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Sweep-free Brillouin optical time-domain analyzer
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Sweep-free Brillouin optical time-domain analyzer
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SWEEP-FREE BRILLOUIN OPTICAL TIME-DOMAIN ANALYZER by Asher Maor A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (ELECTRICAL ENGINEERING) May 2015 Copyright 2015 Asher Maor ii Dedication To the Lubavitcher Rebbe And my family For their perpetual love, support and understanding iii Acknowledgements I find this part of my dissertation the most important, but at the same time most difficult and exciting to write. First of all, I would like to thank my dear advisor Prof. Alan E. Willner, who has been a great mentor whose vision goes beyond the science and engineering. I want to thank him for his patience, encouragement, inspiration, hints and advices. His insight into broad spectra of technical areas is what makes our Optical Communications team so succesfull. I want to thank Prof. Moshe Tur from the School of Electrical Enginerring at Tel Aviv University, who has been my unofficial second advisor. Despite that, he has been definitely a most important advisor in terms of the amount of time and energy spent during multiple-hours over-the-ocean conversations and over 24/6 online support. He is the advisor that every PhD student wishes for himself. Always ready to listen and to analyze together, sometimes at crazy night times. But he is more than just an advisor. He is a good friend, honest person with high moral standards and, at long last, MASHPIA. I am sincerely thankful to number of people who contributed to this success and made it possible for me to come to study in the United States: Brigadiere General (ret.) Shachar Kadishai, Col. (ret.) Avi Elisha, Dr. Igal Klein, Lt. Col. (ret.) Dr. Moshe Weiler and Dr. Jacob Nagel. I would like to thank all members of optical communication lab (OCLab) team during my stay at USC: Dr. Scott Nuccio, Dr. Jeng-Yuan Yang, Prof. Jian Wang, Bishara Shamee, Dr. Faruk Yilmaz, Dr. Irfan Fazal, Dr. Lin Zhang, Dr. Xiaoxia Wu, Dr. Yang Yue, Dr. Salman Khaleghi, Dr. Muhammad Reza Chitgarha, Dr. Hao Huang, Nisar Ahmed, Yan Yan, Morteza iv Ziyadi, Amanda Bozovich, Ahmed Almaiman and Yongxiong Ren. Thank to all of you for your support, for your valuable discussions, sleepless nights at the lab during final hours before submission. I wish you all the best in your careers. I would like to thank the great staff of the Electrical Engineering department at USC, Tim Boston, Anita Fung, Gerrielyn Ramos, and especially, Diane Demetras, our academic advisor, who was always very helpful, kind with enormous patience to answer all kinds of questions starting from the day I applied to university until the day of my defense. In addition, I would like to extend my thanks to Tracy Charles and Jennifer Gerzon from the USC Viterbi School of Engineering for their extreme help with tuition rewards for last two and a half years of my Ph.D. studies. I want to thank all my friends in a Chabad jewish community of Los Angeles among those are Rabbi Yosef Gurevitch and his family, Rabbi Asher Yemini and his family, Rabbi Shmuel Dahan and his family, Rabbi Zohar Eizenberg and his family, Rabbi Shmuel Dovid Cohen and his family, Rabbi Chaim Leibovitch and his family, Rabbi Meir Avitan OBDM and his family. I would like express special thanks to Rabbi Amitai Yemini and his family, the SHLIACH of the Lubavitcher Rebbe to Los Angeles and Rabbi Dov Wagner and his family, the SHLIACH of the Lubavitcher Rebbe to USC. Finally, I would like to thank my family. I am thankful to my wife Shaina, whose patience and love gave me the possibility to accomplish my studies. Her support was crucial for my success. I would like to mention my kids Nir, Adam, Shneor Zalman and Itamar Berel that were just there for me. I would also like to thank my mom Maya and my siblings Albert and Nona for their support. This dissertation is the fruit of my family’s sacrifices. Here, at this v point, I would like to apologize for the times spent apart and hope to compensate that in the near future. Unfortunately, my father Arum is not here with us but I am sure and confident that he is very proud of me. We acknowledge the support of the Defense Security Cooperation Agency (DSCA) under contracts DSCA-4440145260 and DSCA-4440365063. vi Table of Contents Dedication ............................................................................................................... ii Acknowledgements .................................................................................................... iii List of Figures .......................................................................................................... viii Abstract ............................................................................................................. xiii Chapter 1 Introduction ........................................................................................ 22 1.1 Electromagnetic waves ......................................................................... 22 1.2 The origin of nonlinear polarization ..................................................... 23 1.3 Qualitative description of Brillouin scattering ..................................... 25 1.4 Optical fiber sensors ............................................................................. 32 1.5 Distributed sensing using stimulated Brillouin scattering process ....... 35 Chapter 2 SBS-based fiber optical sensing using frequency domain simultaneous tone interogation ......................................................... 38 2.1 Introduction .......................................................................................... 38 2.2 Description of method .......................................................................... 39 2.3 Experimental setup ............................................................................... 42 2.4 Results and discussion .......................................................................... 46 2.5 Sweep-free Brillouin optical distributed sensing ................................. 51 2.6 Conclusions .......................................................................................... 53 Chapter 3 Analytical investigation of the Brillouin interaction between multiple pulsed pump tones and probe waves ................................. 54 3.1 Introduction .......................................................................................... 54 3.2 The analytical method .......................................................................... 54 3.3 Results .................................................................................................. 60 3.4 Conclusions .......................................................................................... 62 Chapter 4 Sweep-free distributed Brillouin time-domain analyzer (SF- BOTDA) ............................................................................................... 63 4.1 Introduction .......................................................................................... 63 4.2 Description of the method .................................................................... 64 4.3 Experimental setup and results ............................................................. 66 4.4 Discussion and conclusions .................................................................. 71 Chapter 5 Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer and sloped assisted FBG sensing ........................................................................................ 73 5.1 Introduction .......................................................................................... 73 vii 5.2 Experimental setup ............................................................................... 74 5.3 Results and discussion .......................................................................... 78 5.4 Conclusions .......................................................................................... 81 Chapter 6 Spatial resolution improvement of sweep-free Brillouin optical time-domain analyzers ....................................................................... 82 6.1 Introduction .......................................................................................... 82 6.2 Concept and principle ........................................................................... 83 6.3 Experimental setup and results ............................................................. 85 6.4 Summary ............................................................................................... 88 Chapter 7 Extending the dynamic range of sweep-free Brillouin time-domain analyzer ............................................................................................... 89 7.1 Introduction .......................................................................................... 89 7.2 Description of original method and its dynamic range limitation ........ 89 7.3 Extending the dynamic range of SF-BOTDA ...................................... 95 7.4 An experimental example ..................................................................... 99 7.5 Discussion ........................................................................................... 102 7.6 Summary ............................................................................................. 105 7.7 Appendix ............................................................................................ 106 Chapter 8 Performance analysis of the sweep-free Brillouin optical time- domain analyzer ................................................................................ 112 8.1 Introduction ........................................................................................ 112 8.2 Simulation ........................................................................................... 112 8.3 Results ................................................................................................ 114 8.4 Summary ............................................................................................. 117 Chapter 9 Differential pulse-width pair BOTDA using simultaneous frequency domain interrogation ..................................................... 118 9.1 Introduction ........................................................................................ 118 9.2 Concept ............................................................................................... 119 9.3 Experimental setup and results ........................................................... 120 9.4 Summary ............................................................................................. 121 Conclusions ............................................................................................................ 123 Bibliography ........................................................................................................... 127 References ............................................................................................................ 134 viii List of Figures Figure 1.1 Interaction picture of SBS interaction .......................................................... 25 Figure 1.2 (a) Annihilation of the pump photon followed by the generation of the phonon and scattered photons (b) momentum conservation for k L=k S+k 0. ......... 29 Figure 1.3 Extrinsic vs. intrinsic types of OFS .............................................................. 33 Figure 1.4 Schematic block diagram of OTDR ............................................................. 34 Figure 1.5.Schematic block diagram of MIFOS ............................................................ 35 Figure 2.1. BGS reconstruction: (a) using the conventional probe frequency sweeping technique; and (b) using the proposed multiple tones, sweep-free concept................................................................................................................. 39 Figure 2.2. Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; ISO: optical isolator; DET – detector; FBG: fiber Bragg grating; MW AMP: microwave amplifier; AWG: arbitrary waveform generator; RFSA: RF spectrum analyzer; OSA: optical spectrum analyzer .......................................................... 43 Figure 2.3 (a) BGS measurement of lower 5 probe tones from 5 pump tones. (b) BGS of 5 tones, superimposed on one another, after proper shifting of their center frequency. Lorentzian shape fit showing FWHM of 28.6MHz and BFS of 10887 MHz. ............................................................................................ 45 Figure 2.4 (a) Pump tones as they enter the fiber. Intermodulated products exist having optical power less than –15 dBm. (b) Probe tones as they enter the fiber.Two sidebands around optical carrier. (c) Lower sideband probe tones. Intermodulated products exist but having optical power less than –52 dBm ...... 48 Figure 2.5 BGS reconstruction using 20 frequency tones at (a) 15 O C, (b) 25 O C (c) 35 O C, (d) BFS variation over the measured temperature range ......................... 50 Figure 3.1 Frequency domain arrangement of SBS interaction for two pump and probes tones ......................................................................................................... 56 Figure 3.3 The calculated BGS as function of detuning parameter for CW probe tones (solid curve). The dots represent experimental results of scanning a pair of CW probe tones against a pair of pump tones. The frequency separation between the members of each pair was 200MHz. .............................. 61 Figure 3.4 (a) The calculated SBS gain as a function of the frequency spacing (b) Measured SBS gain as a function of the frequency spacing ................................ 62 ix Figure 4.1 BGS reconstruction using the newly proposed sweep-free concept accomplished in a single measurement using multiple (N) pump and probe tones. Here the pump spacing is 100MHz, while the additional incremental spacing of the probe tones is MHz 3 Probe . ........................................................ 64 Figure 4.2 Sequential pump launching. For N multiple tones, the pump waveform comprises a sequence of T–wide, N sub-pulses, each riding on a different frequency tone. As described in Sec. 4.3, the figure describes the RF waveform, which is then upconverted to an optical compound pulse. (a) Sub-pulse amplitude vs. time; (b) Sub-pulse frequency vs. time.(c) A spectrogram of the compound optical pulse used for sequential pumping. The laser frequency is located at the center of the horizontal optical frequency axis ...................................................................................................... 65 Figure 4.3 Experimental setups: (a) As used in [9]; and (b) The improved version. MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: Polarization scrambler; ISO: optical isolator; DET – detector; FBG: fiber Bragg grating; RF AMP: radio- frequency amplifier; MW AMP: microwave frequency amplifier; AWG: arbitrary waveform generator; RTAS: real-time acquisition system; OSA: optical spectrum analyser; FUT: fiber-under-test. .............................................. 66 Figure 4.4 (a) Spectrogram of the Brillouin return from an essentially uniform 20m-long fiber, showing the time evolution of each of the 20 optical tones used. The width of each pump sub-pulse was 50ns and the center of the tones (i.e., the frequency of the microwave source in Fig. 4.3) was chosen to coincide with the fiber BFS. (b) Reconstruction of the BGS using 20 frequency tones with 5-m resolution with no stretching applied to the fiber. The distance axis is obtained from the temporal axis of using: Position=Group-velocity x Time/2 ...................................................................... 68 Figure 4.5 (a) Reconstruction of the BGS of a 2-km FUT, comprising two 1km fiber segments with different BFS, spliced together at the position 1000m. 30 frequency tones, spanning 90MHz, were used with a sub-pulse width of T=500ns, resulting in frequency and spatial resolutions of 3MHz and 50m, respectively. The zero frequency is 10877MHz (b) Results of classical BOTDA also with 3MHz sweeping step. (c) Reconstruction of the BGS using 20 frequency tones with 5-m resolution with the central 4-m of the fiber being stretched ............................................................................................ 71 Figure 5.1 Experimental setups: (a) MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: Polarization controller; SC: Polarization scrambler; ISO: Optical isolator; DET1: detector; FBG1: Fiber Bragg grating filter; RF AMP: radio-frequency amplifier; MW AMP: Microwave frequency amplifier; AWG: Arbitrary waveform generator; SCOPE: Real- time acquisition system; OSA: Optical spectrum analyser; FUT: fiber- x under-test; SP: Speaker, ST2: Translation stage. (b) BBS: Broadband source; TOF: Tunable optical filter; C1: capacitor. ............................................. 74 Figure 5.2 Transmission characteristics of TOF2 showing a 3dB bandwidth of ~160GHz. ............................................................................................................ 76 Figure 5.3 The detector voltage when the speaker membrane is driven by a 100Hz signal before (a) and after (b) RC filtering. ......................................................... 77 Figure 5.4 The time-domain results of single tone input as measured at 80 and 120Hz (a,d) before speaker (b,e) using FBG, (c,f) using SF-BOTDA after 200Hz low-pass digital filtering. The time-domain results of FM modulated 120Hz signal with 40Hz span as measured (g) before speaker, (h) using FBG, (h) using SF-BOTDA and digitally processed. .......................................... 79 Figure 5.5 The frequency-domain results for 80Hz, 120Hz and multitone excitations (a,d,g) before speaker (b,e,f) using FBG, (c,f,i) using SF- BOTDA after 200Hz low-pass digital filtering. (j) The results of measuring 400Hz single tone using SF-BOTDA and output of speaker with calibrated microphone. ......................................................................................................... 80 Figure 6.1 Simulation results: (a) The original 6-tone signals; (b) FFT processing of a 10nsec time window; (c) FFT processing of a 90nsec window, made of nine-10nsec concatenated sectionsfrom nine consecutive different traces. ......... 85 Figure 6.2 Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: polarization scrambler; ISO: isolator; DET: detector; FBG: fiber Bragg grating; AWG: arbitrary waveform generator; OSA: optical spectrum analyzer. ........................ 86 Figure 6.3 Experimental results: (a) The measured tones after an FFT of a 20nsec window; (b) The measured tones after an FFT of a 180nsec window made of nine-20nsec concatenated windows from nine consecutive traces; (c) The reconstructed BGS along 30m optical SMF fiber showing the variations of the BFS along the fiber. ....................................................................................... 88 Figure 7.1 Sweep-free Brillouin probing using the simultaneous launching of multiple pump and probe tones. (a) N pump (=25) pump tones (Eq. (1a), magenta stems topped by circles, spaced by 100MHz) are launched into the fiber against N probe (=20) probe tones (Eq. (1(b), blue stems topped by diamonds), spaced by 95MHz (i.e., 5MHz smaller than that of the pump tones) and overall downshifted in frequency from the pump tones by a fixed frequency difference, BFS 0, chosen to be close to the average BFS of the fiber under study (note the different horizontal scales for the two stem plots); (b) The resulting cumulative Brillouin-induced gain spectrum arbitrary units ([A.U.]), generated by the pump tones together with its sampling by the probe tones. Here the actual BFS is assumed to be equal to BFS 0 and we note that each probe tone samples the BGS generated by the xi pump associated with that probe tone: e.g., the middle (11 th ) probe tone, circled at its bottom, samples the BGS originated from the middle (13 th ) pump tone, bolded and circled at top; (c) Plotting the sampled gains (Diamonds) against {h(i)} of Eq. (3) results in an approximate reconstruction of the common gain BGS n( ). More importantly, fitting the upper part of the data to a parabola (not shown) produces an excellent estimation of the zero shift from BFS 0. A Lorentzian, precisely centered at the true BFS=BFS-BFS 0 and having the same height and center as the fitted parabola, is also shown in (c). The reconstructed spectrum is a bit wider than the true Lorentzian, due to the influence of neighboring peaks in (b), but shares the same peak location. (d) and (e) are the same as (b) and (c) but with BFS 0+27.5MHz. Again, the estimation of the 27.5MHz shift from BFS 0 is quite good: 27.49MHz. ........................................................................... 90 Figure 7.2 Erroneous BGS reconstruction for BFS values which are larger than BFS 0 by more than half the pump tone spacing. Here the probe tone spacing is 95MHz as in Fig. 7.1. Left column: BFS=BFS 0+427.5MHz; Right column: BFS=BFS 0+372.5MHz. While the BFS values here are distinctly different from those of Fig. 7.1, they are erroneously estimated as very close to their values in Fig. 7.1, namely: 27.42MHz and -27.5MHz instead of 427.5 and 372.5MHz. The source of this ambiguity is the fact that the probe tones sample Brillouin gains other than those associated with them. Thus, for BFS=427.5MHz (Left column) the 11th (counting from the left, circled at its bottom) probe tone does not sample the Brillouin gain induced by its corresponding pump (the 13 th , bolded one, circled at top), as in Fig. 7.1, but rather by the (13+4) th pump tone. A similar argument holds for BFS=372.5MHz. ............................................................................................... 92 Figure 7.3 BGS reconstruction of ∆BFS=427.5MHz, using 3 pump spacings for BFS values within the dynamic range defined by Eq. (5), which is ±450MHz (around the pre-chosen BFS 0) for the spacing choice of (a=d) MHz 100 0 pump , (b) MHz 91 pump , and (e) MHz 109 pump . Once the spectral shifts of the three measurements are estimated from (c) and (f) as 42 . 27 0 shift , 47 . 27 shift , and 45 . 8 shift (all in units of MHz), n 0 and the ∆BFS can be uniquely estimated, from either the additional sampling at pump or at pump , or from both, see text. Here only the results of the sampling at pump are valid. Indeed, while the 11th probe samples the gain of the (13+4) th pump in both (a=d) and (e), it samples the gain of the (13+5) th pump in (b). ................................................. 96 Figure 7.4 Experimental block diagram: MZM: Mach-Zehnder electro-optic modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; ISO: optical isolator; AWG: arbitrary waveform generator; FUT: fiber-under-test. ................................................................................................... 99 Figure 7.5 Experimental demonstration of the dynamic range extension concept using three different pump tone spacings of 100, 91 and 109 MHz. 16 probe xii tones are used (the 17-th probe tone periodically repeats the effect of the first one). The estimated peak locations are indicated by short vertical lines and their frequency locations also appear in the figure). Based on these estimates, Lorentzian curves have been added. ................................................. 101 Figure 7.6 The dependence of 0 n (blue: solid), est n 0 (red: dashed) and est n 0 (green: dashed-dotted), Eq. (A4), on BFS for the data of the pump tone spacings used in Fig. 7.4: MHz 100 0 pump , MHz 91 pump , and MHz 109 pump . The vertical arrows denote the allowed dynamic range of Eqs. (6), MHz 450 | | BFS , while horizontal arrows point at the maximum allowed values for max n ( 4). ........... 109 Figure 8.1. Sweep-free BOTDA system simulation scheme block diagram ............... 114 Figure 8.2 BFS error results (unless otherwise noted, pump spacing 100MHz and Brillouin linewidth of 28MHz are assumed, the number of tones is 20, the CNR is 50dB, the granularity is 3MHz, the spatial resolution is 4m and no averaging is assumed): (a) BFS error vs. CNR for different granularity values; (b) BFS error vs. CNR for different spatial resolutions; (c) BFS error vs. Granularity for different number of tones; (d) BFS error as a function of the location of BFS within the dynamic range; (c) BFS error vs. the Brillouin gain for different CNR values; and (f) vs. the number of averages. .. 114 Figure 9.1 (a) The concept of speeding up the differential pulse-width pair (DPP) Brillouin sensing technique by replacing the sequential launching of the two different-width pulses with their simultaneous launch, letting each pump pulse to ride on a different optical carrier. Two probe tones, equally spaced from their corresponding pump tones by an arbitrarily chosen ∆ , individually interact, via the Brillouin effect, with the two pump pulses. Each pump pulse gives rise to a Brillouin gain signature of the fiber. Finally, the difference between these two (logarithmic) gain signatures is related to the local strain/temp with a spatial resolution, which is directly related to the difference between the widths of the two pump pulses (50-47=3ns in the figure, corresponding to 30cm of spatial resolution). (b) Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: Polarization scrambler; ISO: optical isolator; DET: detector; FBG - fiber Bragg grating; AWG: arbitrary waveform generator; OSA: optical spectrum analyser. ..................................... 119 Figure 9.2 Experimentally obtained 30-cm spatial resolution, using (a) the original DPP technique [2]; (b) sequential pump pulsing at two different frequency carriers; (c) simultaneous pump pulsing at different frequency carriers; .......... 121 Figure A1. Critical research challenges in distributed optical fiber sensors. ............... 123 xiii Abstract Brillouin-based optical fiber sensing is a promising technology for the monitoring of many types of structural and environmental changes. Sensors based on this technology use the Brillouin nonlinear process [1] in which acoustic phonons in the fiber either spontaneously scatter a forward propagating optical wave (called 'pump') into a backward propagating wave (called 'probe'), or, alternatively, mediate, via a stimulated interaction, power transfer between counter propagating waves ('pump' and 'probe'). In either case, the returning light has a characteristic frequency shift (from that of the pump), which varies with many types of changes in the propagating medium, such as temperature and mechanical stress. Therefore, this Brillouin frequency shift (BFS) can provide information on the surrounding temperature and strain distributions along an optical fiber. There are several major schemes for Brillouin-based optical fiber sensors, including Brillouin optical time domain reflectometers (BOTDRs) [2]-[3], Brillouin optical time domain analyzers (BOTDAs) [4]-[6], and Brillouin optical correlation-domain analyzers (BOCDAs) [7]-[8]. BOTDRs mostly use a single-ended implementation, where a pump wave gives rise to a spontaneous Brillouin back-scattered probe, whose optical frequency is measured via a variety of techniques. The optical power level of the backscattered wave is weak, requiring averaging of multiple measurements (i.e., integrations) in order to reach a sufficiently high signal-to-noise ratio (SNR). This may cause longer sensing times of up to several minutes [9]- [11]. BOTDAs sensors rely on the stimulated Brillouin scattering (SBS) process in which two counter-propagating pump and probe waves generate acoustic waves in the fiber, which then transfer optical power from the pump to the probe if the latter frequency is downshifted from xiv that of the pump by the BFS. Since the emerging probe is typically stronger in BOTDAs than in BOTDRs, shorter sensing times are achievable. Finally, BOCDAs are SBS-based sensors in which counter-propagating probe and pump waves produce spatially correlated interference peaks along the fiber to dramatically improve the spatial resolution. BOCDAs can also sense the dynamic variation of the environmental changes up to 1 KHz [12], but this is typically limited to local stimulation along fiber sections. In many Brillouin-based sensors, e.g., BOTDAs, the evolution of temperature/strain induced BFS is determined from consecutive recordings of the whole Brillouin gain spectrum (BGS). This Lorentzian-shaped spectrum, having a width of ~30MHz (FWHM) at 1550nm in a standard single mode optical fiber (SMF), must be measured as densely as the application requires. Typically the sensitivity of the BFS is 1MHz/ 0 C and 500MHz/(1% strain)[13]. Classically, the BGS is measured by sweeping the optical frequency of either the pump or the probe, over the entire BGS. Since the probe signal is quite weak, especially when long (tens of kilometers) fibers are interrogated, averaging over multiple measurements is required at each frequency point, thereby significantly slowing down the frequency scanning rate and the overall measurement speed. Consequently, such implementations may have difficulty in resolving fast, dynamic changes in the measurands. Recently [14], a technique was introduced to measure fast changes in a BGS but with limited dynamic range. Critically valuable characteristics of an ideal sensor would include: (a) high-resolution 3-D spatial localization and directionality of the disturbance over large distances, and (b) the ability to determine false alarms with high confidence. In general, there has been keen interest in using optics to achieve these goals due to the inherent high frequency of the optical wave, xv the ability for the optical wave propagation to be quite sensitive to changes, and the low loss and large distance capability of optical fiber. As mentioned earlier, one of the major disadvantages of distributed optical fiber sensing is the deficiency in time/frequency information. Common methods scan each frequency of the Brillouin reflected light to determine the center frequency of the shift and require several measurements to yield a single fiber strain value. This greatly limits the collection time of the strain distribution and makes it difficult to detect time varying disturbances. For successful detection and reduction of false positives, it is critical to be able to capture all dynamic events by rapidly retrieving the data set and processing the results. In addition, disturbance localization away from the sensor itself is very limited and usually determined only by spatial resolution along the optical fiber. One key advantage of enabling dynamic event detection is the possibility to measure how an event impacts the fiber in short time scales. In this dissertation, we discuss methods for utilizing the improved techniques we have developed to provide dynamic sensing and enable a large reduction in false positives and accurate localization of disturbance events. This research introduces a novel Brillouin fiber optical sensor which is capable to identify the dynamic signature of different signature of different disturbances in a distributed way in order to reduce false alarms. This novel concept, called SF-BOTDA (for Sweep-Free BOTDA), which retains all the advantages of the classical BOTDA technique together with the potential to be much faster. During our research, we demonstrated the basic concept, where multiple pump and multiple probe tones distributedly pair-wise interact via the Brillouin effect in the fiber to simultaneously probe different parts of multiple replicas of the fiber BGS. Once the tones are detected, the Brillouin amplification experienced by each of them can be xvi determined, resulting in an accurate reconstruction of the BGS, and, consequently, in the determination of the BFS. We have also shown how the technique can be applied to a distributed sensing faster than classical BOTDA by a factor, which could be as high as the number of simultaneous tones used. The idea of ‘sequential pulse launching’ was introduced, where the multiple pump pulsed tones are sequentially launched into the fiber, thereby avoiding nonlinear interactions among them, as well as overloading of the optical amplifiers. In Chapter 1, we overviewed some fundamental electromagnetics theory relevant to the Brillouin sensing. Here, we mentioned several different approached used today in optical fiber sensors field. In Chapter 2, a new multiple-tone concept was presented, where it is possible to interrogate complex data in order to reconstruct Brillouin gain spectra using a single measurements by accurately choosing pumps and probes frequencies. Initial experimental data for continuous-wave case was shown proving the ability to perform similar to state-of-the-art method but potentially much faster. The extension of the method to a pulsed case and, as a result, distributed sensing, has been described. In Chapter 3, the case of the Brillouin interaction between two probe waves propagating against two modulated pump waves was analytically investigated. This investigation is motivated by the sweep-free BOTDA technique, where, to increase sensing speed, the Brillouin gain spectrum is simultaneously interrogated by many probe-pump pairs. It was shown both analytically and experimentally that crosstalk talk becomes negligible only when the pump tones separation is much larger than the width of the Brillouin gain spectrum. The slowly varying envelope approximation, non-moving phonons, the undepleted pump xvii approximation and small Brillouin gain were assumed, resulting in a first order perturbation analysis for the acoustic and probe waves. Results include the Brillouin gain spectrum, which was compared with a corresponding experiment. In Chapter 4, a sweep-free optical time-domain method for distributed Brillouin sensing is proposed, having the potential for fast dynamic strain measurements. In this implementation of the method, multiple probe waves with carefully chosen optical frequencies simultaneously propagate in the fiber against an equal number of sequentially-launched, short pump pulses of matching frequencies, where each of pump-probe pair replaces one sweeping step in the classical BOTDA technique. Experimentally, distributed sensing is demonstrated with a spatial resolution of a few meters. It was shown that there is not more need for the classical step-by-step mapping of the fiber BGS. This proposed method is potentially faster than classical BOTDA by a factor equal to the number of pump-probe pairs used for the BGS reconstruction, since each pair replaces one sweeping step in the classical technique. In Chapter 5, a fast reconstruction of the whole Brillouin gain spectrum is experimentally demonstrated using sweep-free Brillouin optical time-domain analysis. Strain variations with the frequencies up to 400Hz are spectrally analyzed, achieving strain sensitivity of 1 microstrain per root Hz at a sampling rate of 5.5kHz and a spatial resolution of 4m. The results favorably compared with fiber Bragg grating sensing. In Chapter 6, we presented a new implementation of our sweep-free Brillouin optical time-domain technique, involving a novel sequencing of the probe signal with respect to the pump multi-tone pulse, together with advanced post-processing, which removes the trade-off between the required spatial resolution and the inter-tone spacing, allowing the method to xviii achieve spatial resolutions comparable to those of classical BOTDA without sacrificing tone granularity. A spatial resolution of 2m is experimentally demonstrated using around 100MHz inter-tone spacing. In Chapter 7, it was shown that while sweep-free Brillouin optical time-domain analysis (SF-BOTDA) replaces the sequential frequency scanning of classical BOTDA by parallel interrogation of the fiber-under-test using the simultaneous interaction of multiple pump tones with counter-propagating multiple probe tones, its dynamic range is limited to approximately the pump tone spacing, which is of the order of 100MHz. Here, in-depth analysis of our method was performed to significantly extend the dynamic range to the GHz regime. Based on sequential interrogation with up to three sets of multiple tones, each having a different frequency spacing, this method provides a major speed advantage over the classical BOTDA in spite of the use of three sets of tones. With this development, which does not require any additional hardware, SF-BOTDA offers distributed sensing of optical fibers over practical dynamic ranges of strain/temperature variations, with the potential to become one of the fastest sensing techniques. In Chapter 8, the impact of several key parameters of swee-free Brillouin optical time- domain analzer on the BFS error was quantitatively investigated. Once the dynamic range is determined, the pump frequency spacing can be chosen and then the other parameters can be found as suggested. The number of tones times the pump frequency spacing should be smaller than the Brillouin frequency shift. In simple implementations, the dynamic range is on the order of the pump spacing. A too large pump spacing dictates a small number of tones and a large BFS error, while a too small spacing requires a large number of tones to cover a given dynamic, an experimentally difficult requirement. Initial measurements indicated that it is not xix too difficult to achieve CNR better than 45dB. Looking back at our research, SF-BOTDA can offer high sensing speed and low BFS error for spatial resolutions of a few meters. In Chapter 9, multiple-tone method with differential pulse-width pair BOTDA technique were combined together. A novel modification of the differential pulse-width pair technique, where the two pump pulses of slightly different widths, are simultaneously transmitted on different optical carriers, thereby offering a two-fold increase in the sensing speed. The simultaneously propagating two pump tones do not give rise to any crosstalk in the fiber, as long as their frequency separation is larger than a few BGS widths. Here, the BGSs at only two frequencies (10.84 and 10.88 GHz) were sampled using the same experimental setup allowing continuous scanning of the two BGSs. Publications wiitten during this research: "Performance analysis of the sweep-free Brillouin optical time-domain analyzer (SF-BOTDA)", Asher Voskoboinik, Alan E. Willner and Moshe Tur, at OFS201 23rd International Conference On Optical Fiber Sensors, in Santander, Spain. 2014 "Differential pulse-width pair BOTDA using simultaneous frequency domain interrogation", Asher Voskoboinik, Ahmed Almaiman, Zhyong Zhang, Alan E. Willner and Moshe Tur, in CLEO 2013, San Jose, USA 2013 "Analytical investigation of Brillouin scattering in the presence of multiple pump and probes", Asher Voskoboinik, Alan E. Willner and Moshe Tur, in European Workshop on Optical Fibre Sensing, Krakow, Poland 2013 xx "Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer and sloped-assisted FBG sensing", Asher Voskoboinik, Dvora Rogawski, Hao Huang, Yair Peled, Alan E. Willner, Moshe Tur, Optics Express, Vol. 20, Iss. 26, pp. B851-B886 (2012) "Sweep-free Brillouin time-domain analysis (SF-BOTDA) with improved spatial resolution ", Asher Voskoboinik, Alan E. Willner, Moshe Tur, in 22 nd Conference on Optical Fiber Sensors, Beijing, China, 2012 "Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer", Asher Voskoboinik, Yair Peled, Hao Huang, Alan E. Willner, Moshe Tur, in ECOC, Amsterdam, The Netherlands, 2012 "Sweep-free Brillouin optical time-domain analyzer with extended dynamic range ", Asher Voskoboinik, Amanda Bozovitch, Alan Willner, Moshe Tur, in CLEO-2012, San Jose, USA, 2012 "Fast and distributed dynamic sensing of strain using Sweep-Free Brillouin Optical Time Domain analysis (SF-BOTDA)", Asher Voskoboinik, Yair Peled, Alan Willner, Moshe Tur, in APOS, Sydney, Ausralia, 2012 "Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA) ", Asher Voskoboinik, Omer F. Yilmaz, Alan E. Willner, Moshe Tur, Optics Express, Vol. 19, Iss. 26, pp. B842-B847 (2011) "Nondegenerate four-wave-mixing-based radio frequency up/downconversion using a parametric loop mirror", Hao Huang; Xiaoxia Wu; Jian Wang; Jen- Yuan Yang; Asher Voskoboinik; Alan Willner, Optics Letters, Vol. 36, Iss.23, pp.4593-4595, 2011 xxi "All optical reconfigurable radio frequency up/down-conversion using optical parametric loop mirror", Hao Huang; Xiaoxia Wu; Jian Wang; Jen-Yuan Yang; Asher Voskoboinik; Alan Willner, in ECOC, Geneva, Switzerland, 2011 "Sweep-free distributed Brillouin sensing using multiple pump and probe tones", Asher Voskoboinik, Omer F. Yilmaz, Alan E. Willner, Moshe Tur, in ECOC, Geneva, Switzerland, 2011 "Frequency domain simultaneous tone interrogation for faster, sweep-free Brillouin distributed sensing", Asher Voskoboinik, in 21st International Conference on OpticalFiber Sensors, Ottawa, Canada, 2011 "SBS-Based Fiber Optical Sensing Using Frequency-Domain Simultaneous ToneInterrogation", Asher Voskoboinik et. al., Journal of Lightwave Technology, Vol. 29. Issue 11, 2011 22 Chapter 1 Introduction 1.1 Electromagnetic waves The light wave interaction with surrounding media is described by Maxwell’s equations [1]: ) 1 ( ) 1 ( b t E B a t B E where E and B are electric and magnetic fields, respectively, and ε and μ are media permittivity and permeability, respectively. When en electric field is applied to dielectric media, the internal charge distribution is changed causing generation of electrical dipole moments. These dipole elements give a feedback to the total electric field. Thus, additional electric field contribution arises as a result of separation of negative and positive charges. This induced generation dipole per unit volume is called electric polarization P. Further explanation required to fully give intuitive picture of the polarization generation. Usually, dielectric media may consist of polar or nonpolar molecules. Polar molecules, which exhibits mutual permanent dipole moments, are regularly oriented randomly. When the electrical field applied to the isotropic medium, all the dipoles align themselves in the way that they coincide with the direction of the electric field. For non- 23 polar molecules, electric field causes electric dipole moment by rearranging electron cloud around the nucleus. The electrical displacement D is defined by [1] ) 2 ( 0 P E D and the electric field is then given by ) 3 ( 0 0 P D E . In homogeneous, linear, isotropic media, polarization and electric field are in the same direction, giving the expression: ) 4 ( 0 E P where χ is called electric susceptibility, which determines how the medium is susceptible to change its dipole moment concentration with the applied electric field. 1.2 The origin of nonlinear polarization Mathematically, Eq. 4 may be derived from the driven harmonic oscillator model for the motion of the electron, having mass m e and charge -e, and attached to its ion by the spring. Then it moves in response to external electric field E by equation of motion: ) 5 ( ) ( 2 2 2 2 t eE x t x t x m 24 where Γ is a damping constant. The resultant solution for oscillating electric field with frequency ω gives: ) 6 ( . . 2 2 2 2 0 c c i e m eE x t i where E 0 is amplitude of electric field. For electric dipole density N, the polarization induced is P=-Nex, resulting in linear dependence of polarization on the applied electric field: ) 7 ( . 2 0 2 2 0 2 0 E i E m Ne P giving Eq. 4. In practice, anharmonic terms are also presented in the equation of motion due to nonlinear nature of medium. Linearity of the media is possible only for very small values of x. For intense electric field and, as a results, for larger displacements, the spring motion is being distorted. In addition, externally applied electric field is never purely monochromatic and any temporal deviation in electric field amplitude (fluctuations) give rise to additional anharmonic terms in Eq. 5 resulting in appearance of additional oscillating components at the harmonic frequencies (2ω, 3ω, etc). These nonlinearities expand the polarization to the form: ) 8 ( 3 ) 3 ( 2 ) 2 ( ) 1 ( 0 E E E P i where χ (n) are nonlinear susceptibilities of the medium. In our research we are interested in χ (3) terms which is responsible for Kerr effect, four- wave mixing (FWM), two-photon emission/absorption/ionization, “Soliton” pulse 25 propagation, cross-phase modulation, self focusing, phase conjugation, and electrostriction effect which is main mechanism for Brillouin scattering, etc. 1.3 Qualitative description of Brillouin scattering Spontaneous light scattering occurs when there are thermal effects which gives rise to fluctuations in scattered radiation. When these fluctuations are induced by the optical radiation, this kind of scattering is called stimulated. Brillouin scattering is the scattering caused by the variation of the density which is induced by the optical radiation. The stimulated Brillouin scattering (SBS) process is schematically illustrated in Fig. 1.1. In this figure, the incident light (the “pump”) at the frequency ω L is scattered from the refractive index grating induced associated with the acoustical phonons (acoustic waves) with a sound frequency of ω 0. The scattered light (the “probe”) is scattered backwards and its optical frequency is downshifted to the Stokes frequency ω S=ω L-ω 0. Figure 1.1 Interaction picture of SBS interaction There are three competing effects, which cause the generation of acoustical phonons. First effect is electrostriction, which is the susceptibility of the material to the density change due to optical intensity. The second effect is optical absorption, which causes the material to 26 be heated and expanded. As a result, the third effect coming into the picture and it is elasto- optic effect, which causes the change in refractive index due to mechanical stresses induced in the material. In optical fiber, the absorption is extremely low thus the main mechanism is electrostriction. The optical electrostriction interaction is related to the optical field-induced macroscopic acoustic motion. It causes the nonlinear polarization terms in a medium to arise. This acoustic motion is triggered by the intense light-induced refractive index change. The interaction between applied electric field and dielectric medium give rise the change in the dielectric constant and therefore to the density of the medium. The density variation causes the refractive-index to change. This density variation is related to the dielectric constant change by [1] ) 9 ( 0 e where / 0 e is the electrostrictive coefficient and ρ 0 is average material density. In addition, the change in the potential energy as a result of the change of the density is 2 2 2 0 2 0 E E u . For the elastic case, this change in the energy is equal to the work performed by compressing the medium, so in addition st st p V V p u , where p st is the contribution of the pressure of the material due to the presence of optical radiation. Thus, 27 ) 10 ( 2 2 2 0 2 0 E E p e st and st st Cp p p 1 , where 1 2 a V C is compressibility of the medium. Finally, 2 0 2 E C e and . 2 0 0 n n e For fiber glass, the material density is ρ=2.1 gr/cm 3 , electrostrictive constant γ e=0.902, index of refraction n=1.447, sound velocity v s=5.95x10 5 cm/sec. This yields Δρ=1.36x10 -11 g/cm 3 and Δn=4.71x10 -12 for unit intensity. This compression work may be further understood from the fact that the induced dipoles experience the translational force in the non-uniform field and proportional to the field gradient. This electristrictive force tends to move the dipoles into the region of a higher intensity. This is what causes the increase in the local density and, as a result, in refractive index. As we mentioned, Brillouin scattering is caused by the modulation of the refractive index of the media or of the nonlinear susceptibility. Since the polarization is proportional to the nonlinear polarizability and the electric field, the media fluctuations cause the appearance of the polarization beating terms at the frequencies that constitutes to the frequency that are sum and difference of the pump frequency and acoustic frequency. We will deal with the case of difference. According to this description, we will make our attention on the nonlinear polarization term and using Eq. 7: 28 ) 11 ( 0 0 0 E E P e NL where we assumed Δε=Δχ and Eq. (9). We will assume that the polarization, acoustic and electric fields are all have the same state of polarization (SOP). So we will not use vectors for expressing our terms. The pump and the probe wave’s amplitudes described as followed: ) 12 ( . ) , ( ) 12 ( . ) , ( ) , ( ) ( ) ( b c c e A t z E a c c e t z A t z E z k t i S S z k t i L L S S L L as well as by mediating acoustic phonon wave: ) 13 ( . ) , ( ) , ( ~ ) ( 0 0 0 c c e t z t z z k t i Both pump and acoustic waves give rise to the polarization term: ) 14 ( . . , , , 0 0 * c c e t z E t z b t z P z k k t i L L L The maximum mediation of the energy from this polarization term to the probe wave E S is maximized when ) 15 ( ) 15 ( 0 0 b k k k a L S L S 29 The relationship of the ω with the energy and the k with the momentum is defined by De Broglie equations: ) 16 ( ) 16 ( b k p a E Consequentially, it is possible to represent Brillouin scattering as the annihilation of the incoming photon followed by the creation of the acoustic phonon and scattered photon, whereas the energy and the momentum are conserved. The schematic figure is shown in Fig. 1.2 (a). Figure 1.2 (a) Annihilation of the pump photon followed by the generation of the phonon and scattered photons (b) momentum conservation for k L=k S+k 0. The conservation of the momentum or the phase matching condition is shown in Fig. 1.2 (b). For the acoustic wave, ω 0=V ak 0, where V a is sound velocity and k 0 is the acoustic wave vector. Since ω 0«ω L, we may assume that ω L≈ω S, so |k L|≈|k S|. In addition, 2 2 2 2 2 0 sin 4 2 cos 2 L L S L S k k k k k k , so sin 2 0 c V n a L , where θ is the angle between pump and the scattered probe. It is obvious that the maximum scattering occurs for θ=π, i.e. backwards, and there is no forward scattering for θ=0. 30 Three propagating waves are coupled together obeying energy and momentum conservation laws (Eqs. 16). As a result, it is possible to write Navier-Stokes (N-S) wave equations describing the coupling between two counter-propagating light waves via acoustical phonon wave. The generalized N-S equation is described by ) 18 ( 2 ) 18 ( ) 18 ( * 2 2 2 2 * 1 1 c A A ig t t i z qv b A ig z A t A c n a A ig z A t A c n S L A L S S S L L where 0 1 2 nc g e , 2 2 0 2 q g e , 2 ) ( 2 2 B B A i i , P B 1 is the phonon lifetime and Ω is frequency detuning parameter. One of the common solutions to above N-S equations is continuous wave (CW) solution where all introduced waves are in steady-state conditions causing all time derivatives to disappear resulting in ) 19 ( ) 19 ( ) 19 ( * 2 * 1 1 c A A ig b A ig z A a A ig z A S L A L S S L 31 or ) 20 ( ) ( 2 ) 20 ( ) ( 2 2 2 2 0 2 2 0 2 2 2 0 2 2 0 b i A A nc q i z A a i A A nc q i z A B B S L e S B B L S e L The spatial derivatives of the acoustic waves are neglected since they do not propagate significantly during the timescale where the variation of the optical waves is significant. It may be reasonable to introduce optical intensities instead of amplitudes since this Brillouin process is phased-matched: ) 21 ( ) 21 ( b I I g z I a I I g z I L S B S L S B L where g B is a SBS gain equaled to ) 22 ( ) 2 )^ ( 2 )^ (( ) ) )( (( 4 2 2 0 2 2 2 2 B B B B B e B i c n q i g In non-depleted pump approximation (UPA), the solution to Eqs. 21 is given by ) 23 ( ) 0 ( ) ( z gI S S L e I z I 32 which is purely gain solution as assumed before, i.e. the increase in optical power of the Stokes wave increases exponentially with the length of the interaction, the pump intensity and the Brillouin gain coefficient. For simplicity, positive z values are chosen in the negative direction. As may be noticed, the SBS gain coefficient is frequency dependent. This dependence is approximated by Lorentzian shape centered at the Ω B having full-width half-maximum of Γ B. When no optical field is present, it may be shown that Eq. 18(c) has a solution of the form: ) 24 ( ) 0 ( ) ( 2 / t B e z i.e. acoustic wave exponentially decays with characteristic time of ) 25 ( 1 B P The transient solution with UPA of Eqs. 18 will be shown in Chapter 3 where the derivation is performed for multiple pump and probe cases for analytical verification of mutual Brillouin inter-tone cross talk. 1.4 Optical fiber sensors The interest to optical fiber sensors arose, as an alternative to conventional temperature and mechanical stress sensors, for their superior advantages. These include cost, possibility of distributed sensing over large distances (up to hundreds of kilometers), RFI-EMI non- 33 interference, the possibility of performing distributed measurements, no need for the electrical supply as the propagating light makes all the work, etc Figure 1.3 Extrinsic vs. intrinsic types of OFS In general, the optical fiber sensors (OFS) may be separated into two categories: extrinsic and intrinsic. The extrinsic OFS use optical fiber are used as a light guiding device but the actual sensing is performed in the fiber-coupled sensors which is not part of the optical fiber itself, where as intrinsic OFS uses the optical fiber to perform sensing task. Figure 1.3 depicts graphically the difference between two types of OFS. Intrinsic sensors, in their turn, may be divided into several categories depending on the sensing mechanics. Table 1 summarized the basic types of intrinsic OFSs. Type Sensing mechanism Parameters Intensiometric Intensity Micro-bending loss, breakage, fiber-to-fiber coupling, reflectance, absorption, attenuation, molecular scattering, temperature/strain variation Interferometric Phase Polarimetric Polarization Spectrometric Wavelength Table 1.1 Different types of OFSs depending on the sensing principle 34 Figure 1.4 Schematic block diagram of OTDR Intensiometric OFSs measure the intensity of the light to obtain the desired sensing information. One of the very commong intensiometric sensors is optical time-domain reflectometer (OTDR) which measures the amount of Rayleigh scattered light originated from the single pulse launched into the fiber. The schematic block diagram of the OTDR is shown in Fig. 1.4. The laser source of the input into electro-optical Mach Zehnder intensity modulator (MZM), which is driven by the RF pulse signal. Its output is the optical pulse, which is fed into the optical fiber. Once it launched into that, the Rayleigh scattered light is returned from the same side of the optical fiber and is directed to the optical low-bandwidth detector using circulator. The output of the detector is the input to the digital oscilloscope where the signal is recorded for the time defined from the optical pulse launch until the last scattered light is returned to the detector. The attenuation of the return light versus the distance where the scattering occurred is noticed as the intensity of the incoming light is attenuated along the fiber. Once the damage or excessive loss is introduced to the fiber, there is a sudden scattered intensity drop reported in the measurements. The typical example of the interferometric sensor is Michelson Interferometric Fiber Optical Sensor (MIFOS). Its schematic block diagram is shown in Fig. 1.5. The typical sensor is comprised of laser light source where it is coupled into two optical fibers. The first one serves as a sensing arm, which is exposed to the external world and where the actual phase 35 Figure 1.5.Schematic block diagram of MIFOS sensing is performed. The second optical fiber is used as a reference arm, which is held in the known controlled conditions for phase reference. The other side of both fibers are coupled with the mirrors which return incoming light back to the detector through the optical circulator. When nothing happens to the sensing arm there is no phase difference between sensing and reference arms. But, as a result of phase change in the path of sensing arm, the phase difference appears and is given by Df =2k n s L s -n r L r ( ) , where k is the wave vector, n s and n r are the refractive index of sensing and reference arms, respectively, and L s and L r are the length of sensing and reference arms, respectively. 1.5 Distributed sensing using stimulated Brillouin scattering process As mentioned earlier, the Brillouin based scattering is generated by acoustical fluctuations in the propagating medium. These fluctuations cause scattered light to change its spectral properties. This change is given by ) 26 ( 2 0 c nV s B 36 where n is refractive index, c is speed of light, V s is acoustic velocity, and ω 0 is optical light frequency. In this expression, both refractive index and the acoustic velocity may be changed as a result of temperature or mechanical stress. The dependence on the temperature and mechanical stress is around 1MHz/K and 50KHz/µε, respectively, for single-mode fiber (SMF-28). All different types Brillouin-based optical fiber sensors have at least two counter- propagating optical waves. The spatial resolution is commonly achieved by two techniques (i) time-domain pulsing of at least one of the waves, (ii) correlation peak generation along the fiber by spatial interference. We concentrated our research efforts on the first technique. This method is based on the limiting pump-probe interaction distance. When, for instance, the pump wave is modulated into optical pulse, the temporal width determines the spatial resolution. In this concept, propagating pump pulse “meets” CW probe at different location along the fiber and Brillouin amplifies it accordingly, depending on the pump-probe frequency separation. The spatial resolution is limited by the finite phonon lifetime which is around 10nsec, which constitutes to the 1-m spatial resolution. During this pulse, acoustical phonons are generated at every location where the pulse passes. For shorter pulses (< 10nsec), the acoustic wave does not have enough time to arise and the Brillouin gain is very low. The BGS determination is performed by sweeping the relative frequency between pump and probe waves. Usually, the SNRs are low and multiple measurements requred at each frequency step. During each frequency sweep, the single pulse of the pump wave is launched into the fiber. Then, the Brillouin amplified CW probe wave is recorded until it arrived from the most distanced location where it met with the pulse. Right after that, additional pump pulse is sent. The duty cycle of the pulses is determined by the round-trip time which it takes for the light to propogate within the fiber. For instance, 10km long fiber requires the duty cycle to be 10KHz, or to the 100μsec interval between sequential measurement. The accuracy of the BFS determination is 37 roughly defined by the sweeping frequency step. In practice, it is about twice better due to Lorentzian shape fit which is performed on the measured data. 38 Chapter 2 SBS-based fiber optical sensing using frequency domain simultaneous tone interogation 2.1 Introduction It might be quite desirable for a Brillouin sensor system to probe many different optical frequencies simultaneously in order to potentially increase the overall speed of the spectral measurements, thereby enabling the measurement of fast dynamic changes of interest, such as mechanical vibrations. Indeed, the interaction between a single probe tone and densely spaced multiple pump tones was shown to achieve fast strain measurements at the expense of spatial resolution [15]. Here, we propose a concept that replaces the sweeping of a single laser across all frequencies by the simultaneous interrogation of the Brillouin spectrum using multiple pairs of pump and probe tones. The method relies on: (i) using multiple pump and multiple probe tones, and (ii) arranging the probe tone frequencies so that they interrogate different parts of the Brillouin gain spectrum. In principle, the pump tones can be pulsed as short as in classical BOTDA, without compromising the spatial resolution, Following a detailed description of the concept in Sec. 2.2, we experimentally demonstrate in Sec. 2.3 that multiple tones can faithfully reconstruct Brillouin gain spectra. These experimental results have been obtained using continuous wave (CW) tones, but a pulsed version of the concept should work equally well for fast distributed sensing, as described in Sec. 2.5. 39 Figure 2.1. BGS reconstruction: (a) using the conventional probe frequency sweeping technique; and (b) using the proposed multiple tones, sweep-free concept 2.2 Description of method The concept of our sweep-free SBS-based optical fiber sensor is illustrated in Fig. 2.1(b). N pump tones N i i , 1 ), ( 0 generate N BGSs, whose center frequencies are down shifted from the pump tones by the corresponding BFSs: N i i B , 1 ), ( , given by [16]: c i V i n i s B ) ( ) ( 2 ) ( 0 (1) where ) ( 0 i is the optical frequency of the i-th pump tone, ) (i n is the refractive index at ) ( 0 i , c is speed of light in a vacuum and s V is the speed of sound in the fiber. We assume, for the moment, that all N i i B , 1 ), ( are identical, around 11 GHz for SMF at 1550 nm. All BGSs have a Lorentzian shape with a FWHM width of [17]: 2 0 22 2 0 2 ) ( 10 27 . 1 ) ( ) ( ) ( 1550 @ i i const i i nm SMF B B (2) 40 At 1550nm Eq. (2) gives MHz 30 2 ) ( i B for standard SMF [18]. As long as N i i , 1 ), ( 0 span a range of less than 10GHz, N i i B , 1 ), ( do not vary by more than a few KHz, and will be assumed to be constant. To avoid interactions between neighboring pump-probe pairs [19], the pump tones spacing must be significantly larger than the width of the BGS. If it were not for other nonlinear effects in the fiber, fixed pump tone spacing could be chosen, e.g., 100MHz, as depicted in Fig. 2.1(b). Consequently, the spacing of the generated BGSs is also 100 MHz. In addition to the pump tones, a similar number of probe tones are simultaneously launched into the fiber from its opposite side, downshifted by approximately the BFS, but with slightly larger frequency spacings than those of the pump tones. The idea is to arrange the probe tones in such a way that each probe tone is located in a different region of the BGS of the corresponding pump tone. Thus, the lowest frequency probe tone is downshifted from the lowest frequency pump tone by a bit more than the highest BFS expected in the application. The probe tone spacing is then chosen to be somewhat larger than that of the pump tones, such that if the lowest frequency probe tone falls to the left of the leftmost BGS, Fig. 2.1(b), the other probe tones successively sample different regions of the corresponding BGSs, until the whole BGS is mapped. In Fig. 2.1(b), the spacing of the probe tones is 103MHz so that the frequency difference between the pump and probe tones of a given pump-probe pair decreases by 3 MHz from the i-th to the (i+1)-th pair. Through the SBS interaction, the i-th probe tone is amplified by the i-th pump tone, and the gains experienced by the various probe tones depend on their proximity to the center of the BGS, with the closest one having the highest gain. If the individual gains of the many probe tones can be recorded simultaneously, the BGS can be reconstructed in a single measurement (excluding averaging), without the need for 41 frequency sweeping. The number of pairs of pump-probe tones used and the frequency spacing between each pair eventually determine the resolution of BGS reconstruction. Clearly, the higher the number of pairs of pump-probe tones the better is the spectral resolution of the BGS reconstruction. However, the total number of tones is limited by several factors: (i) The maximum optical frequency of the probe tones should be lower than the minimum optical frequency of pump tones to avoid unwanted frequency overlap, Fig. 2.1(b); (ii) The total available bandwidth is limited by BFS, which is around 11GHz for a standard SMF [18]; (iii) As already mentioned above, the minimum frequency spacing between adjacent pump (or probe) tones must be much larger than the width of the BGS, to avoid crosstalk. The actual implementation of this sweep free interrogation concept using equally spaced tones must be somewhat modified in order to combat nonlinear effects, which tend to create intermodulation products, collocated with legitimate tones. Therefore, in the experimental part of this chapter, unequal spacings for both the pump and probe tones are used with no impact on the basic technique. Much like the operation of a sampling oscilloscope, the proposed concept is based on measuring the Lorentzian BGS using many frequency-shifted replicas of the BGS, where each replica contributes one measurement point. For this idea to work as described, all shifted BGSs, excited by the multiple pump tones, must share the same shape and width. As mentioned above, the allowable span of pump tones cannot exceed 11GHz and shape and width variations within this range can be neglected. 42 As for the BFS, its derivative with respect to 0 is given by (see Eq. (1)): 5 0 0 0 10 6 2 2 c n V d dn n c V d d g s s B (3) Thus, under a worst case scenario, where the whole allowable 11GHz range is populated with pump tones, B may vary by up to ~300KHz. If this variation is ignored, an error of up to 0.3 0 C and/or 10 microstrains may contaminate the temperature/strain measurements. Indeed, if this source of error turns out to be the dominant one, slightly more complex processing of the data can easily take into account the variation within N i i B , 1 ), ( , eliminating its effect on the accuracy of the measurement. Finally, distributed sensing can be achieved by pulsing the pump tones, with pulse widths commensurate with the inter tone spacing. The next section deals with the experimental validation of the concept for CW pump and probe tones, while in Sec. 2.5 we discuss the pulsed, distributed sensing case. 2.3 Experimental setup It is the purpose of the block diagram of Fig. 2.2 to experimentally demonstrate that CW multiple pump and probe pairs, simultaneously propagating through the fiber, as per the proposed technique, do provide independent samples of the Brillouin gain spectrum. A coherent tunable laser at wavelength 1547.7nm with an output power of 5 dBm is split into three arms to serve as a probe, a pump and a local oscillator (LO). The LO is used as a reference signal for the coherent detection of the amplified probe. 43 Figure 2.2. Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: erbium-doped fiber amplifier; PC: polarization controller; ISO: optical isolator; DET – detector; FBG: fiber Bragg grating; MW AMP: microwave amplifier; AWG: arbitrary waveform generator; RFSA: RF spectrum analyzer; OSA: optical spectrum analyzer The pump signal is sent to Pre-EDFA2 to reach the maximum allowed insertion power of MZM2 modulator and then to a polarization controller (PC) prior to entering MZM2, which is biased at its zero transmission operating point. The pump tones are generated in a two-step process. First a wideband arbitrary waveform generator (AWG) is programmed to emit a frequency comb, i.e., a superposition of multiple sinusoidal waves, at the desired frequencies. Then, MZM2 is used to upconvert the electronic comb to an optical one. Due to the choice of the biasing point, the number of comb frequencies is doubled in the upconversion process. The output of MZM2 is sent to Pre-EDFA3, followed by EDFA2 for further amplification, and then to the 1-km SMF-28 fiber-under-test (FUT) through an optical circulator. The probe signal is sent to Pre-EDFA1, followed by a polarization controller, so that it enters its modulator, MZM1, with the maximum allowed power and the right polarization. An electronic RF probe comb, generated by a different channel of the AWG is combined with an ~11GHz RF tone in an RF mixer prior to driving MZM1, which is also biased at its zero transmission point. The output of MZM1 is a double-sided optical comb, shifted by around 44 11GHz from the optical carrier. The optical comb is then further amplified before entering the FUT. After the Brillouin amplification process is carried out in the FUT, a narrowband fiber Bragg grating (FBG) is used to filter out the unwanted upper sideband of the amplified probe comb, which anyway, does not participate in the Brillouin process and only adds excessive noise to the detector. The amplified probe signal is then mixed with the -11dBm LO signal [15], after the latter has propagated through 1-km of SMF-28 fiber to ensure highly coherent heterodyning on the surface of 12GHz optical detector. The output of the detector is amplified by a microwave amplifier and sent to an RF spectrum analyzer, which is GPIB controlled. For distributed sensing using this concept, the RF spectrum analyzer is replaced by a fast acquisition system, as described in section 2.5. 45 Figure 2.3 (a) BGS measurement of lower 5 probe tones from 5 pump tones. (b) BGS of 5 tones, superimposed on one another, after proper shifting of their center frequency. Lorentzian shape fit showing FWHM of 28.6MHz and BFS of 10887 MHz. 46 2.4 Results and discussion Before applying the proposed technique, it is important to first verify that in the presence of several pump-probe pairs, appropriately separated from one another (~100MHz or more), each pair can still entertain its own Brillouin interaction, independently of the other pairs. To that end, five probe tones were simultaneously swept against five pump tones. Five RF tones were generated using the AWG at frequencies of 200, 350, 550, 800 and 1,100MHz. Unequal spacings were chosen for the pump tones to ensure that their intermodulation products, originating either from the AWG and/or from four wave mixing in the fiber [20]- [21], do not coincide with any of them. These tones were used to modulate the optical pump, producing a double-sided comb around the optical carrier. For this experiment, which only requires equal spacing for the probe pump and probe, the probe tones were generated by mixing the same RF tones with a microwave synthesizer at frequency f (~11GHz). The mixed signal was upconverted by MZM1 to generate probe tones shifted down from the optical carrier by MHz 200 f , MHz 350 f , MHz 550 f , MHz 800 f , MHz 1100 f (the upper side band is not mentioned since it will be filtered out by the FBG). The BGSs of the five pump tones are measured by sweeping the synthesizer from MHz 10830 f to 10930MHz with 1 MHz step. Fig. 2.3(a) shows measured spectra of the lower 5 BGSs. Lorentzian shape fitting was performed to each of the measured BGS, resulting in measured bandwidths of a 28.6±0.8MHz and BFSs of 10887±1.2MHz. Fig. 2.3(b) shows these 5 BGSs, superimposed on one another, after proper shifting of their center frequency. These experimental values were found to be in good agreement with the results obtained from the classical technique, namely: sweeping a single probe against a single pump. 47 For the demonstration of the proposed BGS reconstruction technique twenty pump- probe pairs were used. Using RF tones from the AWG at 200, 350, 550, 800, 1100, 1200, 1350, 1550, 1800 and 2100MHz, the twenty pump tone optical frequencies after upconversion were positioned ±200, ±350, ±550, ±800, ±1100, ±1200, ±1350, ±1550, ±1800 and ±2100MHz with respect to the laser frequency. The RF frequencies for the probe were: 197, 344, 541, 788, 1085, 1182, 1329, 1526, 1773 and 2070MHz. Note that the frequency difference between corresponding pump and probe RF tones monotonically increases in 3MHz steps. After RF mixing with a tone at 10885MHz and upconversion using MZM1, the resulting optical probe comb frequencies were spread 8815, 9112, 9359, 9556, 9703, 9800, 10097, 10344, 10541, 10688, 11082, 11229, 11426, 11673, 11970, 12067, 12214, 12411, 12658 and 12955 MHz below the laser frequency. This arrangement corresponds to a sweep-free range of 63 MHz with a 3-MHz resolution and 6-MHz gap around the center. The power levels of the 20 pump tones (~6.5dBm), as measured by an optical spectrum analyzer with a 20MHz spectral resolution, are shown in Fig. 2.4(a). Many inter-modulation products can be observed with a maximum level of -17dBm. The amplitude non-uniformity of the optical pump tones is measured to be around 1.5 dBm. This uniformity is used to calibrate the resultant gain of the probe tones. The probe tones (~-30dBm) also appear in Fig. 2.4(b) as they enter the fiber and after FBG filtering (Fig. 2.4(c)). The optical down-shifted carrier has a power of -40 dBm. No significant inter-modulation products are observed due to the low power levels. The amplitude non-uniformity of the optical probe tones is measured to be around 2.7 dBm. The stability of the optical probe tones amplitude, as measured by the RFSA, is around 0.1 dB. This probe tones stability determines the measurement error. Since 48 Figure 2.4 (a) Pump tones as they enter the fiber. Intermodulated products exist having optical power less than –15 dBm. (b) Probe tones as they enter the fiber.Two sidebands around optical carrier. (c) Lower sideband probe tones. Intermodulated products exist but having optical power less than –52 dBm 49 we can measure the optical probe amplitudes with and without the pump we can divide one by other to estimate the actual gain at each frequency tone. The power levels of the 20 pump tones (~6.5dBm), as measured by an optical spectrum analyzer with a 20MHz spectral resolution, are shown in Fig. 2.4(a). Many inter-modulation products can be observed with a maximum level of -17dBm. The amplitude non-uniformity of the optical pump tones is measured to be around 1.5 dBm. This uniformity is used to calibrate the resultant gain of the probe tones. The probe tones (~-30dBm) also appear in Fig. 2.4(b) as they enter the fiber and after FBG filtering (Fig. 2.4(c)). The optical down-shifted carrier has a power of -40 dBm. No significant inter-modulation products are observed due to the low power levels. The amplitude non-uniformity of the optical probe tones is measured to be around 2.7 dBm. The stability of the optical probe tones amplitude, as measured by the RFSA, is around 0.1 dB. This probe tones stability determines the measurement error. Since we can measure the optical probe amplitudes with and without the pump we can divide one by other to estimate the actual gain at each frequency tone. The FUT was kept in a thermal equilibrium in a temperature chamber. After dividing by the unamplified probes (i.e. with no pump) and properly calibrating for non-uniformity of the pump tones, the resultant Brillouin gain spectra as a function of the chamber temperature are shown in Fig. 2.5(a)-(c) (triangles). Lorentzian shaped fitting is performed to estimate the BGS bandwidth and its central frequency. One can see good agreement with a classical measurement, where a single probe is swept against a single pump (dots). The mean 50 Figure 2.5 BGS reconstruction using 20 frequency tones at (a) 15 O C, (b) 25 O C (c) 35 O C, (d) BFS variation over the measured temperature range measurement error of around 0.1 in the normalized gain is related to the stability of the probe tones. An average BGS FWHM of 28.9±0.7MHz is measured, as well as 1±0.1 O C/MHz BFS variation over the measured temperature range (Fig. 2.5(d)). These measurements demonstrate the validity of the proposed sweep-free technique for the BGS reconstruction. While restricted to CW pump tones, the setup of Fig. 2.2 will now be only slightly modified to allow pulsed pump operation, and consequently, distributed sensing. 51 2.5 Sweep-free Brillouin optical distributed sensing Fast distributed Brillouin sensing using multiple pump and probe pairs can be achieved by two modifications of the setup of Fig. 2.2. First, as done in classical BOTDAs, we pulse the pump tones at a rate of RP pulses per second, limited from above by the fiber length (RP <2L/V g, where L is the fiber length and V g is the group velocity of light in the fiber). Each of these multiple pump pulses will Brillouin-amplify its corresponding counter-propagating probe wave, independently of the interactions among the other pump-probe pairs, as experimentally shown in Sec. 2.4 for the CW case. The gain of each probe wave will depend on its frequency distance from its pump companion, as well as on the temperature/strain at the place where the probe and pump meet. Second, the RF spectrum analyzer used for the CW case, is replaced by a digital fast acquisition and processing system. Using modern technology the raw output of the detector of Fig. 2.2 (~11GHz) could be directly digitally acquired. However, down shifting this detector output may relax the digitizing speed to a little over twice the frequency span employed by the multiple tones (e.g., a 2GHz span can contain 30 pump-probe tones). For improved signal to noise ratio, the digitized returns from N a pump pulses are averaged. The collected data are then arranged in a two-dimensional matrix with each row representing averaged samples along the fiber generated by N a pulses, and consecutive rows represent the action of consecutive averaged scans, generated at a rate of RP/N a per second, thereby determining the temporal sampling rate of the dynamic phenomenon under study. For a pulse width of T seconds, each row is then divided into segments of length T. Each segment is Fourier transformed to obtain the heights of the various probe tones, from which, after proper normalization, the BGS is reconstructed and the BFS is determined. This process is repeated for all other segments of interest, and then sequentially applied to corresponding segments in successive rows of the matrix, resulting in a map of the BFS in the 52 time-distance domain. On this map the time resolution can be as low as N a/RP, while the spatial resolution is on the order of V gT/2. Unlike [15], our use of both multiple pumps and multiple probes can support pulse widths as short as in the classical BOTDA (clearly, the tone spacing should exceed 1/T). With infinite processing speed of the acquired records, this multi-tone interrogation concept is faster than classical BOTDA by a factor equal to the number of pump- probe pairs used for the BGS reconstruction since each pair replaces one sweeping step in the classical technique. In order to understand the limitations brought about by the finite available processing speed we'll analyze a concrete example, where N tones=20 tones are used, with a spacing of f=100MHz, the sampling speed is f samp=2N tones f =4GSamples/sec, and the pulse width is T=100nsec, resulting in a record length of R Length=f sampT=2TN tones f=400 samples per segment. Note that in order to properly extract the different tones, the record duration T must be larger than 1/ f. Most processing time will be spent on the required spectral analysis. Let assume a modern hardware implementation that can perform FFTs at the rate of f FFT= /[ R Length log 2(R Length)] FFTs/sec ( ~2 10 9 [22]). If a whole fiber of length L is processed with a pump pulse of width T, the total acquisition time with N a averages is 2N aL/V g and the required processing time is 2L/(V gTf FFT), independent of the number of averages used to acquire the data. Real time dynamic distributed sensing is achieved if 2N aL/V g 2L/(V gTf FFT), or N a 1/(Tf FFT). In our example 1/(Tf FFT)~20 and the above requirement is easily met since normally the number of averages N a is on the order of 100 [15]. Note that higher sampling speed of the varying strain/temperature phenomenon can be achieved by the processing of only selected segments of interest. 53 Finally, using the same notation for the classical BOTDA scenario, we find, as expected, that the sequential use of N tones tones and N a averages, requires 2N aN tonesL/V g seconds, which is longer than the optimal case of the multi-tone method by a factor of N tones. 2.6 Conclusions We have proposed a method for a sweep-free Brillouin sensor capable of reconstructing the Brillouin gain spectrum without the need for frequency sweeping. Based on the use of multiple pump and probe tones and a judicious choice of their frequencies, the Brillouin spectrum is simultaneously interrogated. Results, obtained with CW tones, favorably compared with those obtained from a conventional frequency scanning technique for temperatures varying from 15 O C to 35 O C, showing good agreement. The extension of the method to pulsed pumps and distributed sensing has been described and its experimental implementation is under current research. 54 Chapter 3 Analytical investigation of the Brillouin interaction between multiple pulsed pump tones and probe waves 3.1 Introduction We analytically investigate the case of the Brillouin interaction between two probe waves propagating against two modulated pump waves. This investigation is motivated by the sweep-free BOTDA technique, where, to increase sensing speed, the Brillouin gain spectrum is simultaneously interrogated by many probe-pump pairs. When the spacing between neighboring pump tones is much larger than the Brillouin linewidth, each probe will experience gain from a single pump only. As the inter-tone spacing decreases, the Brillouin amplification of each probe may be affected by several pump tones, thereby hurting the accuracy of the measurement. To address this issue, this chapter analytically solves the relevant Brillouin equations for the case of two pulsed pump tones against two probe tones, and compare the results with experimental data. 3.2 The analytical method In this section we describe the method used to find the solution for an SBS excitation involving a pulsed pump consisting of two frequency tones. We describe the interaction between the pump and corresponding probe tones under the undepleted pump (UPA) and the slowly varying envelop (SVEA) approximations. We follow the analysis of Lichtman et.al. [19], which in turn is based on Tang [23] and extend it to the pulsed pumps case. 55 Assume a pump wave and probe wave, each comprising two optical frequency tones, separated by the angular frequency Ω: c c e e t z E e t z E t z E z k t i c zn t i L c zn t i L L L L . ) , ( ) , ( ) , ( ) ( 2 2 2 1 (1a) c c e e t z E e t z E t z E z k t i c zn t i S c zn t i S S S S . ) , ( ) , ( ) , ( ) ( 2 2 2 1 (1b) The subscripts L and S refer to the pump and probe, respectively. Eqs. (1) represent pump waves at 2 L , 2 L , and probe waves at 2 S , 2 S . For simplicity we assume the pump pulses to be of rectangular shape and, therefore, represented by a superposition of two step functions: c zn T t u c zn t u t z E L L 1 1 ) , ( (2a) c zn T t u c zn t u t z E L L 2 2 ) , ( (2b) where ) , ( z t u is the Heaviside step function , c is speed of light in vacuum, n is refractive index of medium, and T is the pulse width. Here we assumed all waves to have the same light velocity. 56 Figure 3.1 Frequency domain arrangement of SBS interaction for two pump and probes tones The interaction between pump and probe waves (between 1 L E and 1 S E and between 2 L E and 2 S E ) is mediated by an acoustic wave with frequency S L 0 . In addition to these direct interactions, there are cross interactions (between 1 L E and 2 S E and between 2 L E and 1 S E ) which are mediated by acoustic waves with frequencies 0 and 0 . Therefore, the resultant acoustic wave is c c e e t z t z e t z t z z k t i v z t i v z t i . ) , ( ) , ( ) , ( ) , ( ) ( 1 0 1 0 0 (3) Notice that the acoustic wave propagates in the same direction as the pump waves and opposite to the probe waves. Fig. 1.1 shows a schematic picture of the Brillouin interaction, whereas Fig. 3.1 shows the frequency domain arrangement of the interacting waves involved in SBS process. 57 We also assume small Brillouin gain, so that the probe wave amplitudes, 1 S E and 2 S E , can be approximated using a perturbation approach by 1 0 1 1 S S S e E E and 2 0 2 2 S S S e E E . Substituting (1a-b) and (3) into the electromagnetic and elastic wave equations of Ref. [19], and after collecting terms which oscillate at the same frequency, we obtain 5 coupled differential equations for the amplitudes of the probe and acoustic waves. As for the acoustic waves, we adopt the common assumptions of neglecting the z derivatives, as well as the second order time derivative. Following implementation of these assumptions, the resultant equations are: z v i L z c n i L S S e E e E ig z E t E c n * 1 2 * 0 1 1 1 1 (4a) z c n i L z v i L S S e E e E ig z E t E c n * 0 2 * 1 1 1 2 2 (4b) z v i S L A e E E ig t * 2 1 2 1 1 1 (4c) z c n i S L z c n i S L A e E E e E E ig t * 2 2 * 1 1 2 0 0 0 (4d) z v i S L A e E E ig t * 1 2 2 1 1 1 (4e) 58 where ) 2 ( 1 m e nc g , ) 2 ( 2 0 2 d e q g , ) 2 ( ) ( 2 2 d B d d B n i A , and e , q , B , m , B , and d are the electro-strictive constant, the acoustic wave-vector, the phonon recombination rate, the fiber density, the Brillouin frequency shift (BFS) and the detuned frequency, respectively. Under the undepleted pumps assumption, there is no need for equations for the pump waves. We next transform Eqs. (5) into the Laplace domain using the method of [24] and obtain the following equations for the acoustic transformed fields: * 0 2 2 1 1 * 0 1 2 * 0 1 1 ) 1 ( ) ( * 0 A T Ts Ts z c n i S L z c n i S L s c zn A L L s e e s e e E e E e z ig E A (5a) * 0 2 2 1 1 * 0 2 2 * 0 2 1 ) 1 ( ) ( * 0 A T Ts Ts z c n i S L z c n i S L s c zn A L L s e e s e e E e E e z ig E A (5b) * 1 * 1 1 2 2 2 * 1 2 1 ) 1 ( ) ( * 1 A T Ts Ts z v i s c zn A S L L s e e s e e e E z ig E A (5c) * 1 * 1 2 2 1 2 * 1 1 1 ) 1 ( ) ( * 1 A T Ts Ts z v i s c zn A S L L s e e s e e e E z ig E A (5d) 59 Finally, returning to the time domain and using the notation of: ) ( 1 c zn t u U (6a) ) ( 2 c zn T t u U (6b) we obtain the sought-for expressions for the first-order Brillouin-induced contributions to the probe waves: ) )] 1 ( ) [( )] 1 ( 1 ) ([( ) )] 1 ( ) [( )] 1 ( 1 ) ([( ) )] ( ) 1 ( 1 [ )) ( 1 ) 1 ( 1 (( 2 2 ) ( * 1 1 ) ( * 1 * 1 0 1 2 2 2 ) ( * 0 1 ) ( * 0 * 0 0 1 2 1 2 ) ( ) ( * 0 ) ( 1 ) ( ) ( * 0 ) ( 2 * 0 0 2 2 1 2 1 1 * 1 * 0 * 1 * 0 * 0 * 0 * 0 * * 0 U e e c zn T t U e c zn t E U e e c zn T t U e c zn t E U e e i e e i U e e i e i e E n c g g e c zn T t A T c zn t A A S L c zn T t A T c zn t A A S L c zn T t c zn T t i A T T c zn t i c zn t c zn t i A c zn t i z c n i A S L L S A A A A A A A A A (7a) 60 ) )] 1 ( ) [( )] 1 ( 1 ) ([( ) )] 1 ( ) [( )] 1 ( 1 ) ([( ) )] ( ) 1 ( 1 [ )) ( 1 ) 1 ( 1 (( 2 2 ) ( * 0 1 ) ( * 0 * 0 0 2 2 2 2 ) ( * 1 1 ) ( * 1 * 1 0 2 2 1 2 ) ( ) ( * 0 ) ( 1 ) ( ) ( * 0 ) ( 2 * 0 0 1 2 1 2 1 2 * 0 * 0 * 0 * 1 * 1 * 1 * 0 * * 0 U e e c zn T t U e c zn t E U e e c zn T t U e c zn t E U e e i e e i U e e i e i e E n c g g e c zn T t A T c zn t A A S L c zn T t A T c zn t A A S L c zn T t c zn T t i A T T c zn t i c zn t c zn t i A c zn t i z c n i A S L L S A A A A A A A A A (7b) Recalling that the full probe waves are given by 1 0 1 1 S S S e E E and 2 0 2 2 S S S e E E , the probe intensities to first order are proportional to 1 * 0 1 2 0 1 2 1 Re 2 S S S S e E E E and 2 * 0 2 2 0 2 2 2 Re 2 S S S S e E E E , respectively. 3.3 Results First, the Brillouin gain spectrum was calculated for quasi-continuous pump pulse of 40nsec, using Eqs. (7) by varying the detuning parameter Ω D, see the solid curve in Fig. 3. We also performed a corresponding experiment in which the spacing, Ω/2 , between the two CW probes and two CW pump tones was set to 200MHz, while both probe tones frequencies were swept relative to the both pump tones. The BGS for both probes were simultaneously recorded and are shown as dots in Fig. 3.3. It may be seen that both analytical and experimental results match quite well. 61 Figure 3.3 The calculated BGS as function of detuning parameter for CW probe tones (solid curve). The dots represent experimental results of scanning a pair of CW probe tones against a pair of pump tones. The frequency separation between the members of each pair was 200MHz. Let us concentrate on the amplification of a single probe by two pump tones where one pump is spaced B from the probe while the frequency of the second pump varies from zero to a value larger than the width of the BGS. Fig. 3.4 shows the normalized cross-interaction Brillouin gain as a function of the pump spacing Ω while the first pump is switched. As expected, for small values of the frequency spacing severe cross interactions occur, i.e. second pump contributes to the gain of the probe, whereas for higher frequency spacing the contribution of cross interaction becomes smaller and relative gain is lower until the probe "feels" no gain. Here, the direct interaction gain was neglected to show the results in normalized scale. Here too, we performed an experiment in which we introduced a single optical probe tone and two optical pump tones. At the beginning, the optical frequencies of both pumps are set to be the same while the optical probe tone was set to be lower by the exact BFS. Then, the optical frequency of only one of the pumps is shifted until the overall probe gain is equal to the gain as a result of only one pump, whereas we normalized gain for cross- interaction only. The results are shown in Fig. 3.4(b) and also include a Lorentzian fit with 26MHz FWHM. 62 Figure 3.4 (a) The calculated SBS gain as a function of the frequency spacing (b) Measured SBS gain as a function of the frequency spacing Clearly, for large enough pump spacing, i.e. much larger than BGS width, the gain is affected only by direct interactions and less effected by the cross interactions. Thus, all tones behave independently. 3.4 Conclusions In this work we solved the coupled wave equations describing the simultaneous Brillouin amplification of two probe waves, propagating against two pulsed pump waves. The slowly varying envelope approximation, non-moving phonons, the undepleted pump approximation and small Brillouin gain were assumed, resulting in a first order perturbation analysis for the acoustic and probe waves. Results include the Brillouin gain spectrum, which was compared with a corresponding experiment. It was shown that when the frequency spacing between tones is of the order of the width of the Brillouin gain spectrum width, crosstalk effects are observed, where each probe experiences gain not only from its corresponding pump but also for neighboring pump tones. In contrast, when the spacing is significantly larger than Brillouin gain spectrum width, all probe-pump pairs interact independently. 0 10 20 30 40 50 0 0.5 1 Spacing [MHz] Cross-interaction gain (a) 0 10 20 30 40 50 0 0.5 1 Spacing [MHz] Cross-interaction gain Cross-talk gain Lorentzian shape (b) 63 Chapter 4 Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA) 4.1 Introduction One of the most prevalent techniques is the Brillouin Optical Time Domain Analysis (BOTDA) [0], which requires frequency sweeping of one of the counter-propagating waves in order to find the frequency at which the energy mediation is maximal. This frequency is called the Brillouin frequency shift (BFS). The need to make consecutive multiple frequency steps in order to map the Brillouin gain spectra (BGS) and locate its maximum may potentially limit the ability to resolve fast, dynamic changes in the BFS distribution along the optical fiber. Several dynamic Brillouin sensing concepts have been already proposed and demonstrated [14-15, 26]. Recently, [20-0], we described a novel concept, called SF-BOTDA (for Sweep-Free BOTDA), which retains all the advantages of the classical BOTDA technique together with the potential to be much faster. In [0] we demonstrated the concept in which multiple CW pump and probe tones Brillouin-interact pair-wise in the fiber to simultaneously probe different parts of its BGS. Once the tones are detected, the Brillouin amplification experienced by each of them can be determined, resulting in an accurate reconstruction of the BGS, and, consequently, the determination of the BFS. Then in [20] we discussed an extension, where the multiple pump tones are concurrently pulsed to achieve distributed sensing, faster than classical BOTDA by a factor, which could be as high as the number of simultaneous tones used. It turns out, though, that such a scheme has some practical 64 disadvantages, having to do with fiber nonlinearities and overloading of optical amplifiers. Instead, sequential pumping is shown in this chapter to achieve true distributed sensing without significantly compromising the sensing speed. While sequential pumping, described in Sec. 4.2, has been used in our first demonstration of distributed sensing using SF-BOTDA [0], here we report an important improvement of the experimental setup together with new results of distributing sensing with spatial resolution of a few meters, Sec. 4.3. Figure 4.1 BGS reconstruction using the newly proposed sweep-free concept accomplished in a single measurement using multiple (N) pump and probe tones. Here the pump spacing is 100MHz, while the additional incremental spacing of the probe tones is MHz 3 Probe . 4.2 Description of the method The concept of the SF-BOTDA sensor, first described in [20], is illustrated in Fig. 4.1. Multiple pump tones are produced, each generating the ~30 MHz-wide BGS with the corresponding BFS, as determined by the fiber type and strain/temperature environment [Error! Reference source not found.]. In addition, simultaneous multiple probe tones are aunched in the opposite direction with slightly larger spacing than the pump tones. The idea is to arrange the probe tones in such a way that each of them is located in a different region of the BGS of the corresponding pump tone. The probe tones, which are located closer to the BGS center, will see higher Brillouin gain. In this manner the BGS can be reconstructed without the need for frequency sweeping, where the i th tone of the probe is amplified by the i th 65 tone of the pump through SBS. The pump frequency spacing has to exceed the width of the BGS, and was set to 100MHz in Fig. 4.1. Consequentially, the corresponding generated BGSs are equally 100MHz spaced and of equal width [16]. In order to appropriately position the Figure 4.2 Sequential pump launching. For N multiple tones, the pump waveform comprises a sequence of T–wide, N sub-pulses, each riding on a different frequency tone. As described in Sec. 4.3, the figure describes the RF waveform, which is then upconverted to an optical compound pulse. (a) Sub-pulse amplitude vs. time; (b) Sub-pulse frequency vs. time.(c) A spectrogram of the compound optical pulse used for sequential pumping. The laser frequency is located at the center of the horizontal optical frequency axis probe tones in and around the corresponding BGSs, their optical frequencies are downshifted from the pump tones by the approximate BFS. The progression of the frequency spacings between corresponding pump and probe tones determines the resolution of the BGS reconstruction. In our example, the probe frequency spacing is chosen to be 103 MHz, such that the frequency difference between the pump and the probe tones is decreased by 3MHz from the i th tone to the (i+1) th tone. As a result, the different probe tones experience different amounts of Brillouin amplification and thus, simultaneously provide information about the shape of the BGS in a single measurement, without the need for probe frequency sweeping. As in classical BOTDA, distributed Brillouin sensing measurements could, in principle, be achieved by gating the multiple pump tones with a pulse, whose width would determine the spatial resolution. 66 The use of many simultaneous pump tones, as in [20], may strain the Erbium-doped fiber amplifiers (EDFAs). Furthermore, pump inter-tone modulation effects may also become detrimental. To address these issues, we introduce here the use of sequentially launched pump Figure 4.3 Experimental setups: (a) As used in [9]; and (b) The improved version. MZM: Mach- Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: Polarization scrambler; ISO: optical isolator; DET – detector; FBG: fiber Bragg grating; RF AMP: radio-frequency amplifier; MW AMP: microwave frequency amplifier; AWG: arbitrary waveform generator; RTAS: real-time acquisition system; OSA: optical spectrum analyser; FUT: fiber-under- test. tones, where the single pump pulse of width T, comprising the N frequency tones, is replaced by a compact sequence of N equally-wide sub-pulses, each with a different frequency, as described in Fig. 4.2 and Sec. 4.3 below. 4.3 Experimental setup and results The experimental setups used in [20] and in this chapter are shown in Figs. 4.3 (a) and 4.3 (b), respectively. The current setup will be described in detail and its modifications with respect to the old one will be emphasized. A narrow linewidth (80 KHz) tunable laser is split into probe and pump arms. For the probe wave, a radio-frequency (RF) frequency comb is generated by a wideband arbitrary waveform generator (AWG). This RF signal, comprising a 67 superposition of multiple (N) sinusoidal waves (tones) at the desired frequencies, feeds the intermediate frequency (IF) input of the RF mixer, while the latter’s local oscillator (LO) input is driven by a synthesizer running at the average BFS of the fiber (e.g., 10870MHz), resulting in 2N RF tones, symmetrically arranged around 10870MHz. This compound signal now drives the MZM1 Mach-Zehnder modulator, operating at its quadrature point. MZM1 translates this microwave signal to the optical domain, generating two optical multiple-tone sidebands (2N-tone each) around the laser frequency, with the lower sideband to serve as the probe. Note that the laser frequency is also present in the probe wave: It will have no pump counterpart for Brillouin amplification but it will later serve for heterodyne detection of the amplified probe tones. In the older setup MZM1 was biased near zero transmission, allowing only for a much weaker laser frequency component to propagate through the fiber. The pump pulsed wave is also derived from the same laser frequency. Another channel of the AWG generates the signal of Fig. 4.2 (a-b), comprising a compact sequence of equally- wide sub-pulses, each with a different frequency. Modulator (MZM2), operating at its zero- transmission point, is used to translate the RF pump pulse train to the optical domain. Each sub-pulse generates two optical pulsed tones, as seen in Fig. 4.2 (c). For example, the first RF sub-pulse, riding on an RF carrier of 105MHz will generate a pair of time-overlapping pulses, one riding on an optical carrier having a frequency 105MHz higher than that of the laser frequency, while the other is 105MHz below the laser frequency. Using this technique, the overall required instantaneous optical power used for amplification is just 3dB higher than in conventional BOTDA, since at each time slot only two optical tones (generated from a single RF tone) are generated by MZM2. Furthermore, since pulsing of the pump tones is performed in the RF domain, and since MZM2 is a high extinction ratio modulator, biased at its zero 68 transmission point, very high extinction ratio can be achieved for the pump pulses. Noting that normally, the fiber-under-test (FUT) length far exceeds the pump pulse length, no measurement speed is lost if we use sequential pumping, thereby increasing the few nanosecond wide sub-pulse only by a factor of N. The sequential launching of the pump tones Figure 4.4 (a) Spectrogram of the Brillouin return from an essentially uniform 20m-long fiber, showing the time evolution of each of the 20 optical tones used. The width of each pump sub-pulse was 50ns and the center of the tones (i.e., the frequency of the microwave source in Fig. 4.3) was chosen to coincide with the fiber BFS. (b) Reconstruction of the BGS using 20 frequency tones with 5-m resolution with no stretching applied to the fiber. The distance axis is obtained from the temporal axis of using: Position=Group-velocity x Time/2 results in time-shifted Brillouin-amplified probe tones, to be realigned at the post processing stage by a simple temporal correction (Fig. 4.4 (a)). Continuing now with the pump channel, an Erbium-doped fiber amplifier (PRE-EDFA2) preceding MZM2, serves to reach the maximum allowed input power into MZM2. From MZM2 the pump signal continues to EDFA2 for further amplification, and finally to the FUT. A polarization-scrambling device (SC) is located prior to EDFA2, to average out the influence of the polarization dependence of the Brillouin gain. Unlike the older setup, now the narrow linewidth fiber Bragg grating (FBG) is used to precisely block the upper optical sideband, rather than transmitting the lower sideband (Fig. 4.3 (b)), and consequently significantly attenuating the co-propagating laser frequency. This modification along with the previous one significantly improved the 69 obtainable signal to noise ratio. After the Brillouin spectrally selective amplification and additional flat amplification by EDFA2, the probe signal hits the wideband detector, where it mixes with the laser signal that co-propagated with it along the fiber. The resulting ~11GHz electrical signal is amplified by an RF amplifier and sent to a fast 20GHz bandwidth real-time acquisition system for further post-processing. In the experiments below, two pump sub-pulses were used: 500ns and 50ns. For the former the chosen RF pump tone frequencies for the compound pump pulse were: 80, 155, 275, 375, 450, 535, 625, 725, 810, 900, 985, 1080, 1160, 1250 and 1350 MHz. This unequal spacing was used to reduce the detrimental effect of inter-modulation products [0]. The corresponding RF probe tone frequencies were 77, 149, 266, 363, 435, 517, 604, 701,783, 870, 952, 1044, 1121, 1208 and 1305MHz, having a 3-MHz spacing decrement relative to the pump tone spacing. Since the shorter 50ns pump sub-pulses have wider spectral bandwidth, a more spacious selection of (N=10) pump (probe) tones was used: 105 (102), 240 (234), 390 (381), 525 (513), 670 (655), 810 (792), 955 (934), 1090 (1066), 1230 (1203) and 1370 (1340) MHz. After up-conversion, the resulting optical probe comb included 30 (for the 500ns case) or 20 (for the 50ns case) different frequencies located around 10877MHz, corresponding, respectively, to a sweep-free range of 90 or 60MHz, with a 3-MHz resolution, respectively. For each launched compound pump pulse, the Brillouin return from the fiber had to be collected from the beginning of the first pump sub-pulse until the contribution of the last pump sub-pulse returned from the fiber end. In practice, we have collected data beyond the return from the last sub-pulse, thereby recording the unamplified probe signal, to be used later for the estimation of the Brillouin gain of the individual probe tones. The recorded signal was then averaged over 22 launched compound pump pulses. For a sub-pulse of duration T, the recorded 70 signal was divided into T-long sections, each representing a fiber segment of length V gT/2, where V g is the group velocity of the optical signals in the fiber. Each T-long section was then Fourier transformed [20] to obtain the spectrogram of Fig. 4.4 (a), showing the time evolution of each of the 20 optical tones, for an essentially Brillouin-homogeneous, 20m-long fiber. Here T=50ns and 20 (N=10) tones were used, centered around the fiber BFS. As expected, the first two sub-pulses arrived first at the detector. As per our choice, they carry frequencies closest to the fiber BFS, thereby measuring the gain near the peak of the BGS. The last to arrive sub-pulses have frequencies farthest from the BFS and provide information on the gain in the wings of the BGS. Following proper time-shifting and Lorentzian fitting (with peak normalization after fitting) we obtain the commonly recognized distance-frequency distribution of a uniform fiber, Fig. 4.4 (b). The first distributed sensing to be reported dealt with a 2-km FUT, comprising two spliced together, 1-km SMF-28 fiber spools with different BFSs of 10877 and 10892MHz. To minimize temperature effects on the BFS, the FUT was kept in a 35 0 C inside the temperature chamber. Fig. 4.5 (a) shows the resultant BGS variation near their joint. Longer, 500ns sub- pulses were used here, along with 30 tones. Lorentzian fit was performed, giving an average BGS FWHM of 29.1±2MHz. Sweep-free measurements compared favorably with classical BOTDA results of a FWHM of 27.6 ±1.5 MHz, measured using the same frequency sweep step of 3MHz and pulse width, see Fig. 4.5 (b). The slight change in BFS near the end of the first fiber is not due to the effective spatial resolution of 50m, but rather to strain variations resulting from manual spooling. In a higher spatial resolution experiment, we stretched the middle 4m part of the 20m fiber of Fig. 4.4 (b). The pump sub-pulse width was set to 50ns, which reflects an effective 71 resolution of 5m. Fig. 4.4 (b) described the unstretched state of the fiber. Stretching, Fig. 4.5 (c), gave rise to a 14MHz shift in the BFS, indicating a local average strain of ~280με. Only Figure 4.5 (a) Reconstruction of the BGS of a 2-km FUT, comprising two 1km fiber segments with different BFS, spliced together at the position 1000m. 30 frequency tones, spanning 90MHz, were used with a sub-pulse width of T=500ns, resulting in frequency and spatial resolutions of 3MHz and 50m, respectively. The zero frequency is 10877MHz (b) Results of classical BOTDA also with 3MHz sweeping step. (c) Reconstruction of the BGS using 20 frequency tones with 5-m resolution with the central 4-m of the fiber being stretched 22 integrations performed resulting in a total sensing time of ~30μsec, assuming pump pulses at a repetition rate of 1MHz. 4.4 Discussion and conclusions The choice of the number of tones, N , their spacing, Pump , and the additional incremental spacing of the probe tones, Pump Probe Probe (see Fig. 4.1) depends on several considerations [20]: (i) The total frequency range spanned by the tones, Pump N , should not exceed the BFS (~11GHz) in order to avoid disturbing effects of the lowest frequency pump tone on the highest frequency probe tone. While larger frequency spans cause the BFS to slightly change as a result of its dependence on the optical frequency [27], this dependence can be corrected for in the signal processing stage; (ii) The inter-tone spacing, Pump , must be larger than the width of the BGS at its bottom (~60MHz). Otherwise, a probe tone experiences 72 gain from more than one BGS; (iii) In the current implementation of the proposed technique, the sweep-free dynamic range for strain or temperature measurements is given by Probe N [Hz]. While MHz 100 Probe N is probably sufficient for temperature studies, practical strain scenarios may call for Probe N on the order of GHz’s. With N being limited by the two previous considerations, wider dynamic range could be achieved by a larger Probe , but only at the expense of the obtained frequency granularity, potentially resulting in limited strain/temperature resolution. On the other hand, for proper Lorentzian fitting, Probe cannot be made too small since the sweep-free range Probe N must be at least of the order of the natural width of the BGS, which is ~30MHz or larger, as determined by the inverse of the width of the pump sub-pulse. In summary, we successfully demonstrated a novel technique for distributed Brillouin sensing, which does not require the classical step-by-step mapping of the fiber BGS. This proposed method is potentially faster than classical BOTDA by a factor equal to the number of pump-probe pairs used for the BGS reconstruction, since each pair replaces one sweeping step in the classical technique. In the current implementation and for a given number of tones, N, there is a trade-off between the achieved resolution for strain/temperature measurements, and the available sweep-free frequency dynamic range. Current research aims at the removal of this trade-off. 73 Chapter 5 Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time- domain analyzer and sloped assisted FBG sensing 5.1 Introduction Brillouin optical time domain analysis (BOTDA) [25,30] is now successfully applied to a variety of security and structural health monitoring applications, requiring a distributed sensing of temperature/sensing with good distance resolution (<1m in most commercial instruments) [24,31-34]. Its current most prevalent implementations involve sweeping the optical frequency of a pump pulse against a continuous wave (CW) probe wave, thereby determining the Brillouin gain spectrum, whose peak is a measure of the local temperature/strain. This sweeping/scanning process is rather slow but it does not limit long range (50km) scenarios, where quite long averaging is required. Short range sensing may suffer from this slow scanning, limiting the application semi-static situations. Quite a few approaches have been recently proposed to extend BOTDA to the dynamic domain, reaching 1kHz distributed sensing and beyond [14,35-38]. Recently [27,39], we proposed a technique which completely eliminates this frequency sweeping by replacing the two interacting waves with properly matched multiple probe and pump tones. Clearly, the simultaneous use of multiple tones should shorten the sensing time by the factor equals to the number of optical tones used for interrogation. After demonstrating distributed sensing [39] using our Sweep-Free BOTDA (SF-BOTDA) and exploring its dynamic range [40], we extend our preliminary results of [41] and demonstrate distributed monitoring of temporally dynamic events, including spectral analysis, with frequencies up to 74 400Hz achieving strain sensitivity of 1 microstrain per root Hz at a sampling rate of 5.5 KHz and a spatial resolution of 4m along a single-mode optical fiber. The results are now also compared to those obtained using a fiber Bragg grating (FBG). 5.2 Experimental setup Figure 5.1 Experimental setups: (a) MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: Polarization controller; SC: Polarization scrambler; ISO: Optical isolator; DET1: detector; FBG1: Fiber Bragg grating filter; RF AMP: radio-frequency amplifier; MW AMP: Microwave frequency amplifier; AWG: Arbitrary waveform generator; SCOPE: Real-time acquisition system; OSA: Optical spectrum analyser; FUT: fiber-under-test; SP: Speaker, ST2: Translation stage. (b) BBS: Broadband source; TOF: Tunable optical filter; C1: capacitor. A block diagram of SF-BOTDA experimental setup is shown in Fig. 5.1 (a) and it is basically very similar to the one in [41]. A 80kHz linewidth laser is split into two arms, pump and probe. A wideband arbitrary waveform generator (AWG) produces two different radio- frequency (RF) frequency combs, comprising N tones, one for the pump and the other for the probe tones. For the probe arm, this RF signal feeds an RF mixer at its intermediate frequency (IF) input, while its local oscillator (LO) input is driven by a microwave source, running at approximately the BFS of the fiber and is set to be 10914MHz. The mixer output comprises 2N RF tones, symmetrically located around 10914MHz. This signal is now further amplified (to compensate for poor up-conversion efficiency) and fed into MZM1 (Mach-Zehnder 75 modulator), operating at its quadrature point, where the tones are translated to the optical domain, generating two optical multiple-tone sidebands (2N-tone each) around the optical carrier frequency. The lower sideband serves as the optical probe, while the upper side band is eventually removed by the FBG1 – fiber Bragg grating filter. For the pump arm, another channel of the AWG generates the required complex signal, comprising a compact sequence of equally-wide sub-pulses, each riding on a different pump optical carrier [39]. Modulator MZM2, operating at its zero-transmission point to suppress the laser carrier, is fed with the RF pump pulse train. The sequential launching of the pump tones results in time-shifted Brillouin-amplified probe tones traces, which are later realigned at the processing stage by a simple temporal correction [39]. An Erbium-doped fiber amplifier (PRE-EDFA2), preceding MZM2, serves to reach the maximum allowed input power into MZM2. From MZM2 the pump signal continues to EDFA2 for further amplification, and finally to the fiber under test (FUT), comprising ~30m of SMF-28 fiber. The middle 6m section of this fiber was stretched between the center of the membrane of an audio speaker (SP) and a fixed stage. This fiber section could then be subjected to dynamic strain through electrical excitation of the speaker. A narrow linewidth fiber Bragg grating (4GHz) in the setup is used to precisely block the upper optical sideband, without attenuating the co-propagating laser frequency that serves as LO in a heterodyne detection. After the Brillouin amplification, the probe signal hits a wideband detector, where it mixes with the laser signal that co-propagated with it along the fiber. The resulting ~11GHz electrical signal is amplified by an RF amplifier and sent to a fast 20GHz bandwidth real-time acquisition system for digitization and further post-processing. In the experiment, ten (N=10) RF tones were used for the pump signal where each sub-pulse length was 40ns to obtain 4m 76 of spatial resolution. The chosen RF pump tone frequencies were 105, 240, 390, 525, 670, 810, 955, 1090, 1230 and 1370 MHz. This unequal spacing is used to reduce the detrimental effect of inter-modulation products. The chosen RF probe tone frequencies were 102, 234, 381, 513, 655, 792, 934, 1066,1203 and 1340MHz, respectively, having a 3-MHz spacing decrement relative to the pump tone spacing. After up-conversion, the resulting optical probe comb included 20 different frequencies located around 10914MHz and spanning a sweep-free range of 60MHz with a 3MHz resolution. Figure 5.2 Transmission characteristics of TOF2 showing a 3dB bandwidth of ~160GHz. An independent measurement of the displacement of speaker's membrane, missing in [41], was achieved with the help of a parallel fiber attached between the speaker's membrane and a moving stage (ST2), Fig. 5.1 (b). This 40cm fiber included a fiber Bragg grating (FBG2) whose 4GHz narrow transmission window moved in unison with the membrane. The frequency position of the vibrating spectral transmission window of FBG2 was recorded by shining FBG2 with a broadband source and detecting the returned optical signal from FBG2 after it passed through a tunable optical filter (TOF2), whose transmission in the region of 77 Figure 5.3 The detector voltage when the speaker membrane is driven by a 100Hz signal before (a) and after (b) RC filtering. interest varies with frequency as in Fig. 5.2. By working on the linear part of the slope of Fig. 5.3, a good estimate of the membrane displacement can be obtained, from which the strain of the FUT can be independently calculated. A broadband ASE source (BBS) was used. It first entered a tunable optical filter (TOF), whose central frequency was set to match the center frequency of the free FBG2 and its spectral width to match the expected strain variations to be later applied to FBG2. The output of the tunable filter was fed to FBG2. Before turning the speaker on the two fibers had to be somewhat pre-stretched in order to accommodate negative strains without getting the fibers loose. The tunable filter (TOF2) had a linear slope across ~2.6nm and its -3dB point was set to fall on the central wavelength of the stretched FBG2 while the speaker was off. Having in mind that FBG2 wavelength-to-strain coefficient is around 1.2pm/με, the width of the linear slope of TOF2 determines the total dynamic range to be around 2100με. When the speaker is on, its membrane moves the center frequency of FBG2 back and forth and this spectral shift is translated by TOF2 and the following detector and the 78 RC-based (1MΩ, 5μF) low pass filter to voltage variations. This measured membrane displacement may be interpreted as the "input" to the "system" of the Brillouin sensor, whose response is considered as the "output". To save memory on the data acquisition system, we employed down sampling techniques and sampled the ~11GHz signal at 6.25GSamples/s. Such sub-Nyquist sampling creates an isolated replica of the probe baseband signal around 1.5GHz (=|11-2*6.25|). Since the bandwidth of the signal was only ~2.7GHz [2*Highest tone used (=1370MHz)], a 3GHz RF filter can recover the signal with no aliasing [42]. Segmented memory was used to capture a 1µsec record for every 15μsec. The total number of triggered records (=1668), was divided into 834 pairs, whose first member documents the Brillouin amplified probe signal from the whole fiber (with the pump on), while the second member records the trace with the pump off. Then, every six records were averaged into a single one, resulting in an effective sampling rate of 5555 records per second for a total recording period of 25ms. Then, each record was Fourier transformed in 40ns sections to obtain the heights of the various amplified probe tones, from which, after proper normalization with the no-pump trace, the BGS was reconstructed and the time evolution of the BFS was determined. 5.3 Results and discussion The response of FBG2 (i.e., the spectral variations of reflection peak) while a 100Hz signal was applied to the speaker is shown in Figs. 5.3. The noise in Fig. 5.3(a), which originates from the ASE-based BBS, is largely attenuated by the RC filter, Fig. 5.3(b). The responses of the SF-BOTDA and FBG2 sensors were simultaneously measured, while various signals were applied to the speaker. These signal tones were chosen to match (i.e., be multiples 79 Figure 5.4 The time-domain results of single tone input as measured at 80 and 120Hz (a,d) before speaker (b,e) using FBG, (c,f) using SF-BOTDA after 200Hz low-pass digital filtering. The time- domain results of FM modulated 120Hz signal with 40Hz span as measured (g) before speaker, (h) using FBG, (h) using SF-BOTDA and digitally processed. of) our SF-BOTDA 40Hz (1/25ms) spectral resolution, currently limited by the memory depth of the real-time scope. Figures 5.4(a-c) and Figs. 5.5(a-c) show the results of measuring a single 80Hz tone. Figures 5.4(a) and 5.5(a) show the time-domain and frequency-domain inputs to the speaker. Figures 5.4(b) and 5.5(b) show the response FBG2, whereas Figs. 5.4(c) and 5.5(c) show those of the rather wideband SF-BOTDA sensor, after 200Hz low-pass digital filtering. Figures. 5.4(d-f) and Figs. 5.5(d-f) describe the response to a 120Hz single tone. Finally, Figs. 5.4(g-i) and Figs. 5.5(g-i) describe the case where a multitone signal, originating from the FM modulation of a 120Hz carrier with a 40Hz tone is applied to the speaker. The strain induced on the FBG2 is estimated from the SF-BOTDA measurement considering length ratio between SF-BOTDA and FBG2 FUTs. 80 Figure 5.5 The frequency-domain results for 80Hz, 120Hz and multitone excitations (a,d,g) before speaker (b,e,f) using FBG, (c,f,i) using SF-BOTDA after 200Hz low-pass digital filtering. (j) The results of measuring 400Hz single tone using SF-BOTDA and output of speaker with calibrated microphone. We first note that the speaker’s response to the input signal is slightly distorted, probably as a result of the mechanical load presented by the two stretched fibers. As for the actual measured membrane displacement-induced strains, in all cases the SF-BOTDA results are in good agreement with the FGB2 data. Differences do exist and we believe they are due to the fact that FBG2 is part of a parallel fiber, rather than of the FUT used for the SF-BOTDA measurements. In principle, an improved configuration, where FBG2 is an integral part of the SF-BOTDA FUT, is possible using different non-overlapping spectral windows for the Brillouin and Bragg interrogations and a dedicated FBG sensing equipment. With the known [33] conversion factor of 50kHz/µ , the observed peak-to-peak amplitude of the induced BFS vibrations (~1.5MHz), we were measuring strains of the order of 30µ . Spectral analysis of 81 the signals is presented in Fig. 5.4, indicating a BFS signal to noise ratio of ~20dB (@80- 200Hz) for a noise bandwidth of 40Hz (1/25ms), which is equivalent to a strain sensitivity of ~1µ per root Hz. It has been determined that the displacement of the speaker's membrane decreased with applied frequency. Consequently, high frequency strains were more difficult to measure with our setup. Figure 5.5(j) shows the recording of 400Hz single tone with calibrated microphone together with the response of the SF-BOTDA sensor, displaying poorer performance. 5.4 Conclusions We have successfully demonstrated for the first time the ability of an SF-BOTDA setup to measure fast varying phenomena at an effective sampling rate of 5.5kHz. Results were favorably compared with parallel strain readings from an FBG. Strain variations of up to 400Hz were recorded and their spectral characteristics analyzed, achieving a strain sensitivity of ~1µ / Hz. Improvement of the setup sensitivity and the determination of its limitations are under current research. 82 Chapter 6 Spatial resolution improvement of sweep-free Brillouin optical time-domain analyzers 6.1 Introduction Fiber-optic sensing using Brillouin optical time-domain analysis (BOTDA) has proven very useful in various important applications such as security and structural health monitoring. Thfese sensors are based on the process of Brillouin nonlinear scattering [1], in which two optical counter-propagating waves are interacting via acoustical phonons that serve as an energy mediator.One wave is pulsed while its frequency difference from the other wave is scanned, and the value which maximizes the interaction, known as the Brillouin Frequency Shift (BFS), is a function of the local temperature/strain, and therefore, can monitor these two measurands. An important disadvantage of BOTDA sensors is their relatively slow sensing speed, due primarily to the need for frequency scanning. Several approaches to increase the sensing speed have been recently demonstrated[14,37-38,43]. We proposed a sweep-free concept [27,39,44], which is based on the simultaneous introduction of multiple pump and probe tones, with their optical frequencies properly assigned. The minimum spacing of the (pulsed) pump tones is determined by the inverse of the pump pulse width. The BFS is evaluated from the location of the peak of Brillouin Gain Spectrum (BGS), which is constructed from the measured gains of the probe tones. These gains are calculated from a Fourier transform of the Brillouin-amplified multi-tone probe signals, temporally windowed to achieve the required spatial resolution [39,44]. Thus, a 20ns-wide pump pulse would achieve a 2m of spatial resolution in the SF-BOTDA technique, provided the Fourier transform is performed on 20ns sections of the probe signal. However, a Fourier transform of a 20ns 83 record cannot achieve a frequency resolution better than ~50MHz. This may lead to spectral overlap among the not-equally amplified probe tones and to erroneous determination of their peaks, unless the spacing between tones is increased, at the expense of their total number[27].This phenomenon has prevented SF-BOTDA so far from achieving[39] a spatial resolution better than 5m. Here, we introduce a new technique, involving a different coding of the probe tones and a different type of processing, allowing an improved frequency resolution and consequently, an improved spatial resolution. We experimentally demonstrate 2m of spatial resolution, where the Fourier processed record is 180nsec long, rather than the previously used 20nsec one. 6.2 Concept and principle In previous implementations of the SF-BOTDA technique, the input probe wave was of the form: N k k k i Probe t j A t E 1 )] 2 ( exp[ ) ( (1) where N is the number of tones and k is the th k probe frequency. Consecutive pump pulses repeatedly met the wave of Eq. (1). The emerging Brillouin amplified probe waves were individually cut into time slots of length , commensurable with the required spatial resolution, as described above, and then Fourier-processed and P-time averaged to improve the signal to noise ratio, see Refs. 27, 39 and 44 for more details. To achieve better frequency resolution of the individual probe tones, yet with the same spatial resolution, we propose to perform the P-time averaging using a sequence of P slightly non-identical, iteratively defined probe waves given by: 84 , 1 , , 1 ( ) ( ); 1, , ; ( ) ( ) (1) Probe m Probe m Probe m Probe E t E t m P E t E t of Eq. (2) After data is collected from all P traces, we again cut each of them into -long sections. For each trace the first section contains information about the first 2 / g V -long segment of the fiber under test ( g V is the group velocity), the second temporal section relates to the second length segment and so on. Instead of Fourier transforming each temporal section, we first concatenate the first P sections from all traces, generating a P -long section that still contains information exclusively on the first fiber segment. The newly formed time record continuously covers the interaction of pump pulses with the entirety of the probe wave of Eq. (1).Fourier transformation of this P-fold longer time record results in P-fold higher frequency resolution, while the spatial resolution is maintained since only the first fiber segment is being processed. This approach does reduce the sensing speed by a factor of P but remains faster than classical BOTDA (where no averaging is used) as long as P<<N. However, Brillouin sensing normally involves signal averagingand the Fourier transformation of the longer record not only increases the frequency resolution but also effectively provides averaging. It appears, therefore, that whenever averaging is required the proposed new processing of the SF-BOTDA technique still keeps most of its speed advantage. To show the viability of the proposed concept, we performed a simulation in which we generated amultiple tones signal, whosepower spectrumappears in Fig. 6.1(a). Six tones are used at frequencies of 105, 240, 390, 525, 670 and 810MHz. These frequency tones will be later used in the experiment to define the optical tones of probe signal. An FFT (Fast Fourier Transform) of a 10nsec window results in massive broadening, Fig. 6.1(b). Spectral overlap 85 Figure 6.1 Simulation results: (a) The original 6-tone signals; (b) FFT processing of a 10nsec time window; (c) FFT processing of a 90nsec window, made of nine-10nsec concatenated sectionsfrom nine consecutive different traces. will prevent the proper determination of the intensitiesof the tones, especially when they are grossly different in magnitude. Fig. 6.1(c) shows the same spectrum but after the proposed concatenation of nine 10nsec windows into one continuouslyconnected 90nsec window. The spectrum shows much betterdefined frequency peaks.The concatenation of more consecutive traces will further improve the results, at the expense of sensing speed, until an optimum is achieved. 6.3 Experimental setup and results A block diagram of the experimental setup is shown in Fig.6.2. A narrow linewidth (80 KHz) tunable laser is split into two arms: probe and pump. For the probe wave, a radio- frequency (RF) frequency comb, comprising N tones, is produced by a wideband arbitrary waveform generator (AWG). This RF signal feeds the intermediate frequency (IF) input of the RF mixer, while the latter’s local oscillator (LO) input is driven by a microwave source, running at the approximately BFS of the fiber and is set to be 10880MHz. The output of this mixer is 2N RF tones, symmetrically arranged around 10880MHz. This microwave signal now drives the MZM1 Mach-Zehnder modulator, operating at its quadrature point and the tones are translated to the optical domain, generating two optical multiple-tone sidebands (2N-tone each) around the laser carrier frequency, with the lower sideband to serve as the probe. With 86 Figure 6.2 Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: polarization scrambler; ISO: isolator; DET: detector; FBG: fiber Bragg grating; AWG: arbitrary waveform generator; OSA: optical spectrum analyzer. proper programming of the AWG, the generated probe wave accurately implements the optical wave of Eq. (1) or (2). Since MZM1 is driven at quadrature, the laser carrier frequency is also present in the probe wave: it will later serve for heterodyne detection of the Brillouin-amplified probe tones. Regarding the pump arm, its signal is also derived from the same laser frequency. Another channel of the AWG generates the required complex signal, comprising a compact sequence of equally-wide sub-pulses, each with a different frequency [39]. Modulator (MZM2), operating at its zero-transmission point, is fed with the RF pump pulse train. The reason for using this technique, rather than having a pump pulse containing all tones, is that the overall required instantaneous optical power used for amplification is just 3dB higher than in conventional BOTDA, since at each time slot only two optical tones are generated by MZM2.The sequential launching of the pump tones results in time-shifted Brillouin-amplified probe tones, which are later realigned at the processing stage by a simple temporal correction [39].An Erbium-doped fiber amplifier (PRE-EDFA2) preceding MZM2, serves to reach the maximum allowed input power into MZM2. From MZM2 the pump signal continues to 87 EDFA2 for further amplification, and finally to the FUT. A polarization-scrambling device (SC) is located before EDFA2 to average out the influence of the polarization dependence of the Brillouin gain. The narrow linewidth fiber Bragg grating (FBG) is used to precisely block the upper optical sideband, without attenuating the co-propagating laser frequency that serves as LO in heterodyne detection. After the Brillouin spectrally selective amplification, the probe signal hits the wideband detector, where it mixes with the laser signal that co-propagated with it along the fiber. The resulting ~11GHz electrical signal is amplified by an RF amplifier and sent to a fast 20GHz bandwidth real-time acquisition system for further post-processing. To save memory on the data acquisition system, we employed down sampling techniques and sampled the ~11GHz signal at 6.25GSamples/s. Such sub-Nyquist sampling creates an isolated replica of the probe baseband signal around 1.5GHz (=|11-2*6.25|). Since the bandwidth of the signal was only ~2.7GHz [2*Highest tone used(=1370MHz)],a 3GHz RF filter can recover the signal in full and with no aliasing. In the experiment, ten (N=10) RF tones are used for the pump signal, where each sub-pulse length is 20nsec to obtain 2m resolution sensing. The chosen RF pump tone frequencies are 105, 240, 390, 525, 670, 810, 955, 1090, 1230 and 1370 MHz. This unequal spacing is used to reduce the detrimental effect of inter-modulation products. The chosen RF probe tone frequencies are 102, 234, 381, 513, 655, 792, 934, 1066,1203 and 1340MHz, respectively, having a 3-MHz spacing decrement relative to the pump tone spacing. After up-conversion, the resulting optical probe comb includes 20 different frequencies located around 10880MHz. This arrangement corresponds to a sweep-free range of 60MHz with a 3MHz resolution [29].The pump pulse width was 20nsec and the probe signal of Eq. (2) was generated with 20nsec. After acquisition, the consecutive traces were divided into sections, each comprising nine (9) consecutive traces, associated with the same fiber segment. To achieve a 2m of spatial resolution using the 88 Figure 6.3 Experimental results: (a) The measured tones after an FFT of a 20nsec window; (b) The measured tones after an FFT of a 180nsec window made of nine-20nsec concatenated windows from nine consecutive traces; (c) The reconstructed BGS along 30m optical SMF fiber showing the variations of the BFS along the fiber. previous processing of Refs. 39 and 44, we Fourier transformed the probe data with a window of 20nsec. The results, depicted in Fig. 6.3 (a), show hardly distinguishable tones. Fig. 6.3 (b) displays the results of the new technique, using a time record of 180nsec (9X20nsec) for the FFT processing. Here the various tones are well defined. These tones were then used to reconstruct [27,39,44] the BGS along the 30m optical fiber, Fig. 6.3 (c), indicating a 2m resolution. This is the best resolution we obtained so far with our SF-BOTDA sensor. 6.4 Summary The sweep-free BOTDA technique, while offering a substantial sensing speed advantage, requires the accurate determination of the intensities of the multiple tones of the Brillouin-amplified probe wave. These individual tones are isolated and identified by Fourier processing of the probe signal in predefined time windows. But to achieve high frequency resolution of the tones a long time window is required, while good spatial resolution demands a short window. This chapter presents a method to satisfy both requirements, paving the way for the SF-BOTDA technique to achieve spatial resolutions similar to those of classical BOTDA with a large number of tones, ensuring high tone granularity and, consequently, high accuracy in the determination of the local Brillouin frequency shift. 89 Chapter 7 Extending the dynamic range of sweep-free Brillouin time-domain analyzer 7.1 Introduction Sweep-free Brillouin optical time-domain analysis (SF-BOTDA) replaces the sequential frequency scanning of classical BOTDA by parallel interrogation of the fiber- under-test using the simultaneous interaction of multiple pump tones with counter-propagating multiple probe tones. While the basic SF-BOTDA technique boosts the measurement speed by a factor equal to the number of probe tones used, its dynamic range is limited to approximately the pump tone spacing, which is of the order of 100MHz. This chapter provides in-depth analysis of our method to significantly extend the dynamic range to the GHz regime. Based on sequential interrogation with up to three sets of multiple tones, each having a different frequency spacing, this method provides a major speed advantage over the classical BOTDA in spite of the use of three sets of tones. With this development, which does not require any additional hardware, SF-BOTDA offers distributed sensing of optical fibers over practical dynamic ranges of strain/temperature variations, with the potential to become one of the fastest sensing techniques. 7.2 Description of original method and its dynamic range limitation The concept of the SF-BOTDA sensor, as described in [27,39-40,45], is illustrated in Fig. 7.1. Instead of scanning the frequency difference between a single pump tone and a counterpropagating single probe tone, multiple pump and probe tones, Fig. 7.1 (a), are 90 Figure 7.1 Sweep-free Brillouin probing using the simultaneous launching of multiple pump and probe tones. (a) N pump (=25) pump tones (Eq. (1a), magenta stems topped by circles, spaced by 100MHz) are launched into the fiber against N probe (=20) probe tones (Eq. (1(b), blue stems topped by diamonds), spaced by 95MHz (i.e., 5MHz smaller than that of the pump tones) and overall downshifted in frequency from the pump tones by a fixed frequency difference, BFS 0, chosen to be close to the average BFS of the fiber under study (note the different horizontal scales for the two stem plots); (b) The resulting cumulative Brillouin-induced gain spectrum arbitrary units ([A.U.]), generated by the pump tones together with its sampling by the probe tones. Here the actual BFS is assumed to be equal to BFS 0 and we note that each probe tone samples the BGS generated by the pump associated with that probe tone: e.g., the middle (11 th ) probe tone, circled at its bottom, samples the BGS originated from the middle (13 th ) pump tone, bolded and circled at top; (c) Plotting the sampled gains (Diamonds) against {h(i)} of Eq. (3) results in an approximate reconstruction of the common gain BGS n( ). More importantly, fitting the upper part of the data to a parabola (not shown) produces an excellent estimation of the zero shift from BFS 0. A Lorentzian, precisely centered at the true BFS=BFS-BFS 0 and having the same height and center as the fitted parabola, is also shown in (c). The reconstructed spectrum is a bit wider than the true Lorentzian, due to the influence of neighboring peaks in (b), but shares the same peak location. (d) and (e) are the same as (b) and (c) but with BFS 0+27.5MHz. Again, the estimation of the 27.5MHz shift from BFS 0 is quite good: 27.49MHz. generated and counter-propagate within the optical fiber. The frequencies of the pump tones are given by: pump pump pump N i i f i , , 1 ), ( ) ( 0 (1) 91 Here, ν 0 is an optical frequency around which the pump frequencies reside, most commonly near 1550nm. )} ( { i f pump are RF frequencies that define the pump frequencies )} ( { i pump . )} ( { i f pump can be both positive and negative; their spacing must significantly exceed the actual Brillouin linewidth in order to prevent crosstalk. In Fig. 7.1, } 25 ,.., 1 ], MHz [ 1200 100 ) 1 ( ) ( { i i i f pump , so that the pump tones are spaced by 100MHz pump , significantly larger than the assumed natural linewidth of 30MHz (for standard SMF fibers at around 1550nm). Note that for pump pulses shorter than ~50ns, pump must be increased to accommodate the wider Brillouin linewidth, which approaches an inverse dependence on the pump pulse width, T, for T<20ns. These pump tones produce multiple and practically identical, [27], Brillouin gain spectra. Under common low-gain conditions, the otherwise exponential Brillouin gain, [1], can be linearized, resulting in a cumulative linear gain of the form: pump N i pump n i z BFS i BGS P L g z Gain 1 )) ( ) ( ( 1 ) , ( . (2) Here, i P [W/m 2 ] is the optical power density of i-th pump; ) ( n BGS is a normalized Brillouin gain spectrum of Lorentzian shape for long pump pulses, and of more rounded, non- Lorentzian shape for pump pulses shorter than ~50ns; the pump-pulse-width dependent g is related to the line-center Brillouin gain factor [1], and L=V gT/2 (V g is the group velocity in the fiber). Both g and ) ( n BGS may be a function of the distance coordinate, z, along the fiber. The local environmentally-sensitive down-shift in frequency, BFS(z), which is the quantity of interest [39], is assumed common to all pump tones, Fig. 7.1 (b). 92 Figure 7.2 Erroneous BGS reconstruction for BFS values which are larger than BFS 0 by more than half the pump tone spacing. Here the probe tone spacing is 95MHz as in Fig. 7.1. Left column: BFS=BFS 0+427.5MHz; Right column: BFS=BFS 0+372.5MHz. While the BFS values here are distinctly different from those of Fig. 7.1, they are erroneously estimated as very close to their values in Fig. 7.1, namely: 27.42MHz and -27.5MHz instead of 427.5 and 372.5MHz. The source of this ambiguity is the fact that the probe tones sample Brillouin gains other than those associated with them. Thus, for BFS=427.5MHz (Left column) the 11th (counting from the left, circled at its bottom) probe tone does not sample the Brillouin gain induced by its corresponding pump (the 13 th , bolded one, circled at top), as in Fig. 7.1, but rather by the (13+4) th pump tone. A similar argument holds for BFS=372.5MHz. The chosen probe tones, ) 3 ( ; , , 1 ), ( ) ( ) ( 0 0 pump probe probe pump probe N N N j j h BFS k j f j are a down-shifted version of the pump tones with the following distinct properties: (i) The downshifting amount, BFS 0, is predetermined, chosen to be close to the expected average BFS of the fiber under study; (ii) Since for reasons to be explained in Sec. 7.5 the number of probe tones may be smaller than the number of pump tones (20 vs. 25 in all relevant figures), the parameter k associates the j-th probe tone with the (j+k)-th pump tone (k=2 in Fig. 7.1); and (iii) The spacing of the probe tones is slightly larger (or smaller) than that of the pump tones so that each probe tone samples a different region of the BGS induced by the 93 corresponding pump tone. The difference between the spacings of the tone families (5MHz in Fig. 7.1) eventually determines the measurement resolution, much like the frequency scanning resolution in a classical BOTDA implementation [46]. In Fig. 7.1, } 20 . 1 MHz, 5 ) 1 ( - 50MHz ) ( { . . j j j h , counting j from the left, and the probe tone spacing is 95MHz. In Figs. 7.1 (b)-(c) the 'measured' BFS is assumed to be equal to BFS 0 (i.e., zero shift) and all pump tones are of equal power. Since N pump=25 while N probe=20, the j-th tone of the probe is amplified by the (j+2)-th tone of the pump through Stimulated Brillouin Scattering (SBS). Probe tones, which are closer (in frequency) to the BGS centers, experience higher Brillouin gains. The 'measured' gains of the N probe probes are then plotted, panel (c) in Fig. 7.1 (c), against ) ( h of (3) to obtain a line shape whose peak, denoted by shift and calculated [46] from fitting the 30% top part of the sampled gains to a parabola (not shown), provides a measured estimate (~0MHz) of the assumed Brillouin shift of BFS BFS-BFS 0=0MHz. Panels (d) and (e) in Fig. 7.1 are the same as (b) and (c) but with a non-zero Brillouin shift, namely: BFS=BFS 0+27.5MHz. The observed accuracy, 27.49MHz (estimated) vs. 27.5MHz (assumed), is quite good (A Brillouin shift of 10kHz is related to temperature and strain variations of 0.01 0 C and 0.2µ , respectively). However, the ubiquitous presence of noise, ignored in the example, will undoubtedly require better frequency resolution for the same accuracy. In this way and without the need for frequency sweeping, the SF-BOTDA technique estimates the BFS shift from BFS 0 in a single measurement (up to averaging), and therefore, has the potential to increase the measurement speed by a factor of N probe with respect to classical BOTDA [27,39-40,45]. 94 Note that in Fig. 7.1 (e) ( BFS=27.5MHz) the first probe tone on the left (j=1) is no longer amplified by its corresponding pump tone (i=j+2=3), as in Fig. 7.1 (b), but rather by the 4 th pump tone. This behavior, which is also shared by probe tones j=2-6, worsens as BFS approaches 50MHz (half the pump spacing) and is the source of ambiguity to be discussed below. The spacing of the probe tones could be also chosen to be larger than that of the pump tones. In this case, the distances, {h( )}, (3), of the probe signals from the centers of the BGSs induced by their corresponding pump tones progressively increase. Note that an increasing (decreasing) BFS moves the cumulative Brillouin spectra to the left (right), see Fig. 7.1. Consequently, for increasing h(i), the reconstructed Brillouin gain, Fig. 7.1 (e), will be shifted to a negative value -27.49MHz, which is the opposite of the true shift. Since this behavior is systematic, then when working with probe tone spacing larger than that of the pump tones, the negative of the observed shift should be taken as the true value. The above implementation of the multiple pump/probe concept works well when most probe tones are amplified by their corresponding pump tone, as in Fig. 7.1, where the local BFS deviates from BFS 0 by less than half the pump frequency spacing. Otherwise, and in view of the periodicity of the pump spectrum, the reconstruction algorithm described above generates values for the shift of the reduced spectrum, shift , which relate to the true BFS shift through a periodic expression (the 'round( )' function rounds its argument towards the nearest integer): ) / ( round ; 0 0 pump pump shift BFS n n BFS (4) 95 Indeed, for deviations of the BFS larger than half the pump spacing, probe tones are amplified by the Brillouin gain induced by higher-index or lower-index (in frequency) pump tones, Fig. 7.2. Thus, different BFS values separated by an integer multiple of the pump spacing produce the same reduced BGS as shown in Fig. 7.2. Consequently, the above- described implementation of the technique provides reliable measurements only if it is known in advance that the expected dynamic range of the strain/temperature variation in a given scenario is strictly limited to the rather small span of } 2 / | {| 0 pump BFS BFS BFS . Another consequence of large deviations of the BFS from BFS 0 is the loss of Brillouin gain at edge-residing probe tones, causing the estimation of the true BFS (modulo the pump tone spacing) to be a bit worse in Fig. 7.2 (c), as compared with Fig. 7.1 (c) (27.45 instead of 27.42MHz). While the estimation accuracy critically depends on the particular algorithm in use, this issue may be also addressed by having more pump tones than probe tones, as has been done above (N probe=20<25= N pump). 7.3 Extending the dynamic range of SF-BOTDA A straightforward way to increase the dynamic range with no ambiguity is to increase the pump spacing, pump to a value large enough to cover the required dynamic range. For example, pump of 500MHz will cover a temperature measurement range of 500 0 C or a strain dynamic range of 10,000µ or a more limited combination of both. However, as detailed in [47], estimation accuracy depends on the number of pump and probe tones, and for a given value of N pump, the total range spanned by the pump tones, N pump pump, must be smaller than the BFS (~11GHz). This limitation on either N pump (resolution) or pump (dynamic range) calls for more flexible ways to increase the measurement dynamic range of SF-BOTDA. 96 Figure 7.3 BGS reconstruction of ∆BFS=427.5MHz, using 3 pump spacings for BFS values within the dynamic range defined by Eq. (5), which is ±450MHz (around the pre-chosen BFS 0) for the spacing choice of (a=d) MHz 100 0 pump , (b) MHz 91 pump , and (e) MHz 109 pump . Once the spectral shifts of the three measurements are estimated from (c) and (f) as 42 . 27 0 shift , 47 . 27 shift , and 45 . 8 shift (all in units of MHz), n 0 and the ∆BFS can be uniquely estimated, from either the additional sampling at pump or at pump , or from both, see text. Here only the results of the sampling at pump are valid. Indeed, while the 11th probe samples the gain of the (13+4) th pump in both (a=d) and (e), it samples the gain of the (13+5) th pump in (b). Another, although somewhat cruder, approach to deal with an arbitrary dynamic range comprises the following steps: (i) Determine the BFS using a classical BOTDA measurement (other fast methods, e.g. [14], also require this preliminary step to find their operating point on the BGS slope). Additional hardware is not required since our SF-BOTDA setup [27,39- 40,45], is easily software-modified to act as a classical BOTDA; then (ii) Assign the measured value to 0 BFS ; (iii) perform measurements using the SF-BOTDA technique; and finally (iv) avoid ambiguities by continuously tracking the changes in the BFS, which are assumed to be much slower than the sampling rate of the SF-BOTDA technique, so that sudden jumps of the BFS larger than a single pump spacing, should not occur. While providing virtually unlimited dynamic range (limited only by that of the classical BOTDA instrumentation) this approach 97 has its obvious limitations in terms of the time it consumes, as well as the difficulty to correctly determine the BFS under dynamic conditions [48]. Here, we propose and demonstrate an alternative novel solution, which removes the dynamic range ambiguity by employing, consecutively, pump tones of three different spacings: pump pump pump 0 . Using the capabilities of our original hardware, [39-40,45], this reduces the sampling rate of SF-BOTDA by a factor of 3 but, somewhat surprisingly, will further increase the speed advantage of SF-BOTDA over classical BOTDA, see Sec. 7.5. Each measurement, with either 0 pump , pump or pump will produce an estimated shift of the reduced spectrum, panels (c) and (f) of Fig. 7.3, obeying equations similar to (4): ) / ( round ; ) 5 ( ) / ( round ; ) / ( round ; 0 0 0 0 0 pump shift pump pump shift pump pump shift pump BFS n n BFS BFS n n BFS BFS n n BFS Based on these three measurements we now claim (see Appendix for proof) that the values of 0 n and consequently those of BFS , Eq. (5), and ultimately those of the measured BFS BFS BFS 0 , can be uniquely determined in a much wider dynamic range, DR, given by (the 'floor( )' function rounds its argument towards minus infinity): ; ) 5 . 0 ( 0 max 0 pump BOTDA SF n BFS BFS DR (6a) 1 min 5 . 0 floor 0 0 max pump pump pump n (6b) 98 In the example of Fig. 7.3, 0 pump=100MHz, - pump=91MHz, + pump=109MHz so that n max=floor[0.5min(91/9,109/9)]-1=4. Here, the dynamic range is: | BFS|<450MHz, i.e., 9 times wider than the previous 50MHz, and DR SF-BOTDA=900MHz. Hence, as long as the actual strain/ temperature variations to be measured induce Brillouin frequency shifts within this range, the SF-BODTA technique provides both fast and unique results. As shown in the Appendix, 0 n is determined from the measured shift shift shift , , 0 using either pump pump shift shift n 0 0 0 round (7.1) or pump pump shift shift n 0 0 0 round , (7.2) which ever produces a value of 0 n smaller or equal in absolute value to m ax n of (6b). Obtained values for 0 n , which are larger than m ax n are discarded. It is guaranteed, however, that as long as )] /( ) ( 5 . 0 [ floor max pump pump pump pump n (8) (=5 in our example), either (7.1) or (7.2) (or both) will provide the correct value for 0 n , see Appendix. For the example of Fig. 7.3, the smaller, 91MHz, pump tone spacing, gives 6 )] 9 /( ) 42 . 27 47 . 27 [( round 0 n , whose absolute value is larger than n max=4, and, 99 Figure 7.4 Experimental block diagram: MZM: Mach-Zehnder electro-optic modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; ISO: optical isolator; AWG: arbitrary waveform generator; FUT: fiber-under-test. therefore, is discarded. On the other hand, the larger pump tone separation, 109MHz, gives n 0=round[(-8.45-27.42)/(-9)]=4, resulting (see Eq. (5)) in ∆BFS est=4·100+ 27.42=427.42 MHz, which is a very good estimate of the true 427.5MHz one. 7.4 An experimental example In order to illustrate the proposed concept of dynamic range extension, we used a simplified version of the experimental setup of [39-40,45], see Fig. 7.4. A highly coherent laser was split into pump and probe arms: (i) Pump tones: One channel of a wideband arbitrary waveform generator (AWG) was used to generate a comb of 10 RF frequencies, having a programmable spacing, pump. After proper RF amplification this comb drove a Mach- Zehnder electro-optic modulator (MZM2), biased near zero transmission, to produce N pump=21 optical pump tones (the 11 th tone was the laser light); (ii) Probe tones: The other channel of the AWG generated another 8-tone comb, with a programmable spacing of probe. This comb signal fed the IF input of a mixer, whose RF input was connected to a microwave synthesizer. The output of the mixer thus comprised 16 tones symmetrically arranged around the (also 100 programmable) generator frequency. This multi-tone signal drove another modulator (MZM1), where it was up-converted to the optical domain, thereby creating two sidelobes, with N probe=17 optical tones on each side of the laser light. After proper optical magnification the pump and probe signals entered the 95m single mode fiber under test (FUT) from its opposite sides. The emerging probe tones then passed a circulator on their way to a high resolution (20MHz) optical spectrum analyzer. Finally, the Brillouin gains of the amplified lower-sidelobe probe tones were estimated by measuring their optical powers with and without the pump tones. While this simplified setup, using CW rather than pulsed pump tones, cannot perform distributed sensing, it is comprehensive enough to demonstrate the proposed dynamic range extension technique. We used the same 3 sets of pump spacing as in Figs. 7.1-7.3: pump=100, 91 and 109 MHz. The probe tones spacing, though, had to be changed to accommodate their smaller number. For the 17 probe tones to fully cover the pump tone spacing the following corresponding values were used: 93.75, 85.3125 and 102.1875 MHz, resulting in an interrogation resolution of ( pump /16) 6.25, 5.6875 and 6.8125 MHz, respectively. With the above choice of pump spacings the allowed dynamic range is ±450 MHz, which translates into an extremely wide dynamic range of either temperature (1 MHz/ 0 C) or strain (500 MHz/1%). Instead of subjecting the fiber to extreme environments, we have used a completely equivalent and quite a simple way to experimentally test the available dynamic range. We first turned off the AWG and scanned the microwave synthesizer to find out that maximum Brillouin gain was achieved when the synthesizer was set to f osc=BFS fiber=10,058 101 Figure 7.5 Experimental demonstration of the dynamic range extension concept using three different pump tone spacings of 100, 91 and 109 MHz. 16 probe tones are used (the 17-th probe tone periodically repeats the effect of the first one). The estimated peak locations are indicated by short vertical lines and their frequency locations also appear in the figure). Based on these estimates, Lorentzian curves have been added. MHz. Then, in order to challenge the SF-BOTDA setup with a BFS change of BFS we simply moved the synthesizer frequency from f osc=10,058 MHz to BFS f osc . In this way, a situation was created where the setup is set to (see Sec. 7.2) BFS BFS BFS fiber 0 and measures a fiber whose BFS is BFS away from the frequency to which the setup was set: 0 BFS BFS BFS fiber . Figure 7.5 describes the results of a measurement where the synthesizer frequency was set to 10,360MHz, being equivalent to a BFS of -302 MHz. This value is well outside the native dynamic range of ~±50 MHz for the selected pump spacings. Parabolic fitting around the peaks, [46], resulted in 5 . 1 0 shift , 9 . 29 shift , MHz 2 . 27 shift . Here, both Eqs. (7) give valid values for n 0=-3. BFS can now be estimated in three ways: 102 MHz 8 . 299 ) 2 . 27 ( 109 ) 3 ( MHz 9 . 302 ) 9 . 29 ( 91 ) 3 ( MHz 5 . 301 ) 5 . 1 ( 100 ) 3 ( BFS BFS BFS , (9) having a mean of -301.4 MHz instead of the set value of -302MHz. This obtained accuracy is well within the measurement granularity of pump /16~6 MHz. A similar measurement was taken for the case of BFS=-520MHz, which is outside the projected dynamic range of ±450 MHz. The resulting shifts were measured to be ) 20 ( 3 . 21 0 shift , ) 26 ( 5 . 25 shift , MHz ) 25 ( 6 . 27 shift (the numbers in parentheses are those predicted by Eqs. (5)). Applying Eqs. (7.1) and (7.2) we indeed get for n 0 values (5 and -5, respectively), both exceeding (in absolute values) the allowed n max=4 of Eq. (6b). While demonstrated here for the non-distributed CW version of SF-BOTDA, the proposed dynamic range extension technique is fully compatible with complete distributed- measurement-capable setup of [39-40,45]. 7.5 Discussion A few important characteristics of the dynamic extension technique are discussed below: (a) How wide can the extended dynamic range DR SF-BOTDA go? Clearly, the dynamic range of Eqs. (6) is inversely proportional to the difference | | 0 pump pump . However, the dynamic range cannot be increased at will by simply choosing pump to be arbitrarily close to 0 pump . As evident from Eqs. (6) and Fig. 7.3, the smaller | | 0 pump pump , the closer together are the measured values for } , { 0 shift shift and their 103 accurate estimation, and more importantly the accurate estimation of their difference, shift shift 0 , later used in Eqs. (7), becomes more difficult. Practically, a lower bound on the proximity of pump to 0 pump will be determined by the measurement resolution (which is of the order of a fraction of the difference between the pump and probe spacings: | | , 0 , 0 probe pump spacing (, noise issues, and the sophistication of the signal processing techniques used to determine } , { 0 shift shift . (b) Speed advantage of the extended dynamic range SF-BOTDA over classical BOTDA: In a measurement scenario involving Brillouin frequency shifts limited to 2 / | | 0 punp BFS BFS for a pre-chosen 0 BFS , the original SF-BOTDA technique [27,39-40] offers a speed increase by a factor of N probe, assuming both methods use the same number of interrogating tones with the same frequency spacing, spacing. We now show that the extended dynamic range technique of this chapter offers a significantly higher gain in speed. For the same dynamic range, DR, and the same frequency spacing of the interrogating tones, spacing, classical BOTDA requires the sequential measurements of DR/ spacing frequencies. On the other hand, the SF- BOTDA technique will provide the same frequency coverage with the same frequency resolution in only 3 measurements! In our example of spacing=5MHz and DR=900MHz, the speed gain is 180/3=60 (180=900/5). Averaging will reduce the speed of both methods in the same way. This comparison assumes, though, that the more complex implementation of SF-BOTDA will provide the same signal to noise ratio as in classical BOTDA. Streamlining and optimizing the current hardware may come close to this challenging goal. 104 (c) The need for extra pump tones: It has been already noted above, Fig. 7.2 (a-b), that every shift of the BFS by one pump spacing further distances one of the extreme probe tones from the BGS induced by its counter-part pump tone: While in Fig. 7.1 the 20 th probe tone is amplified by its associated 22 nd pump tone, in Fig. 7.2 (a) the 19 th probe is amplified by the 25 th pump tone and the far-right 20 th probe tone, which is supposed to be amplified non-existing pump tone, is not amplified at all. Unless more pump tones are added, these extreme probe tones will experience no gains, deteriorating the accuracy of the estimation of BFS shift. To maintain the measurement accuracy of the zero-order dynamic range ( 2 / | | 0 pump BFS ) over the full dynamic range of Eq. (6), pump N should exceed max 2n N probe (In Fig. 7.2 (a) BFS=427.5MHz<450MHz, pump N should have been 27. Instead, only 25 pump tones were used in order to demonstrate the issue). (d) The correct estimation of shift : Finally, the accurate estimation of the spectral shift of the reduced spectrum, shift , is of paramount importance for the success of the SF- BOTDA method. So far, we assumed the reduced spectrum to have a well-defined peak, which is the case as long as | | shift is not too close to 2 / , 0 pump , i.e., not too close to the edges of the reduced spectrum, Fig. 7.1 (c,e). In the vicinity of 2 / , 0 pump , however, there is no distinct peak and more advanced signal processing of the data is required, probably eased by the method capability to continuously track the changes in the BFS, as well by the fact that the shape of the measured spectrum is known. 105 7.6 Summary This chapter provides an in-depth quantitative analysis of a proposed technique, which significantly extends the strain/temperature dynamic range of SF-BODTA. It shows that by performing at most three sequential measurements, each with a different frequency spacing of the multiple pumps and their corresponding multiple tones, the Brillouin Frequency Shift can be uniquely determined within an extended dynamic range, whose value depends on the chosen three frequency spacings, Eq. (5). The closer these spacings, the wider is the dynamic range. The available signal-to-noise ratio, the number of averages used and other system parameters will set a lower practical bound on their closeness. Neither the BFS estimation accuracy nor the spatial resolution are compromised by this dynamic-range extension technique, which neither requires any additional hardware. While the sensing speed is reduced by (at most) a factor of three (relative to the original SF-BOTDA implementation), its speed advantage over classical BOTDA is even more pronounced in many wide dynamic range applications. To alleviate the three-fold speed reduction, an alternative way to extend the dynamic range of SF-BOTDA by removing the ambiguity of what pump amplifies a given probe, is currently under study using individual coding of the pump tones. With this development, SF-BOTDA offers distributed sensing of optical fibers over practical dynamic ranges of strain/temperature variations, with the potential to become one of the fastest sensing techniques. It is currently hardware-intensive but its speed advantages may merit the effort. 106 7.7 Appendix Starting from Eq. (5), ) / ( round ; ) / ( round ; ) / ( round ; 0 0 0 0 0 pump shift pump pump shift pump pump shift pump BFS n n BFS BFS n n BFS BFS n n BFS (A1) we note that since pump pump pump 0 , the three indices {n 0, n - , n +} may not be equal. If however, n -=n 0 or n +=n 0, then (A1) leads to: pump pump shift shift shift pump shift pump n n n - - 0 0 0 0 0 0 0 . (A2) While n 0 is an integer, measurement errors and noise will cause the ratio in (A2) to slightly deviate from a whole number. Adding the round( ) function (rounding to the nearest integer) produces Eqs. (7). But it may well be the case that n ± measured through (A1) is different than n 0, namely: n ±=n 0+m ±, with m ±≠0. We now investigate this situation and show that for the dynamic range defined by Eqs. (6), only those obtained values for n ± which are smaller or equal in absolute value to n max of (6.1) can be used to predict n 0. Furthermore, once Eq. (8) is satisfied, see below for a proof, it is guaranteed that either n + and/or n - will produce the correct n0. 107 When n ±=n 0+m ±, with m ±≠0, (A1) gives: pump pump pump pump pump shift shift shift pump shift pump K K m n m n n - ; - - - ) ( 0 0 0 0 0 0 0 0 (A3) Our proposed procedure aims at estimating n 0 from either ] - [ round - - round 0 0 0 0 K m n n pump pump shift shift est (A4.1) or ] - [ round - - round 0 0 0 0 K m n n pump pump shift shift est . (A4.2) Clearly, if m ±≠0 then 0 0 n n est and the use of (A4.1-4.2) to predict the correct value of 0 n simply fails. We now prove that whenever the measurement scenario is such that the BFS variations do not exceed the dynamic range of (6), there is a way to detect those cases for which m ±≠0, and to successfully avoid them. Claims: A) If 1 |]} min[| 5 . 0 { floor | | max 0 K n n , as in (6); and if m ±≠0, then max 0 | | n n est and, hence, can be discarded. B) If also ] ) /( ) ( 5 . 0 floor[ max pump pump pump pump n , Eq. (8), then it is guaranteed that either n 0=n - , and/or n 0=n + , so that n 0 can be always correctly estimated. 108 Proof: From our assumption that 1 |]} min[| 5 . 0 { floor | | max 0 K n n and the definition of the ‘floor’ function (y=floor(y)+ , 0 <1) it follows that 1 |] min[| 5 . 0 1 |] min[| 5 . 0 0 K n K , (A5) with 1 0 . The following expressions apply to | | K if | | | | K K or else to | | K . Thus, 1 | | 5 . 0 1 | | 5 . 0 0 K n K . (A6) We now subtract K m from (A6) and use the definition of the round( ) function (y=round(y)+ , | | 0.5) to obtain: 1 | | 5 . 0 1 | | 5 . 0 0 K m K K m K K m n or 1 | | 5 . 0 1 | | 5 . 0 ] [ round 0 K m K K m K K m n And finally, 1 | | 5 . 0 1 | | 5 . 0 ] [ round 0 K m K K m K K m n (A7) If 0 K m then (m ±≠0 is an integer whose absolute value is assumed to larger or equal to 1): 109 Figure 7.6 The dependence of 0 n (blue: solid), est n 0 (red: dashed) and est n 0 (green: dashed-dotted), Eq. (A4), on BFS for the data of the pump tone spacings used in Fig. 7.4: MHz 100 0 pump , MHz 91 pump , and MHz 109 pump . The vertical arrows denote the allowed dynamic range of Eqs. (6), MHz 450 | | BFS , while horizontal arrows point at the maximum allowed values for max n ( 4). ) 2 2 ( 2 2 } 1 | | 5 . 0 { 1 | | 5 . 0 ] [ round max 0 0 n K K m K K m n n est Since 0 ) 2 2 ( we conclude that max 0 0 ] [ round n K m n n est . (A8) 110 Similarly, if 0 K m then max max 0 0 ) 2 2 ( 2 2 } 1 | | 5 . 0 { 1 | | 5 . 0 ] [ round n n K K m K K m n n est (A9) which completes the proof of our claim whenever max 0 | | n n est or max 0 | | n n est they can serve as valid estimators for n 0. In order to prove our second claim we plot in Fig. 7.6 the BFS dependence of 0 n , Eqs. (7) (blue: solid), est n 0 (red: dashed) and est n 0 (green: dashed-dotted), Eq. (A4), for the data of the pump tone spacings used in Fig. 7.3. Also shown are vertical arrows, denoting the allowed dynamic range of Eqs. (6), MHz 450 | | BFS , and horizontal arrows at vertical values of m ax n . It is clearly seen that as long as BFS is within its dynamic range, a correct estimate of 0 n can always be obtained from either est n 0 (the red curve coincides with the blue one) or from est n 0 (the green curve coincides with the blue one) or from both. As BFS grows from 0 BFS , the two estimates work well (i.e., 0 0 0 0 n n n est est until BFS exceeds 2 / pump , where n becomes ) 0 ( 1 0 n , driving est n 0 to a value (-10) smaller than m ax n (- 4). At this point, 0 n can be estimated only from est n 0 . When BFS exceeds 2 / 0 pump , 0 n increases to 1 (=n -) and 0 n can be again correctly estimated from est n 0 but not from est n 0 (=-11<-4). 0 0 0 n n n est est resumes its validity for 2 / pump BFS until BFS crosses pump 5 . 1 136MHz, and so on and so forth. This guaranteed estimation process of 0 n depends on the returning of the est n 0 curve to the 0 n curve before the est n 0 curve departs from 111 the 0 n one. Let return BFS , denote the value of BFS at which the est n 0 returns to the 0 n curve. Similarly, Depart BFS , will denote the value of BFS at which the est n 0 departs from the 0 n curve. Mathematically, 2 / 2 / 0 , 0 , pump pump depart pump pump return n BFS n BFS . (A10) In order for the est n 0 curve to return to the 0 n one before the departure of the est n 0 curve we require that depart return BFS BFS , , , (A11) which leads to the additional condition on m ax n , (8), namely: pump pump pump pump n 5 . 0 floor max (A12) Similar considerations hold for 0 BFS , also resulting in (A12). In our example of Fig. 7.3, (A12) is violated for MHz 5 . 591 | | BFS , outside our allowed dynamic range. More generally, it is easy to show that a sufficient, but by no means necessary condition for (A12) to be obeyed for n max of Eq. (6b), is to choose the three pump spacings such that 0 pump is the average of pump and pump . 112 Chapter 8 Performance analysis of the sweep-free Brillouin optical time-domain analyzer 8.1 Introduction Recently [27,39,44], we have developed the sweep-free BOTDA method (SF-BOTDA), in which multiple pump and probes, Fig. 4.1, make it possible to determine the BFS in a single measurement without frequency sweeping. Thus, the SF-BOTDA method should prove faster than the classical BOTDA by a factor equal to the number of tones used in the interrogation process. In principle it is faster than the F-BOTDA technique [38] if it can provide the same frequency granularity (the difference between the pump tone spacing and the spacing between the probe tones: e.g., 3MHz in Fig. 4.1) and offers a much wider dynamic than slope-based methods if a large enough number of tones are employed. Quite a few parameters impact the performance of SF-BOTDA as measured by the error in determining the true local BFS [46]. These include the (i) number of tones; (ii) granularity; (iii) spatial resolution; (iv) dynamic range; and (v) number of averages. In this chapter, we study the impact of these parameters on the BFS error. 8.2 Simulation A block diagram of the SF-BOTDA system simulation is shown in Fig. 8.1. Modelling in detail the experimental setup of Ref. 39, two arms (pump and probe) are simulated. The pump arm is implemented by generating a finite (N) series of sine functions with predetermined amplitudes, RF frequencies and phases. Then, double-sided modulation and up-conversion of the N tones to an “optical” carrier (set to be 50GHz) are implemented using 113 a model of a Mach-Zehnder Modulator (MZM), working at its zero transmission point. Finally, the resultant pump function is temporally pulsed according to the desired spatial resolution. In the probe arm, a different set of N tones is double-sided modulated around an “optical” carrier whose frequency is lower than that of the pump carrier by BFS of the fiber under study (~11GHz). Here the upconversion to the "optical" domain is performed using the MZM function at quadrature. In this manner, optical carrier and the signal are in-phase so almost no phase noise introduced in the heterodyne detection stage. In order to take into consideration narrow pump pulse widths, the Brillouin amplification is modeled by the convolution of a Lorentzian-based BGS, centered at the local strain/temperature controlled BFS along the fiber, with the spectrum of the pump pulse. Once computed, this strain-dependent Brillouin gain is appropriately applied to each of the probe tones. The detection section includes an optical filter, which filters out unwanted optical carriers, such the probe upper sideband, followed by a square-law detector, where the amplified probe tones are mixed with the "optical" carrier. Here, white-noise is added to the signal to model the overall noise accumulated during the various stages of the setup. Contributions to this noise come from RF amplifiers and spontaneous Brillouin noise, and most predominantly from beat noise between the amplified spontaneous emission of the EDFA amplifiers and the optical carrier. The sampling of the resultant probe signal may be performed at different sampling rates with and without down- sampling depending on the overall bandwidth occupied by the 2N probe tones around the ~11GHz IF. Finally, the post-processing stage includes averaging of sequential probe traces, spectrogram calculation for the determination of BGS along the fiber. Once the sampled shape of the local BGS is obtained, the value of the corresponding BFS is estimated by fitting the data to a Lorentzian. Finally, the BFS error is calculated by Monte Carlo techniques and a root-mean-square statistic. 114 Figure 8.1. Sweep-free BOTDA system simulation scheme block diagram Figure 8.2 BFS error results (unless otherwise noted, pump spacing 100MHz and Brillouin linewidth of 28MHz are assumed, the number of tones is 20, the CNR is 50dB, the granularity is 3MHz, the spatial resolution is 4m and no averaging is assumed): (a) BFS error vs. CNR for different granularity values; (b) BFS error vs. CNR for different spatial resolutions; (c) BFS error vs. Granularity for different number of tones; (d) BFS error as a function of the location of BFS within the dynamic range; (c) BFS error vs. the Brillouin gain for different CNR values; and (f) vs. the number of averages. 8.3 Results One of the most important performance criteria of any Brillouin-based sensor is the BFS error, which is defined by the difference between the measured and actual BFS profiles 115 in the fiber. Specifically, in SF-BOTDA, there is a set of parameters that have a direct impact on the actual performance: CNR: Carrier to noise ratio. Calculated after detection, i.e., in the electronic domain, the carrier is the power of each probe tone, before amplification, divided by the noise power in a bandwidth that includes all relevant tones. Gain: the amount of Brillouin gain. Averaging: As in classical BOTDA, sequential probe traces are averaged to lower the noise. Granularity: The actual BGS reconstruction resolution, which is similar to the sweeping step in classical BOTDA. Number of tones, which defines the overall bandwidth occupied by the tones and, together with the granularity, defines the total measurable dynamic range. Spatial resolution sets the detection bandwidth that defines the accuracy at which the amplitude and the frequency of the probe tones are obtained in the spectrogram calculation process [39], which provides additional averaging of the signal along the time scale. In order to investigate the impact of the above parameters on the BFS error, full SF- BOTDA system simulations, described in the previous section, were performed (unless otherwise noted, pump spacing of 100MHz and Brillouin linewidth of 28MHz are assumed, the number of tones is 20, the CNR is 50dB, the granularity is 3MHz, the spatial resolution is 4m and no averaging are assumed). First, the BFS error vs. the CNR for 20 tones, 3dB gain, spatial resolution of 4m, no averaging and different granularity values, is shown in Fig 8.2 (a). Clearly, CNR values higher than 45dB, actually obtained in our experiments, provide sub- 116 MHz accuracy. Finer granularity (denser sampling of the BGS) decreases the BFS error at the expense of the dynamic range (=the granularity times number of tones), unless dynamic range extension techniques are employed [40]. Next, the BFS error vs. CNR for various spatial resolution values appears in Fig. 8.2(b) (unless otherwise noted, the granularity is 3MHz and 20 tones are used). Again, it is possible to minimize the BFS error at the expense of spatial resolution. Fig. 8.2(c) shows the dependence of the BFS error on the granularity and the total number of tones used for the interrogation (for 4m spatial resolution), indicating there is an optimum region exhibiting low sensitivity to both the granularity and the number of tones. For a given number of tones, too fine granularity cannot provide full coverage of the BGS, resulting in high BFS errors. For example, for a 28MHz-wide BGS the minimum suggested granularity is 3MHz to sustain reasonable and practical number of probe tones. On the other hand, tones with too coarse granularity values sample the BGS too sparsely, again leading to higher BFS errors. Furthermore, increasing the number of tones under these circumstances worsens the situation since many tones only sample noise away from the BGS. While in Figs. 8.2(a-c) it was assumed that the tones are symmetrically spread around the true BFS, Fig. 8.2(d) shows the dependence of the BFS error on the BFS location within the dynamic range, i.e., the range covered by probe tones. As expected, best results are obtained when the BFS is located in the middle of dynamic range, deteriorating towards its edges, where only partial coverage of the BGS is achieved. While outside the scope of this work, this kind of limitation can probably be removed when more advanced fitting algorithms are applied. Indeed, if the dynamic range extends beyond the pump spacing, the i-th probe, instead of being amplified by the i-th pump is amplified by either the (i+1)-th or (i-1)-th pump, opening the door for finding the BFS with low error even when the BFS approaches the edges of the dynamic range. For a given CNR the BFS error decreases with the Brillouin gain, Fig. 8.2(e). While data 117 averaging is quite common in Brillouin interrogators, all of the above results assumed no averaging. Fig. 8.2(f) depicts the dependence of the BFS error on the number of averages. For K averages an asymptotic K / 1 behavior is expected. 8.4 Summary The impact of several key parameters of SF-BOTDA on the BFS error was quantitatively investigated. The sensing scenario and application requirements may dictate the proper set of those parameters to meet the needed performance. Once the dynamic range is determined, the pump frequency spacing can be chosen and then the other parameters can be found from Fig. 8.2. Naturally, these simulations must be corroborated by experiments. Initial measurements indicate that it is not too difficult to achieve CNR better than 45dB. Looking back at Fig. 8.2 we find that SF-BOTDA can offer high sensing speed and low BFS error for spatial resolutions of a few meters. One final consideration to note: the number of tones times the pump frequency spacing should be smaller than the Brillouin frequency shift [27]. In simple SF-BOTDA implementations the dynamic range is on the order of the pump spacing. A too large pump spacing dictates a small number of tones and a large BFS error, while a too small spacing requires a large number of tones to cover a given dynamic, an experimentally difficult requirement. Advanced curve fitting techniques, capable of addressing aliasing situations where a probe tone is not amplified by its parent pump, along with more advanced implementations [40] will hopefully make SF-BOTDA an attractive solution in high speed Brillouin sensing applications, offering a wide range of specifications. 118 Chapter 9 Differential pulse-width pair BOTDA using simultaneous frequency domain interrogation 9.1 Introduction Brillouin based sensing is now serving quite a few important applications with a spatial resolution of ~1m, limited by the phonon lifetime (~10ns) [25]. A leading technique [31] to overcome this limitation in BOTDA (Brillouin optical time domain analysis) configurations [4,25] uses two sequentially launched pump pulses, separated by the round trip time of flight in the fiber under test. Both pulses are much longer than the phonon life time, so that together with the counter-propagating probe CW wave, they fully excite the acoustic field. The essence of the differential pulse-width pair (DPP) technique is that the two pulses are of slightly different widths and the strain/temperature information along the fiber is obtained by subtracting the (logarithmic) measured distributed Brillouin gain in response to the shorter pulse from that of the longer. The achieved spatial resolution is directly related to the width difference between the pulses. Centimetric resolution has been demonstrated [49-50], albeit at the expense of halving the effective probing rate. In order to maintain the full probing rate we propose here a modification of the technique where the two pump pulses are launched simultaneously, using widely separate different frequency carriers. 119 9.2 Concept In the proposed concept (Fig. 9.1(a)), the two pump pulses ride on different optical frequencies (tones). Each pump tone gives rise to a ~30MHz-wide Brillouin gain spectrum (BGS), separated from its generating tone by the same Brillouin frequency shift (BFS), as determined by the fiber type and strain/temperature environment. The spacing between the pump tones is made much larger than the width of the BGS to avoid crosstalk. The two generated BGSs can be independently measured by scanning two probe tones, having the same frequency spacing as that of the pump tones and launched in the opposite direction. In this manner each probe tone is amplified by its corresponding counter-tone of the pump. Finally, to implement the DPP technique, the two pump tones are now simultaneously pulsed for slightly different durations and the difference between the measured Brillouin (logarithmic) gains of the two probes serves as the sensing signal. Note that we expect proper operation in spite the fact that two different acoustic fields are excited. Figure 9.1 (a) The concept of speeding up the differential pulse-width pair (DPP) Brillouin sensing technique by replacing the sequential launching of the two different-width pulses with their simultaneous launch, letting each pump pulse to ride on a different optical carrier. Two probe tones, equally spaced from their corresponding pump tones by an arbitrarily chosen ∆ , individually interact, via the Brillouin effect, with the two pump pulses. Each pump pulse gives rise to a Brillouin gain signature of the fiber. Finally, the difference between these two (logarithmic) gain signatures is related to the local strain/temp with a spatial resolution, which is directly related to the difference between the widths of the two pump pulses (50-47=3ns in the figure, corresponding to 30cm of spatial resolution). (b) Experimental setup. MZM: Mach-Zehnder EO modulator; EDFA: Erbium-doped fiber amplifier; PC: polarization controller; SC: Polarization scrambler; ISO: optical isolator; DET: detector; FBG - fiber Bragg grating; AWG: arbitrary waveform generator; OSA: optical spectrum analyser. 120 9.3 Experimental setup and results A block diagram of the experimental setup is shown in Fig. 9.1(b). The fiber under test (FUT) comprised 10-m of SMF-28 fiber, whose middle 40cm section was placed in a temperature chamber at 40 O C (BFS of 10.88GHz) above that of the rest of the fiber (BFS of 10.84MHz). The tunable laser was split into pump and probe arms. A wideband arbitrary waveform generator (AWG) generated two pulsed pump tones: a 47ns-long 2 GHz one and a 50ns-long 4 GHz one. The pulse width difference of 3nsec corresponds to a spatial resolution of ~30cm. This complex RF pump signal fed biased-at-minimum MZM2 modulator, which translated it to the optical domain. For the probe wave, two electrical sine waves, one at 8.84 [or 8.88, see below] GHz and the other at 6.84 [or 6.88] GHz fed the MZM1 modulator, which operated at its quadrature point. Thus, in the cold [hot] fiber section the 2GHz upper sideband of the pump signal generated a BGS whose peak was 10.84 [10.88] GHz away, coinciding with the 8.84 [8.88] GHz lower sideband of the probe signal. Similarly, the 4GHz upper sideband of the pump signal generated a BGS whose peak was again 10.84 [10.88] GHz away in the cold [hot] fiber section, coinciding with the 8.84 [8.88] GHz lower sideband of the probe signal. The generated BGSs were 2 GHz apart. A polarization-scrambling device (SC) precedes EDFA2 to average out the polarization dependence of the Brillouin process. The FBG-filtered Brillouin amplified probe signal then hit the wideband detector, where it mixed with the co-propagating laser signal that passed through MZM1. The resulting electrical signal was amplified and sent to a fast real-time acquisition system. Post-processing included FFT window spectrogram calculation on each probe trace, with a 3ns window, corresponding to the pulse-width difference. Consecutive traces were averaged for better signal-to-noise ratio (SNR) and the (logarithmic) gains of the two probes were subtracted to obtain the differential gain with the expected 30-cm spatial resolution. The experiment included three types of 121 measurement. Fig. 9.2(a) shows the distributed Brillouin gain at a pump-probe frequency difference of 10.84GHz and 10.88GHz, using the classical DPP technique, where two pump pulses, of the same optical frequency but having a pulse width difference of 3ns, were sequentially launched. The ~30cm resolution is evident in both fiber sections. Fig. 9.2(b) shows similar results when our proposed two-carrier concept was employed, albeit with a sequential launching of the two pump pulses. While in the classical DPP technique, the same acoustic field is excited by the two pulses, here, each carrier excites a different acoustic field. Nevertheless, the DPP method appears to maintain its high spatial resolution characteristics. Finally, the results of the full demonstration of our time-saving technique appear in Fig. 9.2(c). Here, the pump pulses, each riding on a different optical carrier, are simultaneously launched. In all three cases, the same spatial resolution of ~30cm is observed. Clearly, our technique shortens the sensing speed by the factor of 2. Figure 9.2 Experimentally obtained 30-cm spatial resolution, using (a) the original DPP technique [2]; (b) sequential pump pulsing at two different frequency carriers; (c) simultaneous pump pulsing at different frequency carriers; 9.4 Summary In summary, we successfully demonstrated a novel modification of the differential pulse-width pair technique, where the two pump pulses of slightly different widths, are simultaneously transmitted on different optical carriers, thereby offering a two-fold increase in the sensing speed. The coexisting two pump tones do not give rise to any crosstalk phenomena, as long as their frequency separation is larger than a few BGS widths, as has been shown in our previous studies on sweep-free BOTDA [27]. In this work, we sampled the BGSs 122 at only two frequencies (10.84 and 10.88 GHz). However, the same setup allows for continuous scanning of the two BGSs. Alternatively, the method of sweep-free BOTDA [27,51] could be employed together with this proposed modification of the DPP technique, to achieve high spatial resolution, dynamic and distributed Brillouin sensing. 123 Conclusions Optical fiber distributed sensors have recently received significant attention due to the large number of applications they support and enable. Although there have been great strides made in optical fiber sensors, there are still significant research challenges in order to achieve better sensitivity and frequency-domain information. Several of the critical challenges are presented in Fig. A1. State-of-the-art research is aimed at developing novel methods to alleviate each of these challenges. Figure A1. Critical research challenges in distributed optical fiber sensors. (a) Sensitivity/Accuracy: The sensitivity of the sensors determines the ability to measure physical parameters accurately. Usually, the performance is limited by the signal-to- 124 noise ratio (SNR). In Brillouin-based sensors, the optical power level of the backscattered wave is usually weak. As a result, multiple measurements (i.e., integrations) are performed in order to reach a sufficiently high SNR. However, multiple integrations cause a significant increase in overall sensing time and significantly limit the ability to resolve measurements in the frequency domain. This research has focused on determining methods of enhancing sensitivity by utilizing novel measurement techniques. (b) Spatial Resolution Along the Fiber: The spatial resolution at which it is possible to determine the position of the disturbance along the fiber span itself can usually be determined by the acoustical properties of the optical fiber as well as by the signal processing techniques used in the specific sensor implementation. There is a trade-off between spatial resolution, SNR, and overall sensing time. Usually, the compromised spatial resolution is around 1 m, although non-frequency-resolved BOCDAs [7] showed spatial resolution down to several millimeters, which may be applied to localize disturbance events and increase sensing accuracy. (c) Sensing Time: A limitation of current distributed optical fiber sensors is the large overall sensing time for long fibers (over 10 km). This means that it is only possible to detect changes that have slow variations over time and not possible to resolve vibrational signatures. Improving the overall sensing time by adding dynamic frequency resolved information is critical for distinguishing false positives. (d) Strain/Temperature Discrimination: A major challenge is the discrimination of different types of effects on the fiber. Fortunately, the temporal/frequency signature of fiber stress is often unique to its sources (i.e., mechanical vibrations, people, animals, natural 125 tremors, and temperature. With the improved sensing time, resolution, and accuracy, dynamic measurements will help differentiate the signature of each source and greatly reduce false positives. (e) 3D Disturbance Localization: Determining the exact location of a disturbance that exists at some distance away from the sensor may significantly enhance the performance of optical fiber sensors in terms of false alarm rate reduction. The ability to dynamically detect events and measure their time varying effect on the fiber will also allow for the position along, direction from, and distance to the fiber to be determined. (f) Dynamic range: It is necessary to be able to measure the temperature/strain related changes with high dynamic range of variations along which is especially relevant for very long fiber lengths. This Ph.D. dissertation has concentrated with the third bullet that dealt with significant reduction of sensing time. It presented a totally new method that may reduce sensing time from minutes to sub-millisecond periods. This novel concept, called SF-BOTDA (for Sweep- Free BOTDA), which retains all the advantages of the classical BOTDA technique together with the potential to be much faster. During our research, we demonstrated the basic concept, where multiple pump and multiple probe tones distributedly pair-wise interact via the Brillouin effect in the fiber to simultaneously probe different parts of multiple replicas of the fiber BGS. Once the tones are detected, the Brillouin amplification experienced by each of them can be determined, resulting in an accurate reconstruction of the BGS, and, consequently, in the determination of the BFS. We have also shown how the technique can be applied to a distributed sensing faster than classical BOTDA by a factor, which could be as high as the number of 126 simultaneous tones used. 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Thevenaz, M. Nickles, A. Fellay, M. Faccini, P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE, vol. 3330, pp. 301–314, 1998. J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Exp. 20, 26942-26949 (2012). Virtex-5 Processing Benchmark, National Instruments, http://zone.ni.com/devzone/cda/tut/p/id/7242 A. Voskoboinik, Y. Peled, A.E. Willner and M. Tur, “Fast and distributed dynamic sensing of strain using sweep-free Brillouin time-domain analysis (SF-BOTDA)”, 3 rd Asia Pacific Optical Sensor Conference (APOS 2012), Sydney, January 2012 (Proc. SPIE, vol. 8351). 132 A. Voskoboinik, D. Rogawski, H. Huang, Y. Peled, A. E. Willner and M. Tur, “Frequency- domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer and sloped-assisted FBG sensing,” Optics Express, 20, Iss. 26, B581-B-586 (2012). A. Voskoboinik, H. Huang, Y. Peled, A. E. Willner, and M. Tur, “Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer,” ECOC-2012, Amsterdam, Netherlands, September 2012. A. Voskoboinik, J. Wang, A. E. Willner and M. Tur, “Frequency-domain simultaneous tone interrogation for faster, sweep-free Brillouin distributed sensing”, 21st Inter. Conference of Optical Fiber Sensors, Proc. Of SPIE, 7753 (2011). A. Voskoboinik, A. E. Willner and M. Tur, “Performance analysis of the sweep-free Brillouin optical time-domain analyzer (SF-BOTDA),” Optical Fiber Sensor conference, OFS-23, Santander, Spain (2014). A. Voskoboinik, J. Wang, B. Shamee, S. Nuccio, L. Zhang, M. Chitgarha, A. Willner and M. Tur, “SBS-based fiber optical sensing using frequency-domain simultaneous tone interrogation,”, J. of Lightwave Techn., 29, 1729-1735 (2011). A. Voskoboinik, O.F. Yilmaz, A.E. Willner and M. Tur, “Sweep-free distributed Brillouin sensing using multiple pump and probe tones”, ECOC, Geneva, Switzerland, September 2011. A. Voskoboinik, O. F. Yilmaz, A. E. Willner, and M. Tur, “Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA),” Opt. Exp. 19, B842-B847 (2011). 133 A. Voskoboinik, A. Bozovich, A. E. Willner, and M. Tur, “Sweep-free Brillouin optical time- domain analyzer with extended dynamic range,” CLEO-2012, San Jose, USA, May 2012. A. Voskoboinik ; A. E. Willner and M. Tur, "Sweep-free Brillouin time-domain analysis (SF- BOTDA) with improved spatial resolution" 22nd International Conference on Optical Fiber Sensors, OFS2012, Beijing, October 2012. Also: Proc. SPIE 8421. R. Warts, A. Priesem, E. Lichtman, H, Yaffe, R. Braun, “Nonlinear Effects in Coherent Multichannel Transmission Through Optical Fibers,” Proceedings of the EEE, vol. 78, No. 8, pp. 1344-1368, August 1990. 134 References [1] R.W. Boyd, Nonlinear Optics, (Academic Press, 2008), Chap. 9. [2] M. K. Barnoski, S. D. Personick, “Measurements in Fiber Optics,” in Proceedings of IEEE (1978), vol. 66, No. 4, 429-441. [3] K. Shimizu, T Horiguchi, Y. Koyamada,T. “Coherent self-heterodyne Brillouin OTDR for measurement of Brillouin frequency shift distribution in optical fibers,” J. Lightwave Tech., vol. 12, No. 5, 730-736 (1994). [4] T. Horiguchi, M. Tateda, “BOTDA-Nondestructive Measurement of Single-Mode Optical Fiber Attenuation Characteristics Using Brillouin Interaction : Theory,” J.Lightwave Tech., vol. 7, No. 8, 1170-1176 (1989). [5] M. Tateda, T. Horiguchi, T. Kurashima, K. Ishihara, “First Measurement of Strain Distribution Along Field-Installed Optical Fibers Using Brillouin Spectroscopy,” J. Lightwave Tech., vol. 8, No. 9, pp. 1269-1272, (1990). [6] T. Horiguchi, T. Kurashima, M. Tateda, “A Technique to Measure Distributed Strain in Optical Fiber,” IEEE Photonics Tech. Letters, vol. 2, No. 5, pp. 352-354, May 1990. [7] K. Hotate, H. Zuyuan, “Synthesis of optical-coherence function and its applications in distributed and multiplexed optical sensing” J. Lightwave Tech., vol. 24, No. 7, pp. 2541-2557 (2006). 135 [8] K. Hotate, S. Ong,, “Distributed Dynamic Strain Measurement Using a Correlation-Based Brillouin Sensing System,” IEEE Photonics Tech. Letters, vol. 15, No. 2, pp. 272-274, February 2003. [9] L. Thevenaz, M. Nickles, A. Fellay, M. Faccini, P. Robert, “Truly distributed strain and temperature sensing using embedded optical fibers,” Proc. SPIE, vol. 3330, pp. 301–314, 1998. [10] X. Bao, M. DeMerchant, A. Brown, and T. Bremner, “Tensile and com pressive strain measurement in the lab and field with distributed Brillouin scattering sensor,” J. Lightwave Tech., vol. 19, pp. 1698–1704 ( 2001). [11] H. Ohno, H. Naruse, M. Kihara, A. Shimada, “Industrial Applications of the BOTDR Optical Fiber Strain Sensor,” Invited paper, Optical Fiber Technol., vol. 7, pp. 45–64, 2001. [12] K. Y. Song, K. Hotate, “Distributed Fiber Strain Sensor With 1-kHz Sampling Rate Based on Brillouin Optical Correlation Domain Analysis,” IEEE Photon. Technol. Let., vol. 19, No. 23, pp. 1928–1930, December 2007. [13] T. Horiguchi, K. Shimizu, T. Kurashima, M. Tateda, and Y. Koyamada, J. Lightwave Technol., Vol. 13, pp. 1296-1302, 1995. [14] R. Bernini, A. Minardo, L. Zeni, "Dynamic strain measurement in optical fibers by stimulated Brillouin scattering", Optics Letters, Vol. 34, Issue 17, pp. 2613-2615, September 2009. 136 [15] P. Chaube, B. G. Colpitts, D. Jagannathan, A.W. Brown, “Distributed Fiber-Optic Sensor for Dynamic Strain Measurement,” IEEE Sensors Journal, Vol.8, pp.1067-1072, July 2008. [16] M. J. Damzen, V. I. Vlad, V. Babin, A. Mocofanescu, Stimulated Brillouin Scattering, Fundamentals and Applications, (Institute of Physics Publishing, 2003), Chap. 1. [17] K. Ogusu, H. Li, "Brillouin-gain coefficients of chalcogenide glasses", J. Opt. Soc. Am. B, Vol. 21, Issue 7, pp. 1302-1304 (2004). [18] M. Nikles, L. Thevenaz, P. Robert, “Brillouin Gain Spectrum characterization in Single- Mode Optical Fibers,” J. Lightwave Technol., vol. 15, No. 10, pp.1842-1851, October 1997. [19] E. Lichtman, A. Friesem, R. Warts, H. Yaffe, “Stimulated Brillouin scattering excited by two pump waves in single-mode fibers,” J. Opt. Soc. Am. B, vol. 4, No. 9, pp.1397-1403, September 1987. [20] R. Warts, A. Priesem, E. Lichtman, H, Yaffe, R. Braun, “Nonlinear Effects in Coherent Multichannel Transmission Through Optical Fibers,” Proceedings of the EEE, vol. 78, No. 8, pp. 1344-1368, August 1990. [21] K. Chung, G. Yang, W. Kwong, “Determination of FWM Products in Unequal-Spaced- Channel WDM Lightwave Systems,” J. of Lighwave Techn., vol. 18, No. 12, pp. 2113-2122, December 2000. [22] Virtex-5 Processing Benchmark, National Instruments, http://zone.ni.com/devzone/cda/tut/p/id/7242. 137 [23] C. L. Tang, "Saturation and spectral characteristics of the Stokes emission in the stimulated Brillouin process," Appl. Phys. 37, 2945 (1966). [24] S. M. Foaleng, M. Tur, J. C. Beugnot, and Luc Thevenaz, “High spatial and spectral resolution long-range sensing using Brillouin echoes,” J. of Lightwave Techn., 28, 2993-3003 (2010). [25] S. Diaz, S. Mafang, M. Lopez-Amo, and L. Thevenaz, “A high performance Optical Time-Domain Brillouin Distributed Fiber Sensor,” IEEE Sen. J., 8, 1268-1272 (2008). [26] Y. Peled, A. Motil and M. Tur, “Distributed and dynamical Brillouin sensing in optical fibers”, Optical Fiber Sensor conference, OFS21, Ottawa, Canada, (2011). [27] A. Voskoboinik, J. Wang, B. Shamee, S. Nuccio, L. Zhang, M. Chitgarha, A. Willner and M. Tur, “SBS-based fiber optical sensing using frequency-domain simultaneous tone interrogation,”, J. of Lightwave Techn., 29, 1729-1735 (2011). [28] A. Voskoboinik, J. Wang, A. E. Willner and M. Tur, “Frequency-domain simultaneous tone interrogation for faster, sweep-free Brillouin distributed sensing”, 21st Inter. Conference of Optical Fiber Sensors, Proc. Of SPIE, 7753 (2011). [29] A. Voskoboinik, O.F. Yilmaz, A.E. Willner and M. Tur, “Sweep-free distributed Brillouin sensing using multiple pump and probe tones”, ECOC, Geneva, Switzerland, September 2011. [30] X. Bao, and L. Chen, “Recent progress in Brillouin scattering based fiber sensors,” Sensors 11, 4152-4187 (2011). 138 [31] W. Li, X. Bao, Y. Li, and L. Chen, “Differential pulse-width pair BOTDA for high spatial resolution sensing,” Opt. Exp., 16, 21616-21625 (2008). [32] T. Sperber, A. Eyal, M. Tur, and L. Thévenaz, “High spatial resolution distributed sensing in optical fibers by Brillouin gain-profile tracing,” Opt. Exp. 18, 8671-8679 (2010). [33] A. W. Brown, B. G. Colpitts, and K. Brown., “Dark-pulse Brillouin optical time-domain sensor with 20-mm spatial resolution,” J. Light. Tech. 25, 381-386 (2007). [34] Y. Antman, N. Primerov, J. Sancho, L. Thevenaz, and A. Zadok, “Localized and stationary dynamic gratings via stimulated Brillouin scattering with phase modulated pumps,” Opt. Exp. 20, 7807-7821 (2012). [35] K. Y. Song, M. Kishi, Z. He, and K. Hotate, “Hi-repetition-ratio distributed Brillouin sensor based on optical correlation-domain analysis with differential frequency modulation,” Opt. Lett. 36, 2062-2064 (2011). [36] J. Urricelqui, A. Zornoza, M. Sagues, and A. Loayssa, “Dynamic BOTDA measurements based on Brillouin phase-shift and RF demodulation,” Opt. Exp. 20, 26942-26949 (2012). [37] Y. Peled, A. Motil, L. Yaron, and M. Tur, “Slope-assisted fast distributed sensing in optical fibers with arbitrary Brillouin profile,” Opt. Exp. 19, 19845-19854 (2011). [38] Y. Peled, A. Motil, L. Yaron, and M. Tur, “Fast Brillouin optical time-domain analysis for dynamic sensing,” Opt. Exp. 20, 8584-8591 (2012). [39] A. Voskoboinik, O. F. Yilmaz, A. E. Willner, and M. Tur, “Sweep-free distributed Brillouin time-domain analyzer (SF-BOTDA),” Opt. Exp. 19, B842-B847 (2011). 139 [40] A. Voskoboinik, A. Bozovich, A. E. Willner, and M. Tur, “Sweep-free Brillouin optical time-domain analyzer with extended dynamic range,” CLEO-2012, San Jose, USA, May 2012. [41] A. Voskoboinik, H. Huang, Y. Peled, A. E. Willner, and M. Tur, “Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time-domain analyzer,” ECOC-2012, Amsterdam, Netherlands, September 2012. [42] J. Proakis, and D.Manolakis, Digital Signal Processing, (Pearson Prentice Hall 2007). [43] K.Y. Song, M. Kishi, Z. He and K. Hotate, “High-repetition-ratio distributed Brillouin sensor based on optical correlation-domain analysis with differential frequency modulation”, Opt. Lett.,36, 2062-2064 (2011). [44] A. Voskoboinik, Y. Peled, A.E. Willner and M. Tur, “Fast and distributed dynamic sensing of strain using sweep-free Brillouin time-domain analysis (SF-BOTDA)”, 3 rd Asia Pacific Optical Sensor Conference (APOS 2012), Sydney, January 2012 (Proc. SPIE, vol. 8351). [45] A. Voskoboinik, D. Rogawski, H. Huang, Y. Peled, A. E. Willner and M. Tur, “Frequency-domain analysis of dynamically applied strain using sweep-free Brillouin time- domain analyzer and sloped-assisted FBG sensing,” Optics Express, 20, Iss. 26, B581-B-586 (2012). [46] M. A. Soto and L. Thevenaz, “Modeling and evaluating the performance of Brillouin distributed optical fiber sensors,” Optics Express, 21, Iss. 25, 31347-31366 (2013). 140 [47] A. Voskoboinik, A. E. Willner and M. Tur, “Performance analysis of the sweep-free Brillouin optical time-domain analyzer (SF-BOTDA),” Optical Fiber Sensor conference, OFS-23, Santander, Spain (2014). [48] A. Motil, Y. Peled, Lior Yaron and M. Tur, “BOTDA measurements in the presence of fiber vibration,” 3 rd Asia Pacific Optical Sensor Conference (APOS 2012), Sydney, Australia (2012). [49] Y. Dong, H. Zhang, L. Chen, and X. Bao, “2 cm spatial-resolution and 2 km range ... using a transient differential pulse pair,” Appl. Opt. 51(9), 1229–1235 (2012). [50] M. A. Soto, M. Taki, G. Bolognini, and F. Di Pasquale, "Optimization of a DPP-BOTDA sensor with 25 cm spatial resolution over 60 km standard single-mode fiber using Simplex codes and optical pre-amplification," Opt. Express 20, 6860-6869 (2012). [51] A. Voskoboinik ; A. E. Willner and M. Tur, "Sweep-free Brillouin time-domain analysis (SF-BOTDA) with improved spatial resolution" 22nd International Conference on Optical Fiber Sensors, OFS2012, Beijing, October 2012. Also: Proc. SPIE 8421.
Abstract (if available)
Abstract
Brillouin-based optical fiber sensing is a promising technology for the monitoring of many types of structural and environmental changes. Sensors based on this technology use the Brillouin nonlinear process in which acoustic phonons in the fiber either spontaneously scatter a forward propagating optical wave (called 'pump') into a backward propagating wave (called 'probe'), or, alternatively, mediate, via a stimulated interaction, power transfer between counter propagating waves ('pump' and 'probe'). In either case, the returning light has a characteristic frequency shift (from that of the pump), which varies with many types of changes in the propagating medium, such as temperature and mechanical stress. Therefore, this Brillouin frequency shift (BFS) can provide information on the surrounding temperature and strain distributions along an optical fiber. ❧ There are several major schemes for Brillouin-based optical fiber sensors, including Brillouin optical time domain reflectometers (BOTDRs), Brillouin optical time domain analyzers (BOTDAs), and Brillouin optical correlation-domain analyzers (BOCDAs). BOTDRs mostly use a single-ended implementation, where a pump wave gives rise to a spontaneous Brillouin back-scattered probe, whose optical frequency is measured via a variety of techniques. The optical power level of the backscattered wave is weak, requiring averaging of multiple measurements (i.e., integrations) in order to reach a sufficiently high signal-to-noise ratio (SNR). This may cause longer sensing times of up to several minutes. BOTDAs sensors rely on the stimulated Brillouin scattering (SBS) process in which two counter-propagating pump and probe waves generate acoustic waves in the fiber, which then transfer optical power from the pump to the probe if the latter frequency is downshifted from that of the pump by the BFS. Since the emerging probe is typically stronger in BOTDAs than in BOTDRs, shorter sensing times are achievable. Finally, BOCDAs are SBS-based sensors in which counter-propagating probe and pump waves produce spatially correlated interference peaks along the fiber to dramatically improve the spatial resolution. BOCDAs can also sense the dynamic variation of the environmental changes up to 1 KHz, but this is typically limited to local stimulation along fiber sections. ❧ In many Brillouin-based sensors, e.g., BOTDAs, the evolution of temperature/strain induced BFS is determined from consecutive recordings of the whole Brillouin gain spectrum (BGS). This Lorentzian-shaped spectrum, having a width of ~30MHz (FWHM) at 1550nm in a standard single mode optical fiber (SMF), must be measured as densely as the application requires. Typically the sensitivity of the BFS is 1MHz/⁰C and 500MHz/(1% strain). Classically, the BGS is measured by sweeping the optical frequency of either the pump or the probe, over the entire BGS. Since the probe signal is quite weak, especially when long (tens of kilometers) fibers are interrogated, averaging over multiple measurements is required at each frequency point, thereby significantly slowing down the frequency scanning rate and the overall measurement speed. Consequently, such implementations may have difficulty in resolving fast, dynamic changes in the measurands. Recently, a technique was introduced to measure fast changes in a BGS but with limited dynamic range. ❧ Critically valuable characteristics of an ideal sensor would include: (a) high-resolution 3-D spatial localization and directionality of the disturbance over large distances, and (b) the ability to determine false alarms with high confidence. In general, there has been keen interest in using optics to achieve these goals due to the inherent high frequency of the optical wave, the ability for the optical wave propagation to be quite sensitive to changes, and the low loss and large distance capability of optical fiber. ❧ As mentioned earlier, one of the major disadvantages of distributed optical fiber sensing is the deficiency in time/frequency information. Common methods scan each frequency of the Brillouin reflected light to determine the center frequency of the shift and require several measurements to yield a single fiber strain value. This greatly limits the collection time of the strain distribution and makes it difficult to detect time varying disturbances. For successful detection and reduction of false positives, it is critical to be able to capture all dynamic events by rapidly retrieving the data set and processing the results. In addition, disturbance localization away from the sensor itself is very limited and usually determined only by spatial resolution along the optical fiber. One key advantage of enabling dynamic event detection is the possibility to measure how an event impacts the fiber in short time scales. In this dissertation, we discuss methods for utilizing the improved techniques we have developed to provide dynamic sensing and enable a large reduction in false positives and accurate localization of disturbance events. ❧ This research introduces a novel Brillouin fiber optical sensor which is capable to identify the dynamic signature of different signature of different disturbances in a distributed way in order to reduce false alarms. This novel concept, called SF-BOTDA (for Sweep-Free BOTDA), which retains all the advantages of the classical BOTDA technique together with the potential to be much faster. During our research, we demonstrated the basic concept, where multiple pump and multiple probe tones distributedly pair-wise interact via the Brillouin effect in the fiber to simultaneously probe different parts of multiple replicas of the fiber BGS. Once the tones are detected, the Brillouin amplification experienced by each of them can be determined, resulting in an accurate reconstruction of the BGS, and, consequently, in the determination of the BFS. We have also shown how the technique can be applied to a distributed sensing faster than classical BOTDA by a factor, which could be as high as the number of simultaneous tones used. The idea of 'sequential pulse launching' was introduced, where the multiple pump pulsed tones are sequentially launched into the fiber, thereby avoiding nonlinear interactions among them, as well as overloading of the optical amplifiers. ❧ In Chapter 1, we overviewed some fundamental electromagnetics theory relevant to the Brillouin sensing. Here, we mentioned several different approached used today in optical fiber sensors field. ❧ In Chapter 2, a new multiple-tone concept was presented, where it is possible to interrogate complex data in order to reconstruct Brillouin gain spectra using a single measurements by accurately choosing pumps and probes frequencies. Initial experimental data for continuous-wave case was shown proving the ability to perform similar to state-of-the-art method but potentially much faster. The extension of the method to a pulsed case and, as a result, distributed sensing, has been described. ❧ In Chapter 3, the case of the Brillouin interaction between two probe waves propagating against two modulated pump waves was analytically investigated. This investigation is motivated by the sweep-free BOTDA technique, where, to increase sensing speed, the Brillouin gain spectrum is simultaneously interrogated by many probe-pump pairs. It was shown both analytically and experimentally that crosstalk talk becomes negligible only when the pump tones separation is much larger than the width of the Brillouin gain spectrum. The slowly varying envelope approximation, non-moving phonons, the undepleted pump approximation and small Brillouin gain were assumed, resulting in a first order perturbation analysis for the acoustic and probe waves. Results include the Brillouin gain spectrum, which was compared with a corresponding experiment. ❧ In Chapter 4, a sweep-free optical time-domain method for distributed Brillouin sensing is proposed, having the potential for fast dynamic strain measurements. In this implementation of the method, multiple probe waves with carefully chosen optical frequencies simultaneously propagate in the fiber against an equal number of sequentially-launched, short pump pulses of matching frequencies, where each of pump-probe pair replaces one sweeping step in the classical BOTDA technique. Experimentally, distributed sensing is demonstrated with a spatial resolution of a few meters. It was shown that there is not more need for the classical step-by-step mapping of the fiber BGS. This proposed method is potentially faster than classical BOTDA by a factor equal to the number of pump-probe pairs used for the BGS reconstruction, since each pair replaces one sweeping step in the classical technique. ❧ In Chapter 5, a fast reconstruction of the whole Brillouin gain spectrum is experimentally demonstrated using sweep-free Brillouin optical time-domain analysis. Strain variations with the frequencies up to 400Hz are spectrally analyzed, achieving strain sensitivity of 1 microstrain per root Hz at a sampling rate of 5.5kHz and a spatial resolution of 4m. The results favorably compared with fiber Bragg grating sensing. ❧ In Chapter 6, we presented a new implementation of our sweep-free Brillouin optical time-domain technique, involving a novel sequencing of the probe signal with respect to the pump multi-tone pulse, together with advanced post-processing, which removes the trade-off between the required spatial resolution and the inter-tone spacing, allowing the method to achieve spatial resolutions comparable to those of classical BOTDA without sacrificing tone granularity. A spatial resolution of 2m is experimentally demonstrated using around 100MHz inter-tone spacing. ❧ In Chapter 7, it was shown that while sweep-free Brillouin optical time-domain analysis (SF-BOTDA) replaces the sequential frequency scanning of classical BOTDA by parallel interrogation of the fiber-under-test using the simultaneous interaction of multiple pump tones with counter-propagating multiple probe tones, its dynamic range is limited to approximately the pump tone spacing, which is of the order of 100MHz. Here, in-depth analysis of our method was performed to significantly extend the dynamic range to the GHz regime. Based on sequential interrogation with up to three sets of multiple tones, each having a different frequency spacing, this method provides a major speed advantage over the classical BOTDA in spite of the use of three sets of tones. With this development, which does not require any additional hardware, SF-BOTDA offers distributed sensing of optical fibers over practical dynamic ranges of strain/temperature variations, with the potential to become one of the fastest sensing techniques. ❧ In Chapter 8, the impact of several key parameters of sweep-free Brillouin optical time-domain analyzer on the BFS error was quantitatively investigated. Once the dynamic range is determined, the pump frequency spacing can be chosen and then the other parameters can be found as suggested. The number of tones times the pump frequency spacing should be smaller than the Brillouin frequency shift. In simple implementations, the dynamic range is on the order of the pump spacing. A too large pump spacing dictates a small number of tones and a large BFS error, while a too small spacing requires a large number of tones to cover a given dynamic, an experimentally difficult requirement. Initial measurements indicated that it is not too difficult to achieve CNR better than 45dB. Looking back at our research, SF-BOTDA can offer high sensing speed and low BFS error for spatial resolutions of a few meters. ❧ In Chapter 9, multiple-tone method with differential pulse-width pair BOTDA technique were combined together. A novel modification of the differential pulse-width pair technique, where the two pump pulses of slightly different widths, are simultaneously transmitted on different optical carriers, thereby offering a two-fold increase in the sensing speed. The simultaneously propagating two pump tones do not give rise to any crosstalk in the fiber, as long as their frequency separation is larger than a few BGS widths. Here, the BGSs at only two frequencies (10.84 and 10.88 GHz) were sampled using the same experimental setup allowing continuous scanning of the two BGSs.
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Maor, Asher
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Sweep-free Brillouin optical time-domain analyzer
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Doctor of Philosophy
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02/06/2015
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