Phase-based, high spatial resolution and distributed, static and dynamic strain sensing using Brillouin dynamic gratings in optical fibers

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1 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5376 Phase-based, high spatial resolution and distributed, static and dynamic strain sensing using rillouin dynamic gratings in optical fibers ARIK ERGMAN,* TOMI LANGER, AND MOHE TUR chool of Electrical Engineering, Tel Aviv University, Ramat Aviv, Tel Aviv , Israel * ergman.arik@gmail.com Abstract: A novel technique combining rillouin phase-shift measurements with rillouin dynamic gratings (DGs) reflectometry in polarization-maintaining fibers is presented here for the first time. While a direct measurement of the optical phase in standard DG setups is impractical due to non-local phase contributions, their detrimental effect is reduced by ~4 orders of magnitude through the coherent addition of tokes and anti-tokes reflections from two counter-propagating DGs in the fiber. The technique advantageously combines the high-spatial-resolution of DGs reflectometry with the increased tolerance to optical power fluctuations of phasorial measurements, to enhance the performance of fiber-optic strain sensors. We demonstrate a distributed measurement (20cm spatial-resolution) of both static and dynamic (5kHz of vibrations at a sampling rate of 1MHz) strain fields acting on the fiber, in good agreement with theory and (for the static case) with the results of commercial reflectometers Optical ociety of America OCI codes: ( ) cattering, stimulated rillouin; ( ) Dynamic gratings; ( ) Phase shift; ( ) Heterodyne; ( ) Fiber optics sensors; ( ) Vibration analysis. References and links A. Motil, A. ergman, and M. Tur, tate of the art of rillouin fiber-optic distributed sensing, Opt. Laser Technol. 78, (2016). I. ovran, A. Motil, and M. Tur, Frequency-scanning OTDA with ultimately fast acquisition speed, IEEE Photonics Technol. Lett. 27(13), (2015). C. Zhang, M. Kishi, and K. Hotate, 5,000 points/s high-speed random accessibility for dynamic strain measurement at arbitrary multiple points along a fiber by rillouin optical correlation domain analysis, Appl. Phys. Express 8(4), (2015). A. ergman, T. Langer, and M. Tur, High spatial resolution, low-noise rillouin dynamic gratings reflectometry based on digital pulse compression, Opt. Lett. 41(15), (2016). Y. Peled, A. Motil, I. Kressel, and M. Tur, Monitoring the propagation of mechanical waves using an optical fiber distributed and dynamic strain sensor based on OTDA, Opt. Express 21(9), (2013). A. Minardo, A. Coscetta, R. ernini, R. Ruiz-Lombera, J. Mirapeix errano, J. M. Lopez-Higuera, and L. Zeni, tructural damage identification in an aluminum composite plate by rillouin sensing, IEEE ens. J. 15(2), (2015).. Lissak, A. Arie, and M. Tur, Highly sensitive dynamic strain measurements by locking lasers to fiber ragg gratings, Opt. Lett. 23(24), (1998). A. Rosenthal, D. Razansky, and V. Ntziachristos, High-sensitivity compact ultrasonic detector based on a piphase-shifted fiber ragg grating, Opt. Lett. 36(10), (2011). R. ernini, A. Minardo, and L. Zeni, Dynamic strain measurement in optical fibers by stimulated rillouin scattering, Opt. Lett. 34(17), (2009). A. Motil, O. Danon, Y. Peled, and M. Tur, Pump-power-independent double slope-assisted distributed and fast rillouin fiber-optic sensor, IEEE Photonics Technol. Lett. 26(8), (2014). J. Chen, Q. Liu, X. Fan, and Z. He, Ultrahigh resolution optical fiber strain sensor using dual Pound-DreverHall feedback loops, Opt. Lett. 41(5), (2016). Y. Peled, A. Motil, L. Yaron, and M. Tur, lope-assisted fast distributed sensing in optical fibers with arbitrary rillouin profile, Opt. Express 19(21), (2011). A. Motil, R. Hadar, I. ovran, and M. Tur, Gain dependence of the linewidth of rillouin amplification in optical fibers, Opt. Express 22(22), (2014). # Journal Received 19 Dec 2016; revised 6 Feb 2017; accepted 7 Feb 2017; published 28 Feb 2017

2 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE Y. Lu, T. Zhu, L. Chen, and X. ao, Distributed vibration sensor based on coherent detection of phase-otdr, J. Lightwave Technol. 28(22), (2010). 15. D. Arbel and A. Eyal, Dynamic optical frequency domain reflectometry, Opt. Express 22(8), (2014). 16. A. Masoudi, M. elal, and T. P. Newson, A distributed optical fiber dynamic strain sensor based on phase- OTDR, Meas. ci. Technol. 24(8), (2013). 17. J. Urricelqui, A. Zornoza, M. agues, and A. Loayssa, Dynamic OTDA measurements based on rillouin phase-shift and RF demodulation, Opt. Express 20(24), (2012). 18. A. Lopez-Gil, X. Angulo-Vinuesa, A. Dominguez-Lopez,. Martin-Lopez, and M. Gonzalez-Herraez, Exploiting nonreciprocity in OTDA systems, Opt. Lett. 40(10), (2015). 19. A. Minardo, A. Coscetta, R. ernini, and L. Zeni, Heterodyne slope-assisted rillouin optical time-domain analysis for dynamic strain measurements, J. Opt. 18(2), (2016). 20. W. Li, X. ao, Y. Li, and L. Chen, Differential pulse-width pair OTDA for high spatial resolution sensing, Opt. Express 16(26), (2008). 21. A. Motil, Y. Peled, L. Yaron, and M. Tur, Fast and distributed high resolution rillouin based fiber optic sensor, Opt. Fiber Commun. Conf., pp. OM3G.2, J. Urricelqui, M. agues, and A. Loayssa, Phasorial differential pulse-width pair technique for long-range rillouin optical time-domain analysis sensors, Opt. Express 22(14), (2014). 23. K. Y. ong, W. Zou, Z. He, and K. Hotate, All-optical dynamic grating generation based on rillouin scattering in polarization-maintaining fiber, Opt. Lett. 33(9), (2008) Chin, N. Primerov, and L. Thevenaz, ub-centimeter spatial resolution in distributed fiber sensing based on dynamic rillouin grating in optical fibers, IEEE ens. J. 12(1), (2012). 25. A. ergman, L. Yaron, T. Langer, and M. Tur, Dynamic and distributed slope-assisted fiber strain sensing based on optical time-domain analysis of rillouin dynamic gratings, J. Lightwave Technol. 33(12), (2015). 26. A. Zornoza, M. agues, and A. Loayssa, elf-heterodyne detection for NR Improvement and Distributed phase shift measurements in OTDA, J. Lightwave Technol. 30(8), (2012). 27. L. Yaron, E. hahmoon, A. ergman, T. Langer, and M. Tur, pontaneous anti-tokes backscattering in rillouin dynamic gratings, Proc. PIE 9634, 96342X (2015). 28. A. M. cott and K. D. Ridley, A review of rillouin-enhanced four-wave mixing, IEEE J. Quantum Electron. 25(3), (1989). 29. Y. Dong, H. Zhang, D. Zhou, X. ao, and L. Chen, Chapter 5: Characterization of rillouin grating in optical fibers and their applications, in Fiber Optic ensors (Intech Publisher, 2012), pp L. Thévenaz, ed., Advanced Fiber Optics: Concepts and Technology (EPFL press, 2011), Chap H. Kogelnik, Theory of Optical Waveguides, in Guided-Wave Optoelectronics, T. Tamir, ed. (pringer, 1988). 32. A. ergman, T. Langer, and M. Tur, Coding-enhanced ultrafast and distributed rillouin dynamic gratings sensing using coherent detection, J. Lightwave Technol. 34(24), (2016). 33. W. Zou, Z. He, and K. Hotate, Complete discrimination of strain and temperature using rillouin frequency shift and birefringence in a polarization-maintaining fiber, Opt. Express 17(3), (2009). 34. A. Othonos and K. Kalli, Fiber ragg Gratings: Fundamentals and Applications in Telecommunications and ensing (Artech House, 1999). 35. P. Dragic, T. Hawkins, P. Foy,. Morris, and J. allato, apphire-derived all-glass optical fibres, Nat. Photonics 6(9), (2012). 36. J. ancho, N. Primerov,. Chin, Y. Antman, A. Zadok,. ales, and L. Thévenaz, Tunable and reconfigurable multi-tap microwave photonic filter based on dynamic rillouin gratings in fibers, Opt. Express 20(6), (2012). 1. Introduction rillouin dynamic sensing is of importance in many applications [1]. Recent implementations of the rillouin Optical Time Domain Analysis (OTDA) [2] and rillouin Optical Correlation Domain Analysis (OCDA) [3] techniques, have demonstrated sampling rates of the order of kilohertz's with a centimetric spatial resolution (10cm over a range of 145m for the fully distributed case of [2] and 3cm over 6m for the random access approach of [3]). oth techniques, however, require some form of time-consuming scanning of the probe frequency against that of the pump, which limits their acquisition speed. In contrast, slopeassisted (A) techniques, using a single (or at most a few) pair(s) of pump and probe frequencies can be much faster. As such, they have played a key role in taking the rillouin distributed fiber optic sensing to the fast dynamic regime [1, 4], including demonstrations of its practical utilization for monitoring the propagation of mechanical waves [5,6] (for the use of slope-assisted interrogation of a fiber-ragg grating see [7]).

3 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5378 Most commonly, the A techniques employ a tunable laser source (TL) adjusted to the linear region of the slope of either the reflection spectrum of a fiber ragg grating (FG) [8] or the intrinsic rillouin gain spectrum (G) [9], such that changes induced by measurand variations (e.g., strain) are translated to changes in the measured quantity (usually optical power). However, A techniques are inherently sensitive to source optical power fluctuations and frequency drifts, fiber bend losses and spectral shape longitudinal inhomogeneity, introducing errors to the strain measurement. Much ingenuity has been spent on finding sophisticated solutions for these problems, such as using the ratio between readings taken on both slopes of the G [10], locking the laser frequency via a feedback loop [11], and tailoring the probe frequency to the G profile of the fiber [12]. However, problems still remain and new ones are frequently discovered, as evidenced by [13], where it was shown that the G linewidth broadens with increasing pump power (with obvious ramifications on its shape and slopes), which affects the performance of the slope-assisted rillouin optical time-domain analysis (A-OTDA) techniques, indicating an additional drawback of techniques based on the direct detection of optical power. An alternative method, which might avoid such problems, is to exploit the measurand information encoded in the optical phase, which is widely recognized as the workhorse of distributed acoustic sensors (D) based on Rayleigh backscattering in optical fibers. These methods employ a coherent interference between the backscattered components of the interrogating pulse, resulting in a speckle-like trace whose amplitude and phase can be detected by means of coherent detection [14,15]. To obtain quantitative information of the measurand, rather than merely detect dynamic perturbations, the phase difference between two reflections can be measured using an imbalanced Mach Zehnder interferometer with predetermined path difference [16]. Recently, interesting A-OTDA techniques, harnessing rillouin phase-shift, have emerged [17 19]. It should be noted that the spatial resolution of both gain- and phase-based slope-assisted OTDA techniques is practically limited by the phonon lifetime to 1m. Recently proposed combinations of the differential pulse-width pair (DPP) [20] with either the gain [21] or the phasorial [22] OTDA techniques showed an improved spatial resolution of <1m, at the expense of a decreased signal to noise ratio, leading to an increased number of averages and slower dynamic capabilities. A quite different distributed approach to enhance the spatial resolution, without sacrificing the sampling speed, is to take advantage of rillouin dynamic gratings (DGs) in polarization maintaining (PM) fibers [23]. These moving ragg gratings are generated by two strong counter-propagating pumps, whose polarizations are aligned with the slow axis of the fiber. While both the magnitude and phase of the gratings are affected by the measurand, all recent demonstrations of this high-spatial-resolution sensing technique, e.g., [24, static] and [25, dynamic, slope-assisted], have only used the gratings' magnitude, as measured by the reflectivity of an orthogonally polarized narrow probe pulse. While offering the advantage of probe-power-independent measurements, the correct estimation of the local rillouin phaseshift (P) in DG setups is quite challenging, mainly due to non-local contributions to phase of the reflected probe, from which the measurand-induced P is to be deduced. Indeed, the phase of the gratings at the location of interest is critically affected not only by the measurand but also by the phase of the interference pattern generated by the counterpropagating pumps. This latter phase is governed by the environmentally-dependent optical lengths of the down-lead fibers, feeding the two writing pumps. As for the probe itself, on its journey to the point of interest and back it also collects non-local phase contributions. Furthermore, it will be shown below that the probe phase is also affected by inherent longitudinal non-uniformity of the birefringence in PM fibers [4]. Proper measurement of the phase is also an issue. While in OTDA setups, operating in transmission, measurement of the P can be accomplished, with minimum phase drifts, by interference with a copropagating reference [26], DG setups operate in reflection. y the same reasoning and due

4 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5379 to the fact that in DG setups the reflected probe is also shifted in frequency, the technique that employs the nonreciprocal phase shift between the two paths of agnac interferometer allowing for the measurement of P in OTDA setup [18], cannot be efficiently harnessed in DG setups. In this paper, we present a novel technique, which practically combines the benefits of phasorial measurements and high spatial resolution DG reflectometry. Using coherent addition of the tokes and anti-tokes reflections from two simultaneously counterpropagating DGs in the fiber, the technique advantageously offers distributed rillouininduced Phase-hift (ip) measurement with high spatial resolution. The technique is largely immune to variations in laser optical power and frequency drifts, fiber bend losses, and similarly to phasorial A-OTDA techniques, offers an extended dynamic range. Detrimental non-local phases and birefringence-non-uniformity-induced contributions are shown to be significantly reduced, if not completely cancel out. Finally, a measurement of static and dynamic strain fields is demonstrated. 2. Theoretical analysis 2.1 Principle of operation DGs are optically generated longitudinal density (acoustic) waves in optical fibers [23], whose magnitude and phase depend on the amplitudes, phases, and frequency difference of the optical pump waves that generate them, as well as on the electrostrictive properties of the interaction medium. Most commonly, DG-based sensors employ PM fibers, where two counter-propagating optical pump waves (PumpH and PumpL, ν PumpH >ν PumpL ) are polarized along the slow axis of the fiber, and the Probe pulse is orthogonally polarized and propagates along the fast axis of the fiber. For a tokes-dg scenario, the Probe pulse is launched into the fiber from the same side as PumpH. It is then reflected from a co-propagating refractive index grating (the DG), which was generated by PumpH and PumpL. The reflected signal is also Doppler-downshifted by the DG frequency, ν ( = ν PumpH ν PumpL ). The grating amplitude and phase depend on the frequency difference between the writing pumps, as well as on the local strain/temperature of the fiber. Therefore, in classical DG sensing, to obtain the measurand information, the frequency difference between the writing pumps is scanned, looking for the frequency difference that maximizes the intensity of the reflected probe. Much like the case of the A-OTDA technique, a major speed advantage can be achieved if the frequencies of the signals involved in the interaction are tuned to the slope of the DG spectrum [25], so that rapid strain variations are translated to changes in the intensity of the probe reflection. However, the intensity-based slope-assisted DG (A-DG) and A- OTDA techniques share the same disadvantage of measurand dependence on the local optical power, which impairs their performance. Furthermore, in A-DG setups, the PM fibers' birefringence longitudinal variations introduce errors to the measurement through the modification of the conversion factor between the intensity and strain/temperature. While cannot be mitigated using the pre-compensation technique of [12], these manufacturingrelated and measurand-induced birefringence variations introduce additional impediments to dynamic strain measurements. To address these disadvantages, we hereby propose a phasorial A-DG technique which overcomes most if not all these disadvantages. In our proposal, two counter-propagating DGs are generated by the same PumpH and PumpL, both of which are now launched from both sides of the PM fiber (polarized along its slow axis), Fig. 1. To attain maximum gratings strength, the frequency difference between the pumps, ν, is tuned to the rillouin frequency shift (F) of the slow axis of the fiber, ν (~11GHz). An orthogonally polarized dual-tone Probe pulse can be launched from either side of the fiber and propagates along the fast axis of the fiber. The Probe pulse carrier frequency comprises two tones: a higher-frequency tone (ν Probe_HF ) which is reflected from the tokes- DG (a reflection from a receding grating), attaining maximum reflection for

5 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5380 ν Probe_tokes ν PumpH + ν DG (ν DG primarily depends on the fiber birefringence [23], Δn = n slow n fast, ~46GHz in PM Panda fibers), and a lower-frequency tone (ν Probe_LF ν Probe_HF ν), which is reflected from the anti-tokes-dg (a reflection from an oncoming grating), attaining its maximum value for ν Probe_anti-tokes = ν Probe_tokes ν [27]. Upon reflection, the tokes component of the Probe pulse is Doppler-downshifted by the frequency of the receding grating, ν, while the anti-tokes component of the Probe pulse is Doppler-upshifted by the frequency ν of the oncoming grating. The resultant electrical signal from direct photo-detection comprises a beat term oscillating at the RF frequency of ν. In the following section we show that the phase of this electrical RF signal depends almost exclusively on the local rillouin interaction of the pumps, since all other contributions are dramatically reduced. Fig. 1. A schematic diagram of the proposed PM-DG setup for distributed measurement of rillouin-induced phase-shift using two simultaneously counter-propagating rillouin dynamic gratings and a dual-tone probe. P: Polarization beam splitter; PD: Fast photodiode. 2.2 tokes-dg and anti-tokes-dg field-reflection We start with the full differential equations governing the tokes-dg [28] and anti-tokes- DG [29] interactions (Fig. 2). For not too long DGs, PumpH depletion and PumpL amplification, as well as their linear losses, are neglected, and the equations reduce to: z 2 Pr ober, * E = i ge e 2 Probe, ρ z 2 ig ρ = E E Γ EProbe, i ge ikz 2 ρ e Δ = 1 * PumpH, PumpL, A Δ i kz (1) EProbe, i * = ge 2 ρ e z 2 = z 2 ig ρ = E E Γ EPr ober, i ge ikz 2 Probe, ρ e Δ 1 * PumpH, PumpL, A iδkz (2)

6 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5381 Fig. 2. chematic description of the (a) tokes-dg and (b) anti-tokes-dg interactions, described by the equation sets (1) and (2), respectively. Here, ρ and ρ (having the acoustic frequency of ν), E Probe,, E Probe,, E and E (having the optical frequencies of ν Probe_HF, ν Probe_LF, ν Probe_LF and ν Probe_HF, respectively), are the slowly varying complex envelopes of the relevant waves. g 1 and g 2 respectively represent the strengths of the electrostrictive and elasto-optic interactions 2 2 Γ = i ν ν iνγ 2ν is the detuning factor involved in the generation of the DG [30], A ( ) (Γ is the rillouin linewidth), and Δk 2n c ΔΩ DG is the phase mismatch ( ΔΩDG ωprobe _ HF ωprobe _ tokes ( Δ n) = ωprobe _ LF ωprobe _ anti tokes ( Δ n) and n = 0.5(n slow + n fast ) is the mean refractive index). While Δν ν ν ( = ΔΩ /2π, the detuning parameter) measures the deviation from phase-matching conditions for the creation of the acoustic fields (mainly depending on the acoustic velocity in the fiber), Δν DG ( = ΔΩ DG /2π) is a measure of the phase matching between the induced acoustic fields (i.e., the DGs) and the Probe waves (solely depending on birefringence). Equation sets (1) and (2) are readily identified as the coupled-mode equations which govern the wave reflection in ragg gratings under the synchronous approximation [31]. For an undepleted Probe, a condition which DG interactions certainly satisfy, the impulse responses of the tokes- and anti-tokes-dgs can be found using the technique of [32]: ( ct nl) h ( t) Γ rect / 2 exp iarctg 2 ΔΩ ct / 2 n / Γ exp iδω ( ct / 2 n) t ProbeR, DG ΔΩ /2 + Γ ( ct n) exp[ i( ω Ω) t] Probe _ tokes ( ct nl) ( ct n) Probe _ anti tokes [ ( ( ) )] [ ] h () t Γ rect / 2 exp iarctg 2 ΔΩ ct /2 n / Γ exp iδω ( ct /2 n) t ProbeR, DG ΔΩ /2 + Γ exp[ i( ω +Ω) t] (3) [ ( ( ) )] [ ] (4) Here L is the length of the fiber where DG interactions take place. The leading ratio in Eqs. (3) (4) is the amplitude of the reflection. It is a function of the longitudinally-distancedependent ΔΩ. The next phase factors represent the dependence of the phases of the probe reflections from the counter-propagating gratings on the mismatch between the pumps frequency difference ν and ν. These two mismatch-induced phases share their dependence on distance through that of ΔΩ, but they are of opposite signs. This sign difference can be easily understood by way of example. Let s assume the frequency difference between the pumps to be larger than the F of the slow axis: ν>ν. As a result, in the tokes-dg scenario, the density disturbance moves faster than the speed of sound away from the tokes probe, E Probe,, introducing a positive phase-shift to the tokes reflection, E. In the anti-tokes-dg scenario, the density disturbance moves faster than the speed of sound towards the anti-tokes probe, E Probe,, thereby introducing a negative phase-shift to the anti-tokes reflection, E. The third identical phase factors in Eqs. (3) (4) originate from a mismatch between the incoming probe frequency and the resonant frequencies of the moving ragg gratings. These phases too are distance dependent due to the longitudinal

7 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5382 variations of the fiber birefringence, Δn(z), having similar effects on reflections from the two DGs. Equations (3) (4) end with the phasors of the tokes and anti-tokes reflections, having corresponding frequencies of ν Probe_tokes ν and ν Probe_anti-tokes + ν ( = ν Probe_tokes ). The tokes-reflected and anti-tokes-reflected components back-propagate to the detector and interfere to produce the following AC photocurrent (oscillating at the difference between the frequencies of E and E : ν): AC ( ct n) ( ct n) Γ rect / 2 it () h () t + h () t = cos Ω t+δ () t (5) ( φ ) 2 RF AC ΔΩ /2 + Γ where the longitudinally-dependent RF phase-shift is given by: ( ( ) ) Δ φ ( t) = 2arctg 2 ΔΩ ct/ 2 n / Γ. (6) RF We already note that the birefringence-nonuniformity-induced contribution (the last term in the first line of Eqs. (3) and (4)) vanishes. The phase spectra of the tokes-dg ( Δφ Probe _ tokes arctg ( 2 ΔΩ / Γ )) and anti-tokes- DG reflections ( ΔφProbe _ anti tokes arctg ( 2 ΔΩ / Γ )), as well as that characterizing their beat term, Δ φrf, are plotted in Fig. 3. train in the fiber will change the fiber sound velocity, ε and consequently, the F, ν, according to Cν = dν dε which was found to be ~0.05MHz/με [33]. These F changes are translated to rillouin phase-shift changes and demodulated from the RF phase-shift in the electrical domain. Figure 3 shows the theoretical effect of periodic variations in F (black curves) on the detected RF phase-shift. Fig. 3. The theoretical phase-shift spectra of the tokes-dg reflection, the anti-tokes-dg reflection, and the beat term (Γ = 2π 20.5MHz). It is important to note, that since the RF beat term oscillates at ~11GHz, the spatial resolution of this technique is practically limited to ~1cm, due to the increasing phase uncertainty in the electrical signal demodulation process. We now show how the proposed technique is independent of non-local phase contributions rapidly accumulating due to changes in the optical path induced by temperature and/or strain changes along the leading fiber, and to which degree it is immune to variations in laser optical power or/and fiber bend losses. First, let's consider a standard tokes-dg scenario where PumpH signal is launched into the fiber under test (FUT) and propagates towards the location of interest at distance z from the FUT entrance point. The accumulated phase is ψ PumpH = ωpumph nslowz/ c. For a temperature change of ΔT in the leading fiber, the corresponding change in the accumulated phase can be written as Δ ψ = ( ω z/ c)( n / T) Δ T = ψ α Δ T, where PumpH PumpH slow PumpH n

8 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5383 ( 1/ n )( n / T) α = is the thermo-optic coefficient, which is approximately equal to n slow slow C 1 for a germanium-doped, silica-core fiber [34] (the change in the physical length due to thermal expansion is negligible). This detrimental non-local phase rapidly accumulates over few meters even for small temperature changes of 1 C, practically precluding localized rillouin-induced phase-shift measurements in standard DG setups. In our setup, however, owing to the generation of two counter-propagating DGs in the FUT, the phase change in the PumpH signal ( Δ ψ PumpH ) is imparted on ProbeR of the tokes-dg, E, by the receding grating, ρ ( E, E, exp( iδ ψ ) ), and the phase change in the PumpH PumpH PumpH PumpL signal ( Δ ψ PumpL = ψ PumpLαnΔ T, ψ = ω n z/ c) is imparted on ProbeR of the PumpL PumpL slow PumpL PumpL PumpL anti-tokes-dg, E, by the oncoming grating, ρ ( E, E, exp( iδ ψ ) ). Therefore, the manifestation of the temperatureinduced non-local effects is through the phase difference Δψ Δ ψ = (( ω ω ) n z/ c) α Δ T, to appear in the cosine of Eq. (5), PumpH PumpL PumpH PumpL slow n whose impact is ~4 orders of magnitude smaller. imilar conclusion arises from the analysis of strain-induced non-local effects (here, however, the change in the physical length is the main contributor to the accumulated phase). As for the probing signal, the two tones of both the forward propagating Probe and the reflected ProbeR are separated by the frequency ν, and therefore the total phase difference will be zero. This excludes the optical path difference between the 'source FUT' path and the 'FUT detector' path, which can in principle be balanced or thermally controlled. Our technique is also quite insensitive to variations in the pumps optical power and/or fiber bend losses. ased on the assumption of a constant PumpL, Eq. (6) shows complete independence of the RF phase-shift on the local powers of PumpL and PumpH. In practice, however, PumpL may experience some gain, altering both its amplitude and phase. PumpH will be somewhat affected as well. To investigate the implications of these practically encountered power variations on the RF phase shift we have numerically [13] solved Eqs. (1) for the phase shift of the induced DG, as PumpL assumes different optical powers. For the scenarios of interest in this paper, with pumps power below 1W and a few meters long sensing fibers, gain is low ( 0.5d). In this regime of operation, our simulation shows that many d's of variation in the power of the pumps merely affect the phase of the DG by a few tens of a milliradian. Consequently, the resulting strain inaccuracy is of the order of a few microstrains (see below ection 4), practically making this technique quite immune to power variations. 3. Experimental setup A complete phasorial PM-DG system, Fig. 4, was built to experimentally demonstrate the proposed technique. A single narrow-band laser diode was used as a source for all the optical signals in the system. Half the laser power is routed to the pumps branch, where the PumpH and PumpL waves are, respectively, the higher- and the lower-frequency sidebands generated by a low-v π electro-optic Mach-Zehnder modulator (MZM1), biased at its minimum transmission to maximally suppress the carrier. The modulation frequency of the feeding RF signal generator (G1) lies in the vicinity of ν /2 (5.425GHz). The modulator output is split by a 3d coupler, whose outputs are both amplified by Erbium-doped fiber amplifiers (EDFA1 and EDFA2) to 20dm, and after passing through high power PM fiber isolators (IO1 and IO2) are launched into the slow axis of a 5m PM FUT from both its sides (entering the fiber from the side from which the probe also enters requires the use of a polarization beam splitter (P)). In the 'probes' branch, first, the laser frequency is upshifted using MZM2. The modulation frequency of G2 is equal to ν DG (45.5GHz). A tunable optical filter (TOF1) removes the lower frequency sideband, as well as most of the amplified

9 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5384 spontaneous emission (E) of EDFA3, which immediately follows MZM2. The ν Probe_HF and ν Probe_LF tones are, respectively, the higher- and the lower-frequency sidebands generated by MZM3, also fed by G1 (modulation frequency of ~ν /2). Finally, the Probe 2ns pulses are generated by a pulse generator (PG), which feeds a semiconductor optical amplifier (OA) with a high extinction ratio of >40d. ubject to the constraint that no two Probe pulses are allowed to be simultaneously present inside the 5m FUT (plus the leading fibers for a total of 10m), the pulse repetition rate of PG is set at 10MHz. The OA output is amplified by EDFA4, providing a peak pulse power of 15dm. Half the Probe power is launched into the fiber through a P to propagate along the fast axis of the PM FUT. The other half, serving as a reference signal, is routed to the fast photodiode (PD1), whose output is acquired by a wideband digital oscilloscope with a sampling rate of 80 Gsamples/sec. The probe reflection, is guided through the coupler into an acquisition channel comprised of EDFA5 and TOF2, which removes the pumps leakage into the fast axis as well as the E of EDFA5. The amplified and spectrally filtered ProbeR signal is then detected by a second fast photodiode (PD2), and acquired by the oscilloscope. The RF phase-shifts are then demodulated in the electrical domain. 4. Results Fig. 4. Experimental setup. LD: A narrow-band tunable laser diode set at 1550nm; MZM1-3: A low-v π electro-optic Mach-Zehnder modulators, biased at their minimum transmission to maximally suppress the carrier; G1/2: RF signal generators whose modulation frequencies lie in the vicinity of ν /2 and ν DG, respectively; EDFA1-5: Erbium-doped fiber amplifiers; TOF1: A tunable optical filter which removes the higher frequency sideband of MZM2 as well as the amplified spontaneous emission (E) of EDFA3; OA: A high extinction ratio semiconductor optical amplifier; PG: Pulse generator; IO1-3: Isolators; P: Polarization beam splitter; FUT: Fiber under test; TOF2: A second tunable optical filter which removes the pumps leakage into the fast axis as well as the E of EDFA5; PD1/2; Fast photodiodes. In Eqs. (1) (2), we have tacitly assumed that the two counter-propagating DGs do not interact. To establish whether this assumption was justified, we have performed an experiment in which we have measured the reflection from an oncoming grating (standard anti-tokes-dg configuration) while altering the intensity of the receding grating. To that aim, we have disconnected the MZM3 feeding RF signal and changed its bias to maximum transmission point. We have changed G2 modulation frequency to ν DG ν /2 (40.075GHz), such that the Probe pulse carrier frequency comprised only one tone, matched to the anti- tokes-dg. In the lower pumps branch of Fig. 4, after IO2, we have placed a tunable optical filter whose roll-off was adjusted to ν PumpL, while ν PumpH remained in the pass-band. y tuning the filter, we have manipulated the transmitted intensity of PumpL without affecting PumpH, Fig. 5(a). Figure 5(b) shows the ProbeR signal of PD2 for different intensities of the receding grating and a constant intensity of the oncoming grating, to which the Probe signal was matched. It can be seen that the anti-tokes-dg reflection remains unchanged, justifying our assumption that counter-propagating DGs do not interact.

10 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5385 Fig. 5. (a) The transmitted spectrum of the lower pumps branch of Fig. 4, after IO2. (b) The ProbeR signal of PD2 for different intensities of the receding grating and a constant intensity of the oncoming grating, to which the Probe signal was matched. Next, we have experimentally addressed the concern of Rayleigh backscattering of the Probe. Returning to the full phasorial PM-DG setup of Fig. 4, we have placed an optical spectrum analyzer (OA) before EDFA5 and measured the spectrum of ProbeR for two cases: one when the pumps where turned off (representing only the Rayleigh backscattering contribution) and other when pumps where turned on, Fig. 6. The lower/higher wavelength sideband for the case when pumps where turned off, is the Rayleigh backscattering of the higher/lower frequency Probe, and for the case when then pumps where turned on, it s the anti-tokes- / tokes-dg reflection of the lower/higher frequency Probe. It can be seen that the Rayleigh backscattering is ~15d weaker than the DG reflection. Though in principle sufficient, better dynamic range can be achieved by increasing the intensity of the generated acoustic wave with higher intensity pumps or/and through the use of chalcogenide glass fibers with a larger nonlinear coefficient. Fig. 6. The OA measured spectrum of ProbeR for two cases: one when pumps where turned off (representing only the Rayleigh backscattering contribution) and other when pumps where turned on. The expected linear dependence of the DG peak reflectivity on the power of the pumps and the Probe was also measured. To measure the power of PumpH and PumpL, we have placed a tap coupler and an OA1 in the lower pumps branch of Fig. 4, after IO2. Figure 7(a) shows the average measured power of the two tones comprising ProbeR (using OA2 placed before EDFA5) as a function of the average power of PumpH and PumpL that was tuned by altering the output power of EDFA2. Next, Fig. 7(b), we have replaced PD1 with OA1 and measured again the average power of the two tones comprising but this

11 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5386 time as a function of the average power of the two tones comprising the Probe that was tuned by altering the output power of EDFA4. oth graphs show a distinct linear behaviour. Fig. 7. Measured DG reflectivity as a function of (a) pumps power and (b) the Probe power. A static strain experiment was then conducted. First, we have performed a calibration procedure in which a static strain was applied to a 20cm section of the PM FUT, bonded between two linear translation stages, Fig. 8(a). The resulting strain was monitored using another single-mode fiber, bonded in parallel to the PM FUT and interrogated by a commercial Rayleigh-backscattering-based optical frequency-domain reflectometer (OFDR). Figure 8(b) shows the RF phase-shift of the detected signal as a function of the measured strain (blue circles). uperimposed on the experimental points is the solid red curve which shows the theoretical RF phase-shift, Δ φrf, from strain-induced shift in the F, obtained ε with a linear regression coefficient of Cν = dν dε ~0.05MHz/με, in excellent agreement with [33]. The dynamic range for the proposed slope-assisted method may extend over the full slope, Fig. 8(b), while its linear part occupies a few hundred microstrains, making the method quite appropriate for the measurement of vibrations. Fig. 8. (a) tatic strain experimental setup employed for the calibration procedure. (b) RF phase-shift as a function of the measured strain (Γ = 2π 26MHz). Following the calibration procedure, a second static experiment was performed. This time, an additional 1m section of the FUT was bonded to a second pair of linear translation stages, Fig. 9(a). Two types of reference traces of the loose fiber were recorded: one of the Rayleighbackscattered signal using a commercial OFDR interrogator, and other of the rillouininduced phase-shift. The rillouin-induced phase-shift (ip) was obtained by scanning a range of modulation frequencies of G1 around ν, and analyzing the phase-shift of the beat signal of PD2, using our phasorial DG system of Fig. 4. The ip was acquired for two modulation frequencies of G2, ν DG and ν DG + 100MHz, emulating fiber birefringence nonuniformity. A strain of ~110με and ~90με was then applied to the 20cm and the 1m sections of the fiber, respectively, and a second set of OFDR and ip traces was acquired.

12 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE 5387 Figure 9(b) shows the strain analysis employing both methods. In our technique, the strain field was obtained by subtracting the current ip trace from the reference, and recording the maximum phase-shift, occurring in the vicinity of ν. As evident from Fig. 9(b), the conversion coefficient for small strains is ~1rad/100με, in excellent agreement with the calibration procedure of Fig. 8(b). Fig. 9. (a) The setup of the second static strain experiment. (b) Longitudinal strain field along the fiber as measured by a commercial OFDR interrogator, compared vs. the maximum of the difference in the rillouin-induced phase-shift. Finally, a dynamic strain experiment was conducted. A 20cm section of the FUT was bonded to a linear translation stage at one end, and to a mechanical shaker at the other end, Fig. 10(a). The FUT was periodically stretched by the shaker, driven by an electrical function generator at 1kHz / 5kHz. Averaging over 10 repetitions was applied to the raw data, representing an effective sampling rate of 1MHz. RF phase-shifts as a function of time, measured at the periodically stretched section of the fiber, are depicted in Fig. 10(b) / 10(c), clearly showing the 1kHz / 5kHz periodic variations, as predicted by our model shown in Fig. 3. In Fig. 10(c), 10kHz low pass filter was applied. The RM noise level of the measured RF phase-shift, normalized to 1Hz, was found to be 0.1mrad/ Hz (equivalent to 10nε/ Hz). Fig. 10. (a) A 20cm section of the FUT was bonded to a linear translation stage at one end, and to a mechanical shaker on the other end. (b) RF phase-shift as a function of time, measured at the periodically stretched section of the FUT driven by an electrical function generator at 1kHz and (c) 5kHz (in Fig. 10(c), 10kHz low pass filter was applied).

13 Vol. 25, No. 5 6 Mar 2017 OPTIC EXPRE Discussion and conclusions In summary, we have proposed and successfully demonstrated a high-spatial-resolution and ultrafast fiber reflectometry technique based on the distributed measurement of rillouininduced phase-shifts in rillouin dynamic gratings. The main obstacles associated with localized phase measurements in DG setups have been overcome by employing coherent addition of the tokes and anti-tokes reflections from two counter-propagating DGs in the fiber, followed by heterodyne detection. As predicted by the analysis of the phasorial properties of DG operation, most measurand-unrelated non-local common phases were cancelled-out. Two sources of measurement errors still remain, ec. 2.2: strain/temperatureinduced non-local differential phase contributions due to the difference in optical frequency between PumpL and PumpH; and large variations in the power of the pumps. Under a few degrees of temperature change along ~10m of fiber and up to several d of pumps power change, the total measurement error is estimated to be of the order of 10 microstrains. While we have only demonstrated a spatial resolution of 20cm (limited by the 0.5ns switching time of our OA), the fundamental limitation of the method probably lies in the vicinity of 1cm, where the bandwidth of the probing pulse approaches the ~11GHz F of silica fibers. It is likely that higher spatial resolutions may be achieved with materials having larger F, e.g., apphire-derived all-glass optical fibers [35] (the use of narrow probe pulses may be challenged by signal to noise limitations, which may be overcome by coding [32]). Owing to its high-spatial-resolution and speed, this technique may be extremely attractive for applications such as monitoring the propagation of mechanical waves. Here, we have demonstrated a distributed measurement of rillouin-induced phase-shift of a 5m-long fiber with a spatial resolution of 20cm. Measurement of both static and dynamic (5kHz) strain fields acting on the fiber were also demonstrated, in excellent agreement with the theory and reference measurements by a commercial strain interrogator. This technique is expected to manifest increased tolerance to laser optical power fluctuations, fiber bend losses and optical pumps depletion. This first demonstration of high-spatial-resolution rillouin phase-shift measurement may have implications which go beyond the realm of fiber-optic sensors. For instance, it has potential important application in the characterization of DG-based reconfigurable optical filters [36]. Funding This research was supported by the Israel cience Foundation (grant No. 1380/12).