Recent Progress in Brillouin Scattering Based Fiber Sensors

Transcription

1 Sensors 011, 11, ; doi: /s OPEN ACCESS sensors ISSN Review Reent Progress in rillouin Sattering ased Fiber Sensors Xiaoyi ao * and Liang Chen Physis Department, University of Ottawa, Ottawa, ON K1N6N5, Canada; lhen@uottawa.a * Author to whom orrespondene should be addressed; xbao@uottawa.a; Tel.: ext Reeived: 6 February 011; in revised form: 5 Marh 011 / Aepted: 30 Marh 011 / Published: 7 April 011 Abstrat: rillouin sattering in optial fiber desribes the interation of an eletro-magneti field (photon) with a harateristi density variation of the fiber. When the eletri field amplitude of an optial beam (so-alled pump wave), and another wave is introdued at the downshifted rillouin frequeny (namely Stokes wave), the beating between the pump and Stokes waves reates a modified density hange via the eletrostrition effet, resulting in so-alled the stimulated rillouin sattering. The density variation is assoiated with a mehanial aousti wave; and it may be affeted by loal temperature, strain, and vibration whih indue hanges in the fiber effetive refrative index and sound veloity. Through the measurement of the stati or dynami hanges in rillouin frequeny along the fiber one an realize a distributed fiber sensor for loal temperature, strain and vibration over tens or hundreds of kilometers. This paper reviews the progress on improving sensing performane parameters like spatial resolution, sensing length limitation and simultaneous temperature and strain measurement. These kinds of sensors an be used in ivil strutural monitoring of pipelines, bridges, dams, and railroads for disaster prevention. Analogous to the stati ragg grating, one an write a moving rillouin grating in fibers, with the lifetime of the aousti wave. The length of the rillouin grating an be ontrolled by the writing pulses at any position in fibers. Suh gratings an be used to measure hanges in birefringene, whih is an important parameter in fiber ommuniations. Appliations for this kind of sensor an be found in aerospae, material proessing and fine strutures.

2 Sensors 011, Keywords: fiber opti sensors; rillouin sattering; polarization mode dispersion; strain; temperature; dynami measurement; strutural health monitoring; birefringene; aousti wave 1. Introdution In the past deade, the demand for safe ivil infrastruture and power supply has dramatially inreased in our soiety. The pressure on ivil engineering, oil and utility industries has grown similarly. Our soiety requires not only a growth in the supply of servies but also improvement in the safety of the supply hain. Disaster prevention requires that engineers design and maintain ivil engineering strutures based on stress integrity assessments. These requirements turn strutural health monitoring (SHM) into a key element of industrial businesses. Clearly there is a need for a tehnique that allows distributed temperature and strain measurements to be aptured in real time over lengths of a few meters to tens of kilometers, even hundreds of kilometers. The distributed sensing tehnique has the advantage of satisfying all these requirements. For over two deades, distributed optial fiber sensors based on rillouin sattering have gained signifiant interest for their ability to monitor temperature and strain in large infrastrutures and replae thousands of point sensors. This kind of sensor has found appliations in ivil strutures, environmental monitoring, the aerospae industry, power generator monitoring and geotehnial engineering. rillouin sattering ours as a result of refrative-index flutuations aused by quasioherent aousti waves initiated from thermally generated sound wave agitations that are apable of sattering inident lightwaves with shifted frequenies. Stimulated rillouin sattering (SS) enhanes suh sattering in a rillouin optial time domain analysis (OTDA) [1-8] with intense signal and better spatial resolution when ompared with spontaneous sattering based rillouin optial time domain refletometry (OTDR) [9-11]. The highest power of the pump wave is limited by the nonlinear effet in fiber [1,13]. At present, there are two shemes to realize a OTDA, inluding rillouin gain [1-4,6,7] and rillouin loss [8]. Their working priniples will be explained in detail in Setion. The performane of distributed sensors based on rillouin sattering has been improved signifiantly over the years. The highest spatial resolution over two kilometer sensing length is m and the longest reported sensing length is 150 km with m spatial resolution and 1 C temperature resolution, this will be desribed in Setion 1. Simultaneous temperature and strain sensing has been realized in photonis rystal fiber (PCF) and polarization maintaining fiber (PMF) at entimeter spatial resolution. This review paper is an attempt to summarize the evolution of the distributed sensor based on rillouin sattering, and the milestones of the distributed sensor in terms of sensing range, spatial resolution, and temperature/strain resolutions, so that readers will have a glimpse of the advantages, limitations and realized potential of this tehnology. To this end, appliations of distributed rillouin sensors for strutural health monitoring have been summarized, and reent researh efforts to measure

3 Sensors 011, birefringene and its dependene on strain and temperature using rillouin gratings in polarization maintaining fiber (PMF) have also been inluded. The paper is organized as following: The definition of a distributed rillouin sensor is provided in Setion, with bakground information about rillouin sattering, as well as the temperature and strain dependene of the rillouin frequeny presented in Setion 3. Stokes and anti-stokes wave derivation in optial fiber are inluded in Setion 4. The hallenge of long sensing range is to have long sensing length, and high spatial and strain/temperature resolution. After long fiber length indued high fiber loss, low signal to noise ratio (SNR) would reate low temperature or strain resolution, as the temperature resolution is proportional to SNR. The high spatial resolution means short rillouin interation length whih makers the signal even weaker, and sensor performane will be poorer. A few approahes have been proposed to boost the power loss due to the fiber attenuation with Raman amplifiers and they are summarized in Setion 5. Ahieving high spatial resolution remains the greatest hallenge in designing a distributed sensor. Early efforts have been foused on post-data proessing shemes to redue the spatial resolution to a fration of the pulse length, i.e., m, those works, based on the same measurement hardware are summarized in Setion 6. Following the 1st demonstration of narrow linewidth rillouin sattering by pre-pumping aousti wave, different approahes based on the same priniple have been proposed leading to reent breakthroughs in the distributed sensor of 5 m resolution over a few kilometers as desribed in Setion 7. As a result, spatial resolution beomes limited by the onvolution of the digitizer and pulse generator bandwidths, rather than any physis based mehanism. To further improve the spatial resolution, an alternative approah utilizing two ontinuous waves with the differene of the rillouin frequeny ounter-propagating in the fiber, and the spatial information is provided by swept the probe wave at various frequeny, has been proposed and it allows millimeter spatial resolution with the pulses of 10 ns. This tehnique is desribed Setion 8. Setion 9 explains the limitation of the temperature and strain resolution and the fiber birefringene effet on temperature and strain resolution. eause the rillouin frequeny is a funtion of temperature and strain, often the temperature measurements assume that strain is onstant; while for strain measurement; temperature is treated as a onstant. Suh an assumption may not be appliable during field tests, hene different approahes of simultaneous temperature and strain measurement have been disussed in Setion 10 using the power, linewidth and multi-rillouin peak features in addition to the rillouin peak frequeny. Setions 11 and 1 summarize two novel approahes to ahieve high performane distributed sensor systems based on sensing length, spatial resolution and temperature/strain resolution over 100 km sensing length without an inline amplifier. Setion 13 gives a unique approah for ombing the rillouin gain and loss for distributed sensor, and it establishes a model for four-wave-mixing in fiber via SS, whih serves as foundation for Setion 14 on the appliations of rillouin gratings in optial fiber. Setion 15 is on dynami strain measurement with OTDA, and Setion 16 summarizes the effort of the strutural health monitoring with rillouin sattering based distributed sensor. The final setion, Setion 17, gives the remarks and prospet of future researh subjets.

4 Sensors 011, Distributed Fiber Sensors ased on rillouin Sattering This setion explains the onept of distributed sensors based on rillouin sattering and the best performane of a rillouin sattering based distributed sensor under the limitation of the aousti wave relaxation time. A distributed fiber sensor based on rillouin sattering exploits the interation of light with aousti phonons propagating in the fiber ore. The rillouin sattered light has a frequeny shift proportional to the loal veloity of the aousti phonons (also alled aousti waves), whih depends on the loal density and tension of the glass and thus on the material temperature and strain. This rillouin frequeny shift is on the order of 9 13 GHz for radiation wavelengths of miro-meters in standard single mode ommuniation fibers, and it is given approximately by: n ( z) V eff a ( z) (1) where n eff is the effetive mode refrative index of the fiber as a funtion of distane z. The veloity of sound in glass is V a and is the free-spae wavelength. The sensing apability of this sattering phenomenon arises from measurement of the distributed rillouin frequeny shift dependene on both strain and temperature. The onept of using rillouin sattering in fiber for optial sensing was first proposed in 1989 [1] and it was termed rillouin optial time domain analysis (OTDA), using the pump-probe wave approah. This basi approah involved launhing a short pump pulse into one end of the test fiber and a CW (ontinuous wave) probe beam into the other end. If the probe wave is at the Stokes frequeny, then energy flows from the pump to the Stokes wave providing rillouin gain to this CW wave. If the probe wave instead takes the anti-stokes frequeny, it then gives energy to the pump wave (pulsed signal), and the deteted CW signal experienes a rillouin loss. The frequeny differene between the two lasers ould be set to a partiular value orresponding to the rillouin frequeny of the optial fibers, and the CW probe would experiene gain varying along the fiber. The gain as a funtion of position along the fiber ould thus be determined by the time dependene of the deteted CW light. y measuring the time dependent CW signal over a wide range of frequeny differenes between the pump and probe, the rillouin frequeny at eah fiber loation ould be determined. This allowed mapping the strain or temperature distribution along the entire fiber length. The first strain distribution measurement was reported on submarine ables [] using distributed fiber sensors based on rillouin sattering. The reported strain distribution was obtained over a 1.3-km able [3]. Later, another strain measurement on the bent slot-type optial ables was reported [4]. Temperature measurement using rillouin sattering was proposed in 1989 [5] utilizing the linear relationship between rillouin frequeny shift and temperature in a single mode fiber and measured with a Fabry-Perot interferometer. Then, a distributed temperature measurement on a 1. km single mode fiber with a 3 C temperature resolution and a 100 m spatial resolution was demonstrated with a OTDA system [6]. In the next three years this performane had improved to ahieve a km sensing length with 5 m spatial resolution of 1 C temperature resolution [7]. The next development in OTDA was the use of rillouin loss rather than rillouin gain [8] in order to inrease the sensing length. Relative to the pulsed pump wave, the CW probe wave has been

5 Sensors 011, set at the anti-stokes frequeny instead of the Stokes frequeny; hene the deteted signal is a rillouin loss. The differene between the gain and loss is the pulse signal has been swithed from donor to reeiver with respet to energy exhange. For long sensing lengths (>10 km), there are two limitations of the former method: (1) peak pulse power of the pump must be lower than the stimulated rillouin sattering (SS) threshold; and () the finite energy of pump pulses an beome signifiantly depleted, leading to uneven gain along the sensing fiber exessive depletion ours at the beginning. Under the rillouin loss regime, the CW probe therefore experiened loss at loations along the fiber at whih the frequeny differene between the lasers mathed the loal rillouin frequeny of the fiber. As it is muh harder to deplete the CW rather than a pulsed pump, a longer sensing length of 50 km with 5 m spatial resolution and 1 C temperature resolution was reported using the rillouin loss mehanism [8]. The longest reported distributed sensor length using OTDR is 57 km with a spatial resolution of 0 m and 3 C temperature resolution [9]. More reently, a sensing length of 150 km was demonstrated by amplifying the OTDR signal using Raman amplifiers in the fiber [10]; a temperature resolution of 5. C was ahieved with a 50 m spatial resolution. The better spatial resolution in OTDA is attributed by the pump and probe wave interation indued rillouin amplifiation over the entire sensing length, while in OTDR only one pump pulse is used and it works in spontaneous rillouin sattering regime. 3. Spontaneous and Stimulated rillouin Sattering (S) in Single Mode Optial Fibers This setion provides mathematial equations for the spontaneous and stimulated rillouin sattering, to illustrate the temperature and strain dependene of the rillouin frequeny, as well as the amplifiation of the pump or probe wave via rillouin gain or rillouin loss resulting from SS indued by eletrostrition. rillouin sattering is aused by the olletive aousti osillations of the solid state matter. From the mirosopi point of view, the intermoleular interation in the solid state matter reates a tendeny for moleules to stay at some stable separation distane from eah other. There is an energy penalty when the atual intermoleular distane is either farther apart or loser than this stable separation. This mirosopi existene of balaned intermoleular distanes would set a new olletive motion. Imagine if a neighboring moleule beomes loser than stability allows, then it will be pushed away towards the point of stability. However, when it reahes that position it will not stop, rather it will overshoot passing the stable separation distane. One it is farther away it will experiene an attration to pull it bak toward the optimum position. However it will again overshoot when it returns. Suh a repeating yle forms a olletive motion alled aousti phonons. To desribe the above proess, we need to use marosopi parameters, suh as the density, pressure and temperature of the matter. As the aousti wave indues loal pressure hanges, the loal density is affeted, altering the material s polarizability and allowing for diret marosopi haraterization via the Maxwell equations.

6 Sensors 011, Spontaneous S The aousti wave is aptured in the following wave equation [14] desribing the pressure wave with the loal pressure variation parameter p ~ : t ~ ~ P ~ ' P 0 () P t Here ' is a damping parameter related the loal visosity of the material, while V a is the sound veloity. To better understand the nature of an aousti wave, we an find a simple solution for a onedimensional propagating wave: V a ~ i( qzt ) P Pe.. Here,.. stands for omplex onjugate. We obtain the following relation governing the propagation onstant q and angular frequeny Ω, i' q Va q 0 (4) (3) This gives the solution: q ' 1 Va i ' V i (5) a Va It illustrates that the aousti wave has a omplex propagation onstant q desribing the usual attenuation expeted from our physial intuition. From the energy onservation prospetive, this kind of attenuation reflets nothing but the energy transferring proesses. The aousti wave is neessarily oupled to other types of modes of the system. At the level of the thermodynami noise, all the modes have non-zero intensity in a system. This type of noise flutuation serves as the seed for the spontaneous rillouin sattering proess. In order to desribe this proess more quantitatively, we assume a polarizability hange assoiated with an aousti wave in the following form: i( qrt ) ( r, t) e.. (6) Also, if we assume that we have a plane EM wave of the form: i( krt ) E( r, t) E0e.. (7) Then one an find the orresponding polarization hange: ( kq) r( ) t i( kq) r( ) t i P( r, t) ( r, t) E( r, t) E e.. E e.. (8) 0 0 eause of the interation between the aousti wave and the inident light, the anti-stokes (first term in the above expression) and Stokes (seond term in the above expression) waves are naturally reated. For the anti-stokes wave, we have the following momentum and angular frequeny relationships: k' k q ' (9) And for the Stokes wave, we have orrespondingly: k' k q ' (10)

7 Sensors 011, We reall that the dispersion relationship between the propagation onstant and angular frequeny of a light wave is quantified by the refrative index: while the dispersion for aousti waves is desribed by ' k n( ), k' n( ' ), (11) q. Aousti angular frequenies are muh smaller than optial frequenies, Ω Ω' <<, where k' and k propagate in opposite diretions along the fiber. Considering the ase of anti-stokes rillouin sattering, and assuming aousti wave propagation in the +z diretion, we have the following momentum onservation for the anti-stokes domain: n( ' ) ' n( ) n( ) d [ n( ) ] d V a n( ) V a n( ) n ( ) g (1) Here, ng () is the group refrative index. Let us solve for the rillouin angular frequeny: n( ) n V a g ( ) n( ) Va n( ) Va n( ) Va n( ) n n g ( ) Va g ( ) Va (13) V We see that to the first order of a, the rillouin angular frequeny in the anti-stokes domain is proportional to the aousti veloity V a and the loal phase refrative index, while being inversely proportional to wavelength. However, to the seond order V a we find an extra term, and this term is of different sign in the Stokes domain. Therefore, the rillouin angular frequeny shift in the anti-stokes domain is different from that in the Stokes domain. This differene an be verified experimentally and is useful in measuring hromati dispersion, and ould be potentially for measurement of polarization mode dispersion through group veloity measurement, beause the rillouin gain is proportional to loal state of polarization (SOP) of the pump and probe wave. Fiber sensors based on rillouin sattering (mostly ignore the seond order effet) utilize the fat that the rillouin frequeny is proportional to the material's loal thermodynami properties suh as sound veloity and phase refrative index, two quantities whih in turn depend on loal temperature and strain. Over quite a large range of temperature and strain, the rillouin frequeny shifts of most fibers are proportional to loal hanges in temperature T and strain, i.e., C T C T. Here, C T is the temperature oeffiient and C is the strain oeffiient for the fiber. Thus, variations in either temperature or strain an ause the rillouin frequeny to hange, hene making it diffiult to distinguish between these two effets, if one measures the rillouin frequeny hange alone. To overome this problem, various methods have been proposed to measure temperature and strain simultaneously using speialty fibers. This will be explained in Setion Stimulated S and Eletrostrition Eletrostritive pressure results from the propagation of two lightwaves in a fiber medium. The frequeny differene between two optial waves equals the indued aousti wave frequeny, namely,

8 Sensors 011, the rillouin frequeny. The inident and Stokes waves produe a beat signal at the rillouin frequeny, whih then indues a density wave enhaning the aousti wave and onsequently inreasing the number of phonons. This provides an improved effiieny of the sattering proess haraterized as operating in the stimulated regime. With a high power of single pump wave, SS an be reated when the pump power is above the threshold value, and it is initiated from spontaneous sattering, the medium is said to be a rillouin generator. SS an also be generated by launhing another beam from the opposite end of the material at the Stokes frequeny, in addition to the pump wave. This is the so-alled Stokes signal, while the input is alled the pump signal. The Maxwell equations an be used to desribe the beat signal indued nonlinear polarization ontribution via the eletrostrition effet that is assoiated with the mass density hange as follows: (14) Here denotes the mean mass density of the material, and is the mass density variation assoiated with the aousti waves. The equation governing the aousti waves is diretly quoted from the book by referene [14]. The above equations form the foundation for the gain and loss formulas presented in Setion 14 for the transient four wave mixing proess of SS and in Setion 15 for the stati ondition of rillouin gratings in optial fiber. 4. Stokes and Anti-Stokes Frequeny Shift From the preeding derivation of the density flutuation, we see that temperature and strain dependene arise from pressure and density waves, whih are also assoiated with birefringene of the optial fiber via n eff and sound veloity. oth of them hange with temperature and strain. eause the birefringene dependene varies with frequeny, the dependene of the temperature and strain ould be different for Stokes and anti-stokes waves, as they are assoiated with two different gratings representing opposite traveling diretions of the aousti wave. Note suh a hange depends on fiber position, whih ould lead to a position dependent temperature and strain oeffiients, namely, C T (z), and C (z). The introdution of the polarization srambler may redue suh position dependene, and inrease the auray for the temperature and strain measurement. The Stokes and anti-stokes rillouin frequeny an also be derived based on the relativisti Doppler effet, and its first order expansion gives the same result as momentum onservation of the Stokes and anti-stokes frequenies for rillouin sattering. eause of the slight frequeny differene between the anti-stokes and Stokes domains, it is very diffiult to measure. The ommon measurement makes use of two proesses: rillouin gain for the anti-stokes frequeny and rillouin loss for the Stokes frequeny. Note that during the two proesses the optial frequeny of the probe wave in the rillouin gain must be kept the same as that of the pump wave in the rillouin loss proess, so that the Stokes and anti-stokes domain of the rillouin frequenies are relative to the same arrier [15,16]. (15)

9 Sensors 011, rillouin sattering viewed on the basis of the relativisti Doppler effet an be illustrated as in Figure 1. Figure 1. Shemati diagram for the Doppler effet. n n As plotted we desribe the rillouin sattering in a view that light of angular frequeny 0 is inident on a moving aousti wave at speed V a, and then a head-on ollision reates refleted light (anti-stokes) with an angular frequeny shifted upward aording to the relativisti Doppler effet, to be preise, we inlude the dispersion in refrative index n for optial fibers, as the single mode fiber has non-negligible dispersion whih an be aount through n: AS n ( 0 V a n V a AS ) [ 0 ( ( )] 0 0 n ( 0 ) V a n[ AS 1 0 ( 0 )] V a 1 0 ) (16) Here, n( 0 ) is the refrative index of the fiber at frequeny 0, and is the speed of light in vauum. Similarly, the tail-end ollision indues a refleted light (Stokes) with an angular frequeny shifted downward by: S n ( 0 ) Va n[ 0 ( 0 )] Va S 1 1 ( 0 0 n ( 0 ) Va n[ S 1 0 ( 0 )] V a 1 0 ) (17) S AS Obviously the Stokes angular frequeny ) and anti-stokes angular frequeny ) must ( 0 be different aording to the solutions of Equations (16) and (17). The seond view of unequal Stokes and anti-stokes domain rillouin frequeny shift is the onventional energy and momentum onservations that are widely used in the disussion of spontaneous and stimulated rillouin sattering as illustrated in the previous setion. The frequeny differene between Stokes and anti-stokes wave, AS S, is measured in single mode fiber (SMF) in both stimulated rillouin sattering (SS) and spontaneous S at a wavelength of 1,550 nm. Experimental results by our group show that in SS this value hanges with varied state of polarization (SOP) and polarization srambling of the pump light, the minimum and maximum of is MHz and MHz; while in spontaneous S this value varies between MHz and MHz for an SNR of 60 d. ( 0

10 Sensors 011, Long Sensing Length for the Distributed Fiber Sensors with OTDA Having established the theoretial bakground of OTDR and OTDA, in this setion we will explain the evaluation of the distributed sensor system. In general, high optial power is required for both pump and probe waves to overome the fiber loss; this however may introdue uneven rillouin gain along the optial fiber. As a uniform signal to noise ratio (SNR) is required from the design perspetive of a distributed sensor, low gain aross a long sensing length is needed. This an be illustrated in Figure. One ompromise of the low gain system over the long sensing length is that there is a orrespondingly low SNR assoiated with small setions of fiber, ompared with that of short sensing lengths. Hene the spatial resolution or temperature (strain) resolution are ompromised for long sensing length. Figure. Small stress response in short and long fiber lengths. (a) Short fiber (b) Long fiber Stokes Pump Stokes pulse Stress setion CW pump Pump power loss Pump power loss 1 10 Time Absolute and relative ontributions of stressed setion are easily measurable Relative ontribution of stressed Setion is hardly measurable Time In order to maintain low rillouin gain with high SNR, the pump power should be kept at a minimum and probe power maximized, but kept below the onset of modulation instability (MI) [13]. MI is a proess that the amplitude and phase modulation of the wave grow as a result of interplay between nonlinearity and anomalous dispersion. In the frequeny domain MI leads to the generation of sidebands symmetrially plaed about the pump frequeny, hene the energy in the high power pump or probe waves will be transferred to those sidebands instead of ontributing to the rillouin gain or loss proess [11,1]. It is also known that via MI new wavelengths an be generated in onventional optial fibers by parametri four-wave mixing (FWM) when they are pumped lose to the zero-dispersion wavelength, as the phase-mathing ondition is sensitive to the exat shape of the dispersion urve, and it an be obtained only in the normal dispersion regime when nonlinear effets are negleted. To avoid the MI effet, a dispersion shifted fiber with normal dispersion has been used [17] in long sensing range. An alternative solution is to use an optial pulse oding tehnique to enhane the SNR [16,18]. For example, MHz rillouin frequeny resolution, and 1 m spatial resolution were ahieved using non-return-to-zero (NRZ) oded pulses over 50 km of SMF-8 fiber [0], while 0.5 m spatial resolution ombined with 0.7 C temperature resolution were obtained using return-to-zero (RZ) ode over a 50 km LEAF (Large Effetive Area Fiber of Corning In.) fiber [1]. eause the RZ oded

11 Sensors 011, pulses have minimized nonlinear effets, better spatial resolution and rillouin frequeny resolution are ahieved. Also, sine there are 4 rillouin peaks in LEAF fiber, higher input pump power an be launhed, thereby yielding better spatial and temperature resolution, with sub-meter spatial resolution using RZ oded pulses. For fiber lengths beyond 60 km, an inline amplifier has been applied for a OTDA based sensor system. Reently, inline Raman amplifiers were used to extend the sensing length to 75 km obtaining spatial resolutions of m of 75 km [] and m of 10 km with bi-diretion of amplifiation [3] 10 m over 75 km [4], as well as 13 m of 46 km sensing length [5] for hybrid FG points and distributed sensor, respetively. Pump depletion ould be avoided by low pump and probe power levels with the fiber loss being ompensated by the distributed Raman gain. Although the Raman amplifiation has allowed for longer sensing lengths, the noise introdued by nd order Rayleigh sattering of Raman amplifiation has the same frequeny as that of the rillouin pump or probe waves depending on uni- or bi-diretional Raman amplifiation. As a result, spatial and temperature resolution have been signifiantly ompromised due to the low SNR in above demonstrations. y dividing the entire sensing length into several sensing setions and then reovering them through frequeny division multiplexing (FDM) [6] of OTDA or time division multiplexing (TDM) [7], one an obtain similar or even better performane of the distributed sensor without Raman assisted OTDA. This means the rillouin interation happens only within the sensing setion having maximum rillouin gain, while the remaining setions are only subjeted to the fiber loss. In FDM, fibers with different rillouin frequeny shifts at distint setions redue the effetive rillouin amplifiation length to one resonant rillouin frequeny setion rather than the entire sensing fiber. Thus, a moderate pump wave an be used to enhane the rillouin interation in the individual setion without pump depletion or exessive amplifiation of the probe wave, due to the short rillouin interation length for a speifi setion. Therefore, the limitation of self-phase-modulation (SPM) effet is also mitigated due to the short interation length for a speifi rillouin frequeny setion or a speifi long pump pulse overed setion length, For the detetion of the CW, the low power should be used, so that highest ontrast an be obtained with high power of the pulse wave. eause of the relatively short effetive sensing length, the true rillouin gain in the setion is in fat larger than the gain if it was operated for the entire sensing length. Multiplexing is realized by sweeping a larger rillouin frequeny range whih spans different loations. eause of larger rillouin gain in eah individual setion, SNR has been improved in omparison with long sensing length using oded pulse shemes and Raman amplifiation assisted long distane OTDA. ased on this onept we demonstrated a 75 km OTDA using three types of 5 km fiber with a spatial resolution of 1 m and an auray of 1 C/0 µ at the end of 75 km, and a spatial resolution of 0.5 m and an auray of 0.7 C/14 µ at the end of 50 km [5]. The limitation of this tehnique is the long measuring time required due to the larger rillouin frequeny range. In TDM, the restrition of the effetive length is realized by two pulses: both pump and probe pulses, in whih the pump pulse provides the effetive length for the rillouin interation and amplifiation, while the probe pulse provides the spatial resolution. Using this idea, one an multiplex different setions by delaying the pump pulse time relative to the probe pulse and then the temperature and strain an be mapped. Using this tehnique, spatial resolutions of 0.6 m and m have been

12 Sensors 011, demonstrated at the end of 75 km and 100 km respetively with a rillouin frequeny shift resolution of MHz, whih is equivalent to C temperature resolution. The high performane of FDM and TDM without inline amplifiation is due to the fat that pump depletion and gain saturation indued rillouin gain distortion on the probe wave, are aumulated only within the single setion of the time or frequeny domain, rather than ontinuously aumulating over the entire sensing length. This idea is similar to regenerating a ommuniation system's signal, when its SNR no longer meets the aepted level. 6. Spatial Resolution Limitation and Improvement by Various Signal Proessing Shemes Spatial resolution is determined by pulse width, and an be improved by using a short pulse; meanwhile, a shorter pulse provides a broadened rillouin gain spetrum (GS) and a weaker rillouin signal, espeially, when it is muh shorter than the material's phonon lifetime (~10 ns in silia fiber, whih is equivalent to 30 MHz bandwidth of the rillouin spetrum). As the measured rillouin spetrum is a onvolution of the pulse and the atual rillouin spetra, for a 1 ns pulse the equivalent pulse spetrum width is 1 GHz. The pump power spreads over 1 GHz instead of 30 MHz resulting in an effetive power drop by a fator of 30. Obviously, the SNR will be redued signifiantly. Even if high pump power is used to ompensate for this power loss and enhane spatial resolution, the measurement auray of the rillouin frequeny shift remains low due to diffiulty of measuring 1 MHz over suh a broadband frequeny base. These limitations prohibit high preision distributed sensor operation by simply shortening the pulse-width [8]. Generally, it is regarded that the spatial resolution annot be better than 1 m for onventional rillouin time-domain sensors, either OTDR or OTDA. Early efforts to improve spatial resolution have foused on various signal proessing shemes. Three suh methods are introdued to obtain spatial resolution values shorter than the pulse length by (1) identifying the stress boundary using the ompound spetral method; () exploiting the seond order derivative of frequeny and loation; and (3) introduing the Rayleigh Equivalent Criterion (REC) De-Convolution of Compound rillouin Spetrum to Improve the Spatial Resolution For a fixed pulse length, one an send pulses twie at different times with one pulse length delay for the seond pulse, so that the rillouin spetrum is de-onvoluted in the same position twie to over the half of the pulse length, whih means the spatial resolution is improved by a fator of two [9]. Similar idea an be used to get a fator of four improvements with half of the pulse length delay, so that in any given position, the rillouin spetrum will be de-onvoluted four times. Under uniform strain within the pulse length, the rillouin loss spetrum is a single peak at a beat frequeny orresponding to the strain and temperature in the fiber. The line width depends on the optial pulse length used. If the strain or temperature within the pulse width is non-uniform, the rillouin loss profile ontains multiple peaks. The individual omponents of the ompound spetrum may be resolved using signal proessing, if the first setion of the strain or temperature is known.

13 Sensors 011, Figure 3. Time-domain waveforms and rillouin loss spetra for various pulse widths [9] (Copyright 1999 IEEE, Reprinted with permission). Assuming the rillouin gain oeffiient is onstant over the length of a fiber setion under onstant strain, the time-domain signal is a onvolution of the shape of the setion of uniform strain (retangular) with the shape of the pulse (also approximately retangular). Considering a fiber setion shown in Figure 3a, as the pulse enters the setion the signal inreases to the point where the pulse is entirely within the setion. Then the signal remains at this level for as long as the pulse is within the setion, dereasing as the pulse leaves. For a pulse of the same width as the strained setion, this results in a triangular waveform (Figure 3b). A pulse twie the width of the setion will produe a trapezoidal shape in the time-domain waveform (Figure 3). If there are two adjaent setions of different uniform strain (and thus different rillouin frequeny), the trapezoidal shape from the latter setion will be partially overlapped by that of the earlier setion. If the time-domain signal is measured at a point in this overlap, the frequeny domain signal will ontain the spetra of both setions (Figure 3d). A pulse width twie the length of a single fiber setion generates a spetrum ontaining two rillouin lines orresponding to the strains of the two setions overed by the pulse. It is possible to use the ompound spetra of N setions measured twie at a time, together with a prior knowledge of the signal from one of the setions to determine the rillouin loss spetrum of the other N-1 setions. 6.. Seond-Order Derivative of the Frequeny and Position to Identify Strain Change Finding the boundary of two strained setions is a diffiult task, espeially for a large strain gradient or a small strain hange. It involves multiple peaks (for large rillouin frequeny variation) or a broadened rillouin profile (for small rillouin frequeny variation). etween different strains in two setions, there is a point of disontinuity in the rillouin gain spetrum of the two peaks. As a result, the first derivative of the frequeny will pik up this transition point. One an take

14 Sensors 011, P P( san, z) P(, z) (, z) [30] to get the first order derivative, where P(v,z) is the san Stokes intensity near the peak frequeny and P( san, z) is the intensity at san, san is the laser frequeny sanning step size. Then alulate the nd order partial derivative of the Stokes (, z) (, z z) (, z) intensity with respet to position, (, z), where z is the step z z size of the digitizer. Figure 4 shows data of 0 m spatial resolution, improved to 5 m loation auray with suh proessing. It is limited by the readout resolution, i.e., the time resolution of the digitizer. This means, the loation auray is a quarter of the pulse length [30]. Hene one an get four times improvement for the loation auray without using narrower pulses, whih ould otherwise require expensive broadband eletronis and lead to higher noise. Instead, the signal proessing is done by omputer programming rather than by hardware. Figure 4. rillouin loss at three different strains for ns pulse (equivalent to 0 m spatial resolution [30] (Copyright 005 OSA, Reprinted with permission) Rayleigh Equivalent Criteria to Identify a Strain Setion Shorter than the Spatial Resolution The optial imaging Rayleigh riterion allows for determination of the smallest resolvable angular separation of two idential objets. It uses two distributions of equal intensity, whose equations have the generi form I sin, where the phase is related to the distane between two objets. This riterion assumes that these two peaks an be resolved as soon as the maximum intensity of the first peak oinides with the first minimum of the seond peak, whih happens at δ = π. The separation between these two objets is then defined as the smallest resolvable distane. The intensity at this minimum distane is 8/π. In a similar fashion, this idea an be applied to the distributed rillouin sensor in the rillouin gain or loss spetrum to identify the two separated strain or temperature peaks. The original intensity is replaed by the rillouin spetrum, while the phase is replaed by the rillouin frequeny. Figure 5 shows the rillouin loss spetrum obtained by simulation of the phenomenologial model [31]. The dip amplitude (minimum of the rillouin loss spetrum between the two peaks) is 0.75 orresponding to s res Here s s /, and res represents the smallest resolvable frequeny differene. is the bandwidth of rillouin spetrum; s is the rillouin frequeny of the resonane, and is the rillouin spetrum s entral frequeny. The dip amplitude is defined as the Rayleigh Equivalent Criterion (REC).

15 Dip Amplitude Normalised rillouin Loss Sensors 011, Figure 6 represents experimental data obtained within ontrolled laboratory onditions. A setion of 1.5 m out of 40 m is subjeted to tration by applying a linearly inreasing weight. The unstrained fiber s rillouin frequeny is 1, MHz. y introduing the REC, the minimum spatially resolvable stress setion is redued to ½ the spatial resolution, with the rillouin frequeny unertainty of 5% ompared to the normal spatial resolution, whih equals to the pulse width. Apparently, the REC is an effiient threshold to unambiguously detet stress setions that are shorter than spatial resolution with an unertainty lower than 5%. Thus using omputer proessing to apply the REC without introduing hardware hanges an improve the loation auray by a fator of two. Figure 5. Definition of the REC for simulated rillouin loss spetrum with the fiber length of 1,000 m, z = 0, Pump = 30 mw, Probe = 5 mw, pulse length = 0 m [31] (Copyright 005 IEEE, Reprinted with permission) res = REC= Figure 6. Normalized rillouin loss spetrum dip plotted as a funtion of the normalized rillouin frequeny shift. Simulation results (plain urve) and experimental data (diamond) at the middle of sensing length 40 m, Ppump = 5 mw, Pw = 3 mw, pulse length of 0 m, ER = 11 d [31] (Copyright 005 IEEE, Reprinted with permission) s 7. Spatial Resolution Improvement by Pre-Pumping the Aousti Wave In reent years, great attention has been paid to improving spatial resolution, and several novel tehniques have been proposed, bringing spatial resolution to the order of m [33-37]. Among these tehniques, there is one ommon working priniple of pre-exitation, whih was first observed in [33]. In this method, a pre-ativated aousti field is reated via eletrostrition through the interferene of a CW pump wave (or a long duration pulse), and a ounter-propagating CW signal wave, having a

16 Sensors 011, loally mathed rillouin frequeny shift with respet to the pump wave. When the aousti wave is developed with a natural rillouin line-width, a very short pulse (ns) arrives and takes a sample of the eletrostrition effet reated aousti wave in the narrow line-width. In this way, the Stokes signal is muh stronger than its amplified portion, generated by the short pulse interation with the CW pump itself, hene spatial resolutions of entimeters have been demonstrated [34,35] with high strain or temperature resolution. Although pre-pumping has enhaned the aousti wave, it indues a minimum rillouin frequeny shift for small setion of temperature or strain hange to be equivalent of at least 1/ of a rillouin spetral width, as the intensity of the non-hanged stress or temperature setion is muh larger than that of the hanged stress or temperature setion, at 1,550 nm it is 10 MHz whih is equivalent to 00 miro-strains, unless a dark base is implemented [38], whih removes the pre-pumping indued depletion effets through an inverse bakground of the pulse. This approah allows high frequeny and spatial resolution over longer sensing lengths. However, the time duration of the dark base depends on the sensing fiber length and pulse width. This means one must hek the dark base length for eah different sensing length and spatial resolution. It makes the implementation of this tehnique in field diffiult. More reently, a differential pulse-width pair rillouin optial time-domain analysis (DPP-OTDA) for high spatial resolution sensing has been proposed, still using the pre-pumping idea to measure the differential rillouin gain signal instead of the rillouin gain itself [39,40]. This tehnique uses two different pulses of nearly idential duration, having high extintion ratios of d to remove the pre-dc effet. Two separate measurements are implemented with respet to the individual pulses, and the differential rillouin gain signal is then obtained by subtration of the two rillouin signals [17,35]. The differential tehnique an be realized by two methods: -phase-shift pulse pair [38] and differential pulse-width pair [39]. The idea of -phase-shifted pulse added to non-phase-shifted pulse is similar as that of a bright pulse being added to a dark base [38], whih is intensity modulation rather than phase modulation format. In the -phase-shifted pulse pair, two pulses share the same pulse-width exept that the last portion of the seond pulse is phase inverted ( phase shift). As a result, the spatial resolution is limited by the fall-time of the pump modulation and the phenomenon of seondary eho signals as was previously proposed. The differential pulse-width pair on the other hand, simply uses two pulses with different pulse-widths. oth tehniques have shown the ability to ahieve high spatial resolution and long-range sensing [40,41], however the -phase-shifted pulse pair yields a 3-d improvement in signal at the ost of a ompliated data reovery proess, due to the ompound rillouin spetrum reated by two onseutive pulses of different phase. The best performane of a differential rillouin gain signal system has been a km sensing length with m spatial resolution, for a rillouin frequeny shift resolution of MHz whih is equivalent to C temperature resolution [4]. For long sensing lengths, performane examples inlude a 30 m spatial resolution for a 5 km sensing length having a rillouin frequeny shift auray of 1 MHz [17], and 0.3 MHz auray of 1 m spatial resolution over a 1 km sensing length [43]. While the best performane with the rillouin ehoes tehniques ( phase shift) has been a 5 km sensing length with 5 m spatial resolution, and 3 MHz rillouin frequeny shift [44]. Further exploration of DPP-OTDA tehnology requires its realization in the optial field domain based on oherent interation of the rillouin gain and loss via optial differential parametri

17 Sensors 011, amplifiation (ODPA) [45]. eause it is not a rillouin gain or loss as demonstrated in DPP-OTDA, ODPA provides a ombined rillouin gain and loss proess with two aousti waves reated by both arrier and Stokes, and arrier and anti-stokes waves. eause the same arrier wave is involved in both the Stokes and anti-stokes wave generation proesses, the arrier wave sees the phase shifts from gain and loss proesses, and both enhaned aousti waves experiene interferene. As a result, a narrowed parametri rillouin gain spetrum is generated. 8. Frequeny Domain Sensor of rillouin Optial Correlation-Domain Analysis (OCDA) The spatial resolution improvement in Setions 6 and 7 are based on time domain, but there is another tehnique based on frequeny domain, OCDA [46,47]. The spatial resolution of the OCDA system is determined by the modulation parameters (amplitude and frequeny) of a light soure, rather than by the deay time of an aousti wave. In this approah, two CW light waves with a rillouin frequeny differene are injeted from both ends of the fiber. The effetive rillouin gain spetrum is built up upon a summation of the rillouin signal at all positions of the sensing fiber. The signal proessing of orrelation between different positions provides a sharp peak for the mathed rillouin frequeny, and the spatial resolution of OCDA an be as high as 1 m [47], even 3 mm spatial resolution has been demonstrated with dynami measurement [48]. For these examples the sensing range has been limited to meters, whih is imposed by the reovery of the relative phase shift between two CW waves. With a double lok-in amplifier and a single-sideband (SS) modulator to stabilize both probe and pump waves at different frequenies, the sensing range has been improved to 300 m. However the spatial resolution has been inreased to 0 m [49]. This tehnique introdues its own omplexities, inluding a trade-off between spatial resolution and range. 9. Polarization Effet on the rillouin Frequeny In the previous setions we have identified the best performane to date of distributed rillouin sensors in terms of shortest spatial resolution and longest sensing length. In this setion we will disuss the fundamental limit of the temperature and strain auraies. rillouin frequeny resolution is one of the key parameters that determine the sensor s auray of temperature or strain measurement. Currently, it is widely believed that frequeny resolution is ultimately determined by extrating the rillouin peak frequeny through fitting of the measured Lorentz spetrum. The minimum detetable hange of the sensor an be denoted by the well known equation [50]: 1 (18) ( SNR), SNR 1/4 Here SNR is eletri signal to noise ratio, is full width at half maximum (FWHM). For the pulsed OTDA, represents the onvolution of the pulse spetrum and natural rillouin line width. We know, however, the imperfetions of the fiber ore size and density non-uniformity in SMF-8 will ause the two possible polarizations to propagate at different phase veloities, dependent upon

18 Sensors 011, fiber loation, and this is the so-alled polarization mode dispersion (PMD) [51]. As a result, even if temperature and strain remain onstant the rillouin peak frequeny hanges at different fiber loations due to the varying birefringene (as it is related to n eff ). This means that even if SNR an be very high, e.g., 60 d, the unertainty of the measured rillouin frequeny due to PMD will not improve. The introdution of a polarization srambler has removed some of the polarization indued flutuation on the rillouin gain, however due to large PMD introdued by the srambler itself on the rillouin frequeny measurement; it has redued the strain and temperature sensitivity of the rillouin frequeny dependene ontributed by the birefringene hange, and the response time of the sensor system due to the speed of a srambler. The impat of PMD effet on the rillouin sattering proess has been previously studied in detail from the aspet of rillouin gain variation [8,5]. It is demonstrated both by theory and experiment that the maximum rillouin gain ours when pump and probe waves have idential polarization, and the maximum gain is twie the minimum rillouin gain. Reently, it has been found that the output state of polarization (SOP) of an arbitrarily polarized input probe wave would onverge to an output SOP orresponding with the maximum rillouin gain, through a so-alled polarization pulling fore at the high rillouin gain ondition [53]. This pulling effet as well as the loal birefringene of SMF altogether govern the SOP evolution of pump and probe waves. In fat, PMD not only affets the SOP of the output probe wave, but also the peak rillouin frequeny, beause n ( z) E ( z) E ( z) follows the hanges in SOP of the pump and probe waves due to indued pump probe loal hanges in fiber polarization harateristis. This means the rillouin frequeny will also hange along the fiber due to non-uniform density and non-irular shape variations of the fiber ore. Obviously, the rillouin frequeny varies with the SOP of the pump and probe waves at different loations, and so do the Stokes and anti-stokes frequenies, beause it is unlikely that n, z) n (, ), espeially when we onsider two polarization modes, when PMD eff ( 0 eff 0 z exists in the fiber, beause of the limited bandwidth of SOP. This means PMD introdues two error soures: (1) on the rillouin frequeny itself due to birefringene hange at different loation; and () on the rillouin gain dependene from the loal SOP hange of the pump and probe wave. For the SNR of this distributed sensor system to be 60 d with a rillouin spetral width of 0 MHz, a rillouin frequeny unertainty is of 0.44 MHz aording to Equation (18). This unertainty is slightly different in spontaneous and stimulated rillouin sattering due to the indued n hange. The introdution of a PMD srambler would itself introdue the peak frequeny unertainly of about MHz depending on the speed of srambler and average number of waveforms. However, SOP variations in the fiber reate a range of the measured rillouin peak frequeny: on the order of 0.1 MHz for spontaneous rillouin sattering SS SS, SOP, SOP, and 0.4 MHz for, even though the Lorentzian shape fitting error of the spontaneous S and SS is 0.1 MHz in both ases. The ultimate temperature and strain resolution should be the ombination of these two ontributions: (, SOP, SNR z z) ( z) ( ) (19)

19 Sensors 011, Simultaneous Temperature and Strain Sensing Using the Distributed rillouin Sensors One problem with the implementation of rillouin sattering based sensing systems in the field is the sensitivity of the rillouin frequeny shift to both strain and temperature. This effet leads to ambiguity in the measurement, as one does not know whether the observed frequeny shift was aused by the hange of strain or temperature. In a laboratory environment, the temperature is essentially onstant and its effets an generally be negleted when measuring strain. In many field onditions this is not the ase. An early solution to this problem proposed the use of two fibers plaed adjaent to one another, in whih one fiber was isolated from any strain effets [54]. The isolated fiber would be used to monitor the temperature, while the other fiber would measure the effet of both strain and temperature. Innovative approahes to measuring the strain and temperature simultaneously have been developed reently. y ombining the Landau-Plazek ratio with the frequeny shift, the temperature and strain were determined simultaneously (in the spontaneous rillouin sattering regime) at a spatial resolution of 40 m [55]. Using the same priniple, an improved system has been reported, whih ahieved a temperature resolution of 4 C, a strain resolution of 90 and a spatial resolution of 10 m for a sensing length of 15 km using LEAF fiber [56]. The analysis of both rillouin gain (i.e., intensity) and rillouin shift provides better performane for simultaneous temperature and strain measurements over the standard ommuniation fiber: it gives 3 m spatial resolution at a temperature resolution of 3 C and strain resolution of 180 [57]. Centimeter resolution has been ahieved with simultaneous temperature and strain sensing using rillouin loss based distributed sensors based on polarization maintaining fibers (PMF) and photoni rystal fibers (PCF). The simultaneous temperature and strain sensing using the PMF an be realized with Stokes power (intensity), line-width and rillouin frequeny. Unlike the single mode fiber where the intensity flutuation is overwhelmed by the PMD indued polarization hanges, the intensity flutuation in PMF is only aused by power flutuations of the light soure, provided temperature and strain oeffiients are onstant along the fiber and the light is launhed in one of the PMF prinipal axes. If the intensity hange of the light soure is negligible, then intensity hanges aused by temperature and strain an be measured aurately [58,59]. Furthermore, when frequeny-stabilized lasers are used, the line-width of the laser is very narrow and hanges slowly with time, allowing for aurate orrelation of the rillouin spetrum width with temperature and strain. Thus, three parameters (rillouin frequeny, Stokes power, and rillouin spetral width) an be simultaneously used for temperature and strain measurements. Resulting in temperature and strain unertainties have been listed for different pairs of these parameters in the following Table 1 [60]. This table provides performane examples for simultaneous temperature and strain measurements with three kinds of PMFs using rillouin power, line-width, and peak frequeny.

20 Sensors 011, Table 1. Unertainty of temperature and strain alulated with measured rillouin frequeny (F), power (P), and bandwidth () from [60] (Copyright 004 OSA, Reprinted with permission). In PCFs with a solid silia ore, the guiding mehanism is the same as in onventional SMF, exept the effetive ladding index is the average of the air and silia refrative indies. The solid silia ore with a Ge-doped enter region an inrease the nonlinear refrative index of the ore and reate a smaller mode field diameter. As a result, the rillouin spetrum of PCF shows multiple peaks with omparable intensities [61], with a main peak and several sub-resonane peaks due to guided aousti modes. In one example, a PCF with a partially graded Ge-doped ore was used, with the main resonane and a peak originating from a higher-order guided longitudinal aousti mode being identified for simultaneous temperature and strain measurement using their rillouin frequeny shifts alone. It gave high temperature and strain measurement auray with spatial resolution of 0 m [6]. 11. TDM-ased OTDA Instead of the pulse and ontinuous wave ombination used in onventional OTDA, in this sheme two pulses, both a probe pulse and a pump pulse are used to perform the measurement. The spatial resolution is still defined by the probe pulse width, while the sensing length is determined by the pump pulse width. The delay between the probe pulse and the pump pulse an be hanged to selet a sensing setion where the probe pulse interats with the pump pulse. The measurement of the entire sensing fiber is realized by implementing the measurement for eah sensing setion through hanging the delay between the two pulses, whih is named as time-division multiplexing of different fiber setions. eause the interation length is only determined by the pump pulse width instead of the entire fiber, the pump power an be inreased to enhane the rillouin interation in the individual setion and improve SNR without exessive amplifiation of the probe pulse. The TDM-OTDA is most effetive on the same fiber type, for instane, SMF8. The effetive sensing length is seleted by a large pump pulse width as explained in Figure 7, and the differential rillouin gain spetrum is measured with two smaller pulse widths of the probe waves, so that high spatial and temperature resolution an be obtained over the entire sensing length. The measurement of the entire sensing length is obtained by adding a sequene of the large pump pulses with eah of them mapped by muh smaller probe pulses; hene this is a time division multiplexing proess. The key to this tehnique is to maintain equal gain over the entire fiber length. While TDM-OTDA allows long sensing lengths, the high spatial resolution is ahieved with DPP-OTDA [39]. In this way, high spatial resolution and long sensing length ombined with high temperature resolution is possible. The ombined TDM and differential OTDA tehniques offer