Investigation on the Impact of Hi-Bi Fiber Length

Investigation on the Impact of Hi-Bi Fiber Length on the Sensitivity of Sagnac InterferometerYing Cui,Zhifang Wu,Perry Ping Shum,Senior Member,IEEE,Xuan-Quyen Dinh,and Georges HumbertAbstract—Opticalfiber Sagnac interferometers(OFSIs) constructed by a3-dB coupler and a high-birefringence(Hi-Bi)fiber has been developed into various sensors in recent decades. However,the discussion on the length of Hi-Bifiber in this setup remains limited.In this paper,the sensing length of the Hi-Bi fiber is separated from the total length of the Hi-Bifiber for thefirst time in analysis and the impact of Hi-Bifiber length on the sensitivity of the Sagnac interferometer is investigated. It is found that the sensitivity of OFSI is linearly proportional to the ratio of the sensing length over the total length of the Hi-Bifiber.This dependence is confirmed by the experimental results of an OFSI-based strain sensor.The highest sensitivity achieved is about20times of the lowest sensitivity achieved using the same setup but different sensing length to total length ratios.This paper provides a general guideline for the sensitivity enhancement and optimization of OFSI-based sensors.Index Terms—Birefringence,opticalfiber sensors,Sagnac interferometers,strain measurement.I.I NTRODUCTIONT HE OPTICALfiber Sagnac interferometer(OFSI)[1] orfiber loop mirror has been studied for many years since itsfirst proposal and has been developed into various sensors,such as strain[2],[3],transverse load[4],[5], pressure[6],torsion[7],displacement[8],curvature[9]and temperature[10]sensors taking advantage of the merits of simple configuration,flexible operation and high sensitivity.A considerable amount of OFSI-based sensors are constructed by inserting a piece of high-birefringence(Hi-Bi)fiber in between two ports of a3dB coupler.Polarization maintaining photonic crystalfiber(PM-PCF) is a new kind of Hi-Bifiber.It is made of single material with porous structures.Single material fabrication allows for extremely weak temperature response thus can reduce the temperature crosstalk with other monitoring parameters. The porous structure provides higher sensitivity of certain parameters,such as transverse load.Therefore PM-PCF has been widely utilized in the OFSI as the substitute of traditional Hi-Bifibers.Manuscript received October1,2013;revised December19,2013and January25,2014;accepted January27,2014.Date of publication February4,2014;date of current version April16,2014.The associate editor coordinating the review of this paper and approving it for publication was Prof.William N.MacPherson.Y.Cui,Z.Wu,P.P.Shum,and X.-Q.Dinh are with CINTRA CNRS/NTU/THALES,Nanyang Technological University,Singapore637553, and also with the School of Electrical and Electronic Engineering,Nanyang Technological University,Singapore639798(e-mail:ycui2@.sg; wzh.fang@;shum@;xddinh@.sg).G.Humbert is with the University of Limoges/CNRS,Limoges Cedex 87060,France(e-mail:georges.humbert@xlim.fr).Color versions of one or more of thefigures in this paper are available online at .Digital Object Identifier10.1109/JSEN.2014.2304521Although much effort has been put into the study of OFSI-based sensors,the discussion on the influence of the length of the Hi-Bifiber on the sensitivity of the OFSI-based sensors remains limited.The length of the Hi-Bifiber used in the reported works varies from several meters[1]to a few centimeters[2]without much explanation,which seems to be randomly picked for convenient operation.Under the category of strain sensor,the difference of Hi-Bi fiber length from setup to setup does also exist.Some works even lead to contradictory conclusions regarding the relation-ship between OFSI sensitivity and Hi-Bifiber length.For example,in[2]an8.6-cm-long PM-PCF was used in an OFSI and a strain sensitivity of0.23pm/μεwas achieved.In[11] a longer length of PM-PCF(38cm)was used in the same setup and an enhanced sensitivity of1.11pm/μεwas achieved. However in[12]a shorter length of PM-PCF(3.9cm)was used again in the same setup and an even higher sensitivity of 2.34pm/μεwas achieved.Although the contradiction may be relative to the differences exist in PM-PCFs,it is still interesting and well-worthy to explore further the role of Hi-Bi fiber in this classic Sagnac loop sensor setup.We aimed tofind the intrinsic link between Hi-Bifiber length and the sensitivity and explain why longer and shorter Hi-Bifiber both potentially can lead to higher sensitivity. Therefore we built the same setup with the above mentioned works,which is an OFSI-based strain sensor using PM-PCF. During the experiments we realized that one parameter intro-duced by practical experiment,i.e.the sensing length of the Hi-Bifiber,has been neglected in the previous discussions.By ‘sensing length’we mean that when doing the experiments how long the Hi-Bifiber is stretched in the strain sensor, how long the Hi-Bifiber is pressed in the transverse load sensor or how long the Hi-Bifiber is heated in the temperature sensor.In most occasions this‘sensing length’is regarded as the same with the total length of the Hi-Bifiber in analysis. However it is not always the case under different experimental configurations.There are cases like the temperature sensor[10] and the pressure sensor[6]where the whole Hi-Bifiber was used for sensing,i.e.the sensing lengths are the same as the total lengths.In these cases,the length of Hi-Bifiber does not affect the sensitivity.However there are also cases like the strain[2]and the transverse load[4]sensors in which sensing length is only a portion of the total length.In these cases,the ‘sensing length’plays an important role on the sensitivity of the OFSI-based sensors,thus has to be considered carefully in the analysis.In this work the concept of‘sensing length’is proposed for thefirst time.Both theoretical analysis and experimental1530-437X©2014IEEE.Personal use is permitted,but republication/redistribution requires IEEE permission.See /publications_standards/publications/rights/index.html for more information.Fig.1.Schematic diagram of the opticalfiber Sagnac interferometer strain sensor.Inset:SEM image of the cross section of the PM-PCF used. investigation shows that the sensitivity of the OFSI-based strain sensor is approximately linearly proportional to the ratio of Hi-Bifiber sensing length to the total length.By playing with this ratio alone,the highest sensitivity achieved is about 20times of the lowest sensitivity achieved,which confirms the significance and necessity of considering sensing length in developing and optimizing OFSI-based sensors.An optimal Hi-Bifiber length is proposed considering both the sensitivity and dynamic range of the OFSI-based sensor.Further analysis shows that this dependence is applicable to other OFSI-based sensors as well.The following discussion uses OFSI-based strain sensor as an example to illustrate the discovery of this work.II.T HEORETICAL A NALYSISThe OFSI as shown in Fig.1is composed of a3dB coupler and a piece of PM-PCF inside thefiber loop.Light is input into the3dB coupler and split into two counterpropagating beams,which interfere with each other when recombine at the coupler.The optical path difference(OPD)between the two counterpropagating waves provided by the PM-PCF is O P D=B L,where B is the birefringence of the PM-PCF and L is the total length of the PM-PCF.Thus the phase difference is given byϕ=2πB L/λ.(1) The transmission of the OFSI is approximately a sinusoidal function given by the following equation ignoring the insertion loss[13]:T=[1−cos(ϕ)]/2(2)The free spectral range(FSR),i.e.the spacing between transmission dips is inversely proportional to the birefringence and length of the PM-PCF as is given byS=λ2/B L.(3) Strain is added to the OFSI by stretching a portion of the PM-PCF.The corresponding length is the sensing length L1 as indicated in Fig.1.The strain is defined asε= L/L1, where L is the elongation caused by the strain and L1is the sensing length since the strain is only applied to this portion. The phase difference change of the two counterpropagating waves is given byφ=2πλB L1(4) where B is the birefringence change caused by the strain (photoelastic effect)and is proportional to the strain applied B∝ε.Considering the dip wavelength shift λ=S ϕ/(2π),the relationship of the dip wavelength shift with the birefringence change is found as follows:λ=λBL1LB∝λBL1Lε(5) Therefore the sensitivity of the strain sensor is given bySens=λε∝λBL1L=C L1L(6) where C=λ/B is a constant.The sensitivity is proportional to the ratio of L1/L.If L1=L,i.e.the whole length of the PM-PCF is used for strain sensing,Eq.(5)turns to λ=λ B/B and the sensitivity does not depend on the length anymore. However this is not easy to realize practically because it always takes some length tofix thefiber and to avoid the splicing point.III.E XPERIMENT R ESULTS AND D ISCUSSION Experiments were carried out to explore the dependence of the sensitivity of the OFSI-based strain sensor on the ratio of sensing length over the total length of PM-PCF.The schematic diagram is shown in Fig.1.Light from a broadband Amplified Spontaneous Emission(ASE)source(wavelength range1520-1620nm)was launched into the input port of the3dB coupler and the transmission spectra were monitored by an optical spectrum analyzer(OSA)with a wavelength resolution of0.02nm.A piece of PM-PCF was connected to the two ports of the 3dB coupler by fusion arc splicing.The cross-section of the PM-PCF utilized(PM-1550-01)is shown in the inset of Fig.1. There are two large air holes and a number of small ones running along the whole length of the PM-PCF.The diameters of the air holes are4.5μm and2.2μm respectively.The spacing between adjacent air holes is4.4μm.The modefield diameters for the orthogonal polarizations are3.6and3.1μm respectively.The group birefringence at1550nm is about 8.7×10−4.The strain was applied to the PM-PCF by stretching one section of the PM-PCF.A point of the PM-PCF wasfixed on a stage and another point was attached onto a translation stage while keeping the PM-PCF in between straight and well aligned with the elongation direction.The PM-PCF in between was stretched by moving the translation stage.Both the sensing length L1and the total length L were recorded for analysis. The resolution of the translation stage is1μm.First to study the influence of total length three samples with different total lengths of∼2.4cm,∼6.8cm and∼44cm were tested.The transmission spectra are approximately sinusoidalFig.2.Transmission spectra of the Sagnac interferometer with PM-PCF length of(a) 2.4cm,(b) 6.8cm,and(c)44cm inside thefiber loop.(d)One of the transmission dips of the6.8-cm PM-PCF loop shifts with different strainsapplied.Fig.3.The dip wavelength shift against the strain applied on the strain sensor using different total length with the same sensing length of1.7cm. form as shown in Fig.2(a)–(c).The extinction ratios are around32dB,23dB and17dB respectively.As predicted by Eq.(3)the spacing of the transmission dips is inversely proportional to the total length of PM-PCF L.Hence,the dip spacing of the2.4-cm sample is larger than80nm and the previous and next dips are outside the OSA range;the spacing of the6.8-cm sample is∼41nm and the spacing of the44-cm sample is∼6nm.The sensitivities of these samples were examined under the same sensing length of∼1.7cm.The three samples share the same variation trend when strain was applied.With the increase of the strain the transmission spectra shifted to longer wavelengths.The transmission dip around1560nm of the6.8-cm sample was chosen as an example to describe this variation trend as shown in Fig.2(d).While the strain increased from0to23mεthe transmission dip shifted from 1557.1to1562.4nm,totally5.3nm.For the44-cm sample the strain increased from0to26mεand the transmission spectra shifted1.2nm in total and for the2.4-cm sample the strain increased from0to13mεand the transmission spectra shifted 12.3nm.The wavelength shifts with the strain of the three samples were summarized in Fig.3.Linear curvefitting was applied to the experimental data.The sensitivities achieved are0.835, 0.237and0.049pm/μεrespectively with good linearity.The highest sensitivity is17times of the lowestsensitivity.Fig.4.The dip wavelength shift against the strain applied of the strain sensor using different sensing length with the same totallength.Fig.5.The sensitivity of the strain sensor against the sensing length ratio. Therefore under the same sensing length the OFSI withshortest PM-PCF gives the highest sensitivity.Since it takes some length tofix thefiber,an OFSI with too short PM-PCF isdifficult to use in practice.Thus there exists a limit of around2cm when reducing the Hi-Bifiber length to enhance the sensitivity.To study the influence of sensing length,another group of samples were tested with the same total length around44cm but different sensing lengths of∼1.7cm,∼8.5cm and ∼37.7cm.The transmission spectra are similar to Fig.2(c). The wavelength shifts with the strain applied were summarizedin Fig.4.The sensitivities achieved are0.0488,0.2026,and0.9661pm/μεrespectively.The highest one is20times the lowest sensitivity.Therefore for the same total length a longer sensing length corresponds to a higher sensitivity.Since the FSR of the Sagnac interferometer is kept the same under the same total length,higher sensitivity results in a smaller dynamic range, thus for an OFSI with long PM-PCF(i.e.relatively small SFR) there exists a tradeoff between sensitivity and dynamic range. More samples were tested using different sensing lengths L1 and total lengths bined with the previously mentioned samples the sensitivity dependence on the sensing length ratio L1/L is shown in Fig.5.A good linearity(R2=0.9968)has been achieved which confirms the linear relationship predicted by the theoretical analysis.The slope of this line is determined by the wavelength,birefringence and the photoelastic constant of the PM-PCF.In our case the slope is1.154.The highest sensitivity possible for the category of PM-PCF used in our experiments corresponding to the ideal scenario when L1/L=1is about1.14pm/με,which is quite close to theresult of[11]mentioned in the introduction.For the high sensitivity in[12],we believe it is related to the specific PM-PCF they utilized.For example it may have a higher photoelastic constant.Since it has been verified that the sensitivity is determined by the sensing length to total length ratio,it is possible tofind an optimal Hi-Bifiber length for OFSI experiments consider-ing both the sensitivity and the dynamic range.There exists a maximum sensing rangeεm determined by the mechanical strength of the Hi-Bifiber and a highest sensitivity Sens m when the sensing length ratio is near to1.Therefore the following condition should be satisfied:S=λ2B L≥Sens mεm.(7)In the case of this work,εm is around25mε,Sens m is around0.97pm/μεandλis around1560nm,so the total length of the PM-PCF should be smaller than11.5cm to achieve the largest possible dynamic range.For example ifa total length of11cm is chosen,a sensing length larger than9.4cm will give85%the ideal sensitivity.Thefinding that the sensitivity is linearly proportional to the sensing length ratio is also applicable to OFSI-based other sensors because Eq.(5)is still suitable for parameters like pressure or temperature which can change the birefringence of the Hi-Bifiber.As long as that the birefringence change happens only on the sensing length while the OPD of the two counterpropagating waves corresponds to the total length,this dependence can be derived.IV.C ONCLUSIONIn conclusion,the ratio of Hi-Bifiber length used for sensing has a linearly proportional relationship with the sensi-tivity of the OFSI-based sensors.The optimal PM-PCF length for OFSI sensors is proposed giving the best sensitivity and dynamic range.To the best of our knowledge,it is thefirst work separating the sensing length from the total length of Hi-Bifiber in analysis and emphasizing its impact on the performance of the sensor.The relationship found is applicable to OFSI-based other sensors.R EFERENCES[1] C.L.Zhao,X. 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Since2002,he has been appointed as the Director of the Network Tech-nology Research Centre,Nanyang Technological University.He received the Singapore National Academy of Science Young Scientist Award in2002 for his contributions on optical communication technology.He is currently the Director of the Photonics Centre of Excellence,Nanyang Technological University.Dr.Shum has published more than300papers.He was the chair, a committee member,and an international advisor of many international conferences(e.g.,CIOEC,OECC,ECOC,ACP,ICICS,and Photonics Global). His current research interests include concerned with optical communications,fiber technology,andfiber-based devices.Xuan-Quyen Dinh is currently a Thales Researcherwith CNRS/NTU/THALES Research Alliance(CIN-TRA UMI3288),Singapore.Dr.Dinh received thePh.D.degree in optics-physics from Ecole NormaleSupérieure de Cachan,Cachan,France,in2007forhis work in optoelectronics.After the Ph.D.,hejoined the photonics group of the UMI2958GeorgiaTech Centre National de la Recherche Scientifique,Metz,France,as a Post-Doctoral for two and a halfyears.In Metz,he investigated and implementeda securedfiber-optic communication system and a continuous-variable quantum key distribution experiment.His current research interests includefiber-optic communications,fiber lasers,and micro-nanofibers for microwave and sensingapplications.Georges Humbert was born in1975.He receivedthe Ph.D.degree from the University of Rouen,Mont-Saint-Aignan,France,in2002.During histhesis,he studied and fabricated opticalfiber compo-nents.Then,he spent two years as a Research Officerwith the University of Bath,Bath,U.K.,where hehas designed,fabricated,and characterized state-of-the-art photonic crystalfibers,including solid andhollow corefibers.In2005,he joined the XLIMResearch Institute,French National Centre for Sci-entific Research(CNRS),University of Limoges, Limoges,France,as a CNRS Post-Doctoral Researcher.Since2006,he has been a CNRS Researcher with the XLIM Research Institute.His current research interests include the conceptions,fabrications,and characterizations of specialty opticalfibers,including solid-core and hollow-core photonic crystalfibers,for high-power delivery,fiber sensing,and nonlinear optic applications.They also include conceptions,fabrications,and characterizations of photonic band-gap crystal materials for developing microwave resonators and terahertz waveguides.。