller than the natural Brillouin line width. Acknowledgments The research was artly suorted by the Israel Science Foundation and realized through a mission for Early Stage Researchers suorted by the Euroean COST Action 299 FIDES. (C) 2010 OSA 12 Aril 2010 / Vol. 18, No. 8 / OPTICS EXPRESS 8679