FIBER-OPTICSENSORSBASEDONFIBERBRAGGGRATINGSFORDYNAMICSTRAIN MEASUREMENT By YupengZhu ADISSERTATION Submittedto MichiganStateUniversity inpartialful˝llmentoftherequirements forthedegreeof ElectricalEngineeringDoctorofPhilosophy 2020 ABSTRACT FIBER-OPTICSENSORSBASEDONFIBERBRAGGGRATINGSFORDYNAMICSTRAIN MEASUREMENT By YupengZhu Thisdissertationinvestigateshowtomeasuredynamicstrainincludingquasi-staticstrain,vibration, acousticemission,andultrasonicwaveswith˝berBragggratingbasedoptical˝bersensors.Fiber opticsensorsareinherentlyimmunetoelectromagneticinterference,lightweight,smallsize, corrosionresistance,andcapableofmultiplexing.Withnarrowlinewidthtunablelasers,thestrain inducedspectralshiftoftheBraggwavelengthofthesensorcanbedemodulated.However,the spectrumoftheuniform˝berBragggratingcannotsatisfythesensitivity,resolution,anddynamic rangerequirements.Toaddressthesechallenges,weproposeanddemonstrateasensorstructure basedonchirped˝berBragggratingscombinedwithFabry-Perotcavity.Takingadvantageoflarge bandwidthprovidedbythechirped˝berBragggratingandthenarrowresonancepeaksformedby theFabry-Perotcavity,itcansimultaneouslyachievehighresolution,highsensitivity,andlarge dynamicrangemeasurement. Thesecondchapterprovidesthetheoreticalanalysisandnumericalsimulationonthespectraof chirped˝berBragggratingsandFabry-Perotcavities.Basedonsuchcontext,wearemotivatedto proposeadynamicstrainmeasurementscenariowhichtakeadvantageofbothhighresolutionand largedynamicrangeofthesensor.Duetothedi˙erentanduniquespectralintervalsofthenotches inthewavelengthbandwidthusedformeasurement,thespectralnotchescanbeunambiguously recognizedineachspectralframewithouttheneedforfringecounting.Usingthisprinciple,we demonstratedhigh-resolutionandabsolutestaticanddynamicstrainmeasurement.Inchapter three,westudytheacousticemissiondetectionwiththeproposedsensorbasedonhigh˝nesse shortcavitystructureandexplorethepotentialofusingthenarrowresonancepeakasthelaser lockingsourcetoreducethelasernoisewhilefunctionsasultrasoundsensor.Additionally,sincethe Braggwavelengthishighlyrelatedtothepolarization,birefringencecausespolarizationdependent center-wavelengthshift.Weproposea90-degreerotationmethodforgratingfabricationintheUV laserbeamsideexposuretechniquetoreducethebirefringence.Thereforethesensorisinsensitive tothepolarizationstateofthelaser,theultrasounddetectionsystemcanbesimpli˝edbyomitting thepolarizationcontroller.Chapterfourexpandsourworkonultrasonicsensorbyusingcoiled ˝berwithlow-˝nesseFabry-Perotinterferometerformedbytwochirped˝berBragggratings. Ourworkhassuccessfullydemonstratedastrainandtemperatureinsensitive˝ber-opticultrasonic detectionbycombiningthecoilstructure,widespectralrange,andquadraturedemodulation.The ultrasonicsensingschemeisimmunetothelaserwavelengthdrift,thereforenowavelengthlocking mechanismisneeded.Futureworkwillcontinueonexploringnewdesignofthesensorstructure andoptimizingthemeasurementsystemtofurtherimprovethefeasibilitywhilereducetheoverall cost. Tomyfamilyandfriends,whoalwayssupportandtrustme. iv TABLEOFCONTENTS LISTOFTABLES ....................................... vii LISTOFFIGURES ....................................... viii CHAPTER1INTRODUCTION ............................... 1 1.1MotivationoftheWork................................1 1.2DissertationOutline..................................5 CHAPTER2FABRY-PEROTINTERFEROMETERFORMEDWITHCHIRPEDFIBER BRAGGGRATINGS ............................. 7 2.1CoupledModeTheoryandTransferMatrixMethodforChirpedFiberBraggGrating7 2.2Simulation.......................................9 2.2.1CFBG-FPwithsamechirpdirection.....................11 2.2.2CFBG-FPwithdi˙erentchirpdirections...................13 2.3DynamicstraindemodulationoftheFBG-basedsensors...............15 2.4Fabry-PerotSensorUsingCascadedChirpedFiberBraggGratingswithOpposite ChirpDirections....................................18 2.4.1Introduction..................................19 2.4.2Sensorcalibrationandstaticstrainmeasurement...............20 2.4.3Dynamicstrainmeasurement.........................25 2.5Summary.......................................29 CHAPTER3ACOUSTICEMISSIONSENSORSBASEDONHIGH-FINESSESHORT- CAVITYFPI .................................. 31 3.1Crackdetectionwith˝ber-opticacousticemissionsensorbasedonachirpedFBGpair31 3.1.1Introduction..................................32 3.1.2Systemandoperationprinciple........................33 3.1.3Experimentalsetupandresults........................35 3.2Ultrasensitiveultrasounddetectionusinganintra-cavityphase-shifted˝berBragg gratinginself-injection-lockeddiodelaser......................38 3.2.1Introduction..................................41 3.2.2Principleofoperation.............................43 3.2.3Experiments..................................45 3.2.4Resultsanddiscussion............................48 3.2.5Conclusions..................................53 3.3E˙ectofLaserPolarizationonFiberBraggGratingFabry-PerotInterferometer forUltrasoundDetection...............................54 3.3.1Introduction..................................54 3.3.2TheoreticalAnalysis.............................56 3.3.3StructureandFabricationofPolarization-InsensitiveFBG-FPISensor...62 3.3.4SensorTestingforUltrasonicDetection...................65 v 3.3.5Conclusions..................................68 3.4Summary.......................................69 CHAPTER4ACOUSTICEMISSIONSENSORSBASEDONLOW-FINESSEFIBER- COILFPI .................................... 70 4.1Passivequadraturedemodulationofcoiledpolarizationmaintaining˝berFabry- Perotinterferometerforultrasonicsensing......................70 4.1.1Introduction..................................70 4.1.2Sensordesignandtheoreticalanalysis....................73 4.1.2.1FPcavitywithlinearbirefringence................73 4.1.2.2Quadraturedemodulation.....................74 4.1.3Experimentaldemonstration.........................76 4.1.3.1Systemsetup............................76 4.1.3.2Ultrasounddetection........................84 4.1.4Conclusions..................................85 4.2Polarization-insensitive,omnidirectional˝ber-opticultrasonicsensorwithquadra- turedemodulation...................................86 4.2.1Introduction..................................87 4.2.2Principleofoperation.............................88 4.2.3Sensorstructureandexperimentsetup....................92 4.2.4Directivityofthesensor...........................94 4.2.5Ultrasounddetectionwithquadraturedemodulation.............95 4.2.6Conclusions..................................97 CHAPTER5CONCLUSIONANDFUTUREWORK ................... 99 5.1Summary.......................................99 5.2FutureWork......................................99 BIBLIOGRAPHY ........................................ 101 vi LISTOFTABLES Table2.1:ParametersoftheCFBGusedinthesimulation...................9 vii LISTOFFIGURES Figure1.1:FBGstructureandspectrum............................2 Figure1.2:FBG-FPstructureandspectrum..........................3 Figure2.1:StructureofasingleCFBG(top)andthesimulatedtransmissionspectrum (bottom).......................................10 Figure2.2:Relativee˙ectivelengthofaFBGversusitsre˛ectivity ' .............12 Figure2.3:StructureoftheCFBG-FPwiththesamechirpdirection(top)andthesimu- latedtransmissionspectrum(bottom).......................13 Figure2.4:StructureoftheCFBG-FPwithlargerpitchperiodsidesclosetoeachother (top)andthesimulatedtransmissionspectrumandtheFSRfeature(bottom)...14 Figure2.5:StructureoftheCFBG-FPwithsmallerpitchperiodsidesclosetoeachother (top)andthesimulatedtransmissionspectrumandtheFSRfeature(bottom)...15 Figure2.6:Schematicinterrogationsetupwithspectrometricmethod............16 Figure2.7:Exampleofexperimentalset-upforedge˝lterinterrogationtechnique......16 Figure2.8:Theprincipleoftheedge˝lterdetectioninterrogationtechnique.........17 Figure2.9:Re˛ectionspectrumofthesensormeasuredbyanOSAandthespectral spacingof12spectralnotches...........................21 Figure2.10:SystemsetupforCFBG-FPIcalibrationandstaticstrainmeasurement.TEC: temperaturecontroller;LDC:laserdiodecontroller;DFBLD:DFBlaser diode;PC:polarizationcontroller;PD:photodiode;DAQ:dataacquisition; FG:Functiongenerator...............................22 Figure2.11:DFBlasercalibrationcurve.............................22 Figure2.12:Scanningsignaltodrivethecurrentcontrollerforthelaser(uppermost)and there˛ectionspectrawhendi˙erentstrainsof(a)0 `Y ,(b)400 `Y ,(c)800 `Y ,and(d)1060 `Y wereappliedtoCFBGssensor................23 Figure2.13:MeasuredwavelengthshiftwithstrainappliedontheCFBG-FPIsensor.....25 viii Figure2.14:Characterizationofsensorresolution:signal˛uctuationswhensensorwas freefromstrain...................................26 Figure2.15:Systemsetupfordynamicstrainmeasurement.AMP:ampli˝er;TEC:temper- aturecontroller;LDC:laserdiodecurrentcontroller;FG:functiongenerator; PC:polarizationcontroller;DAQ:dataacquisition.................26 Figure2.16:MeasuredspectrausingtheupanddownscanningoftheDFBlaserwhenthe sensorwasunderstaticstrain............................27 Figure2.17:MeasuredspectrausingtheupanddownscanningoftheDFBlaserwhenthe sensorwasunderdynamicstrain..........................28 Figure2.18:MeasureddynamicstrainchangebytheCFBG-FPIsensor.Reddashline: shakersignalforevaluation.............................28 Figure2.19:Zoom-inofthemeasureddynamicstrainchangebytheCFBG-FPIsensor. Reddashline:shakersignalforevaluation.....................29 Figure3.1:Schematicofthecrackdetectionsystem.LD:Laserdiode............33 Figure3.2:Re˛ectionspectrumoftheCFBG-FPI.......................34 Figure3.3:PrincipleofAEsignaldetection..........................34 Figure3.4:SchematicdiagramdemonstratingthecrackAEdetectionsystem.LD,laser diode;PD,photo-detector;Cir.,circulator;PC,polarizationcontroller;Amp., ampli˝er;BPF,band-pass˝lter;Osc.,oscilloscope;FG,functiongenerator....35 Figure3.5:Photographofthealuminumsheetonwhichaslotwasinitiallyintroduced (left)andthecrackexpandedaspartofthealuminumsheetwasbentdownward (right)........................................36 Figure3.6:SpectrumofthewavelengthnotchusedforAEdetection.............37 Figure3.7:CapturedAEsignalswhenitwasgeneratedbyPZT................38 Figure3.8:CapturedAEsignalswhenitwasgeneratedbypencilleadbreaktest.......38 Figure3.9:CapturedAEsignalswhenitwasgeneratedbycrackwithinthealuminumplate.39 Figure3.10:FFTspectrumoftheAEsignalsgeneratedbyPZT.................39 Figure3.11:FFTspectrumoftheAEsignalsgeneratedbypencilleadbreaktest........40 ix Figure3.12:FFTspectrumoftheAEsignalsgeneratedbycrackwithinthealuminumplate..40 Figure3.13:Schematicoftheultrasonicsensorsystemwiththe c FBGsensorinsidethe self-injectionfeedbackloop.............................43 Figure3.14:Illustrationshowingthelaserlineislockedtoanexternalcavitymodeonthe slopeofthe c FBGtransmissionspectrum.Schematicoftheultrasonicsensor systemwiththe c FBGsensorinsidetheself-injectionfeedbackloop.......44 Figure3.15:ExperimentalsetupforDFBlaserself-injectionlockingandAEsignalmea- surement.TEC:temperaturecontroller;LDC:laserdiodecontroller.......45 Figure3.16:Transmissionspectrumofthe c FBGmeasuredbyanOSA............47 Figure3.17:Transmissionspectrumofthe c FBGmeasuredbyawavelength-scanninglaser..47 Figure3.18:Noisebehaviorofthefree-runningDFBdiodelaser(redline)andtheself- injectionlockedDFBdiodelaser(blueline)tothe c FBGsensor.........48 Figure3.19:TemporalAEresponsesobtainedfromtwodi˙erentlasersettingforthe c FBG sensor........................................49 Figure3.20:ThenoiseoutputlevelwithoutAEsignalobtainedfromtwodi˙erentlaser settingforthe c FBGsensor.............................50 Figure3.21:Thelockingrangoftheself-injectionlockinglaserandthreeworkingpoints setbyadjustingthe˝berstretcher..........................51 Figure3.22:UltrasonicresponsesatworkingpointsAandC..................52 Figure3.23:UltrasonicresponsesatworkingpointsB.....................52 Figure3.24:Schematicsof(a)anFBG-FPIwithxandybeingthetwoprincipalaxesof thesensorandtheredarrowindicatingthepolarizationoftheprobelaser,and (b)there˛ectionspectrameasuredbylightpolarizedalongitstwoprincipal axesaswellasalonganarbitrarydirectionforthecasesof E¡ 0 and E 0 ..57 Figure3.25:Minimumnormalizedsensitivityobtainedbyvaryinglaserpolarizationangle vs.normalizedsensorbirefringence........................59 Figure3.26:Normalizedsensitivityvs.polarizationangelforseveralsensorbirefringence levels........................................60 Figure3.27:Relativee˙ectivelengthofaFBGversusitsre˛ectivity ' .............62 x Figure3.28:Fabricationofpolarization-insensitiveFBG-FPIsensoranditstransmission spectrum......................................62 Figure3.29:(a)measuredbyanOSAandthere˛ectionspectrum(b)measuredbya wavelength-scanninglaser.(c)and(d)arethere˛ectionspectraofaregu- larFBG-FPIfabricatedwithout˝berrotationmeasuredbythewavelength- scanninglaserattwodi˙erentpolarizationstates.................64 Figure3.30:Experimentalsetupforsensorpolarizationdependencymeasurementand ultrasounddetection.PC:polarizationcontroller,PD:photodetector.......65 Figure3.31:Ultrasonicresponsesofthepolarization-insensitiveFBG-FPIsensor.......67 Figure3.32:Ultrasonicresponsesoftheconventionalone-sideexposedFBG-FPIsensor...68 Figure4.1:Schematicsof(a)asensorwithabirefringentFPcavityand(b)spectral fringeswithquadraturephaseshiftprobedbylightlinearlypolarizedalong twoprincipalaxesofthecavity...........................73 Figure4.2:TheCFBG-FPsensorstructure...........................74 Figure4.3:SimulatedCFBG-FPItransmissionspectrumwithlow-˝nesseFPIfeatures sinusoidalfringes..................................75 Figure4.4:Schematicsofthesensorsystemwithpolarimetricpassivequadraturedemod- ulationforultrasonicdetection...........................77 Figure4.5:ThePM˝ber-coilFPsensor............................77 Figure4.6:Spectralfringesattwopolarizationsandthecorrespondingslope(absolute value)whenthephaseshiftofthefringesis90degree...............79 Figure4.7:Spectralfringesattwopolarizationsandthecorrespondingslope(absolute value)whenthephaseshiftofthefringesis104degree..............80 Figure4.8:NormalizedtransmissionspectraofoneCFBGandtheFPsensormeasured byawhitelightsourceandanOSA.........................81 Figure4.9:3Dprintedstructureofthemold..........................82 Figure4.10:PictureofthesensorbondedontheplatewiththeCFBGsprotectedandlaid freelyontheplate..................................83 Figure4.11:Measuredspectralfringesatthetwopolarizationsafterthesensorwasbonded ontheplate.....................................83 xi Figure4.12:(a)-(d)Operatingpoints(indicatedbythegreenlines)relativetothetrans- missionspectraofsensoratthetwopolarizations.(e)-(h)Corresponding detectedultrasonicsignalsfrombothpolarizationchannels............85 Figure4.13:Schematicillustrationofthesystemcon˝gurationforconceptdescription. TheFBGsaresuspendedfromthestructuretoisolatelargebackgroundstrain. Pha.Mod.,phasemodulator;Ch.,signalchannel;Ult.Sig.,ultrasonicsignal; BPF,band-pass˝lter;FSR,freespectralrange...................89 Figure4.14:(a)sensorspectrumandphasemodulatedlaser,and(b)signaldemodulation channels.......................................90 Figure4.15:Experimentalsetuptostudythesensitivityofthesensortolaserpolarization andanimageofthe˝bercoil............................92 Figure4.16:SpectraoftheFPIsprobedbythelaseratdi˙erentpolarizations.........93 Figure4.17:Experimentalsetupandanimageofthesensorgluedontothealuminumplate..94 Figure4.18:Demonstrationofsensordirectivity,sensorresponsesatdi˙erentincidentangles.95 Figure4.19:Experimentalsetupforthequadraturedemonstrationofthesensor.Amp., ampli˝er.......................................96 Figure4.20:Spectrumofthephasemodulatedlasermeasuredbythescanning-FPI......97 Figure4.21:Ultrasoundwaveformscapturedbythetwochannels(bottom)whenthelaser isatdi˙erentoperatingpoints(upper).......................98 xii CHAPTER1 INTRODUCTION 1.1MotivationoftheWork Forthepastfewdecades,˝beropticsensors[1]arewidelyresearchedandutilizedinsensingof temperature[2],strain[3],pressure[4],magnetic˝eld[5],andultrasonicwaves[6].Especiallyin theareaofnon-destructiveevaluation(NDE)andstructuralhealthmonitoring(SHM),˝beroptic sensorsprovidenumerousadvantagescomparetotheirelectroniccounterparts[7,8].Asofthe glassmaterial,theyareinherentlyimmunetoelectromagneticinterference(EMI)andcorrosion resistance.Also,˝beropticsensorsarelightweightandsmallsize,makethemeasilyembedded intothestructureofmeasurand.Furthermore,˝berBragggrating(FBG)based˝ber-opticsensors o˙erextraordinarymultiplexingcapabilities,makingthemidealforapplicationsrequiringminimal cableswithmultiplesensinglocations. AnFBGisaperiodicrefractiveindexmodi˝cation(grating)structureatthecoreofanoptical ˝ber.Theoptical˝bercanbeeithersingle-mode˝berormulti-mode˝ber.Thetypicaldiameterof coating,cladding,andcoreofthesingle-mode˝berareabout250,125,and8 `< .Themode-˝eld diameterisabout10 `< at1550nm.Figure1.1ashowsthegratingstructureonasingle-mode˝ber. Duetotheperiodicstructure,FBGre˛ectsaspeci˝cpartoftheinputbroadbandlightandallows otherlighttotransmit.There˛ectedlighthasacentralwavelengthcalledthe"Braggwavelength," whichisexpressedas[9] _ = 2 = 455 0 (1.1) where = 455 denotesthee˙ectiverefractiveindexofthemodespropagatinginthe˝ber,and 0 is theperiodofthegrating.Anyexternalparametersthatcanchangeeither = 455 or 0 canintroduce ashiftintheBraggwavelength.Therefore,thevalueofexternalparametercanbederivedby demodulatingtheBraggwavelengthoftheFBG.Asastrainsensor,thegratingperiodaswellas thee˙ectiverefractiveindexarechangeddirectlybythestrainthroughtheelasto-optice˙ect.With 1 (a)Thegratingstructureinanoptical˝ber. (b)ThetransmissionspectrumoftheFBG. Figure1.1:FBGstructureandspectrum. appliedaxialstrain,theBraggwavelengthvariationsensitivitycanbewrittenas[9,10] _ = ¹ 1 d Y º _ Y (1.2) where d Y istheelasto-opticcoe˚cient,whichisgiveby d Y = = 2 455 2 » ? 12 a ¹ ? 11 ¸ ? 12 º¼ (1.3) where ? 11 and ? 12 arethescoe˚cientsoffusedsilicamaterialofthe˝ber,and a is Poisson'sratio.ThetypicalmeasuredsensitivityofBraggwavelengthshiftsonsingle-mode˝ber SMF-28isabout1.2 ?< š `Y inthe1550nmwavelengthregion[11]. AstheFBGonlyfunctionsassensorinthesystem,eitherthebroadbandlightsourceorthe probelaserisusedtointerrogatethesensorandthedemodulationsystemdetectsthere˛ectionor transmissionlight[3].Theresolutionofthesystemistypicallylimitedbythelinewidthofthe 2 FBGsensorandthenoiseofthelightsource,includingintensitynoise,andthermodynamicphase noise.ThelinewidthofauniformregularFBGsensorwithatypicallengthof10mmatBragg wavelengthof1550nmhasare˛ectionlinewidthontheorderof200pm.Becausetheinterested externalparameterisderivedfromtheBraggwavelengthofthesensor,thespectrallinewidthof theFBGdeterminesthesensorresolution.Themeasurementresolution,whichisde˝nedasthe minimumchangeoftheexternalparameterofinterestthatcanberesoledbythesensor,islimited. Inourwork,FBG-basedresonatorsareinvestigatedwithsub10pmlinewidthwhichsigni˝cantly increasethemeasurementresolutionofthesensingsystemcomparedtotheregularFBGs. (a)TheFabry-PerotinterferometerformedbyacoupleofFBGs. (b)ThetransmissionspectrumoftheFBG-FPsensor. Figure1.2:FBG-FPstructureandspectrum. InmostFBGsensors,thegeneralprincipleofoperationisbasedontheBraggwavelengthshift causedbyameasurandsuchasstrain,temperature,pressure,etal.Therefore,themeasurement resolutionofaFBGsensorisdeterminedbythelinewidthandtheslopeofthere˛ectionspectrum.In 3 ordertorealizenarrowerlinewidthorasharperslopeofthespectrum,aFabry-Perotinterferometer withapairofFBGs(FBG-FP)[12]isintroducedasshowninFig.1.2a.Withhighrefractiveindex modi˝cationandproperdistancebetweentheFBGs,high˝nessecavityfeaturesextremelynarrow transmissionpeakswithinthere˛ectionspectrumofthesensorasshowninFig.1.2b.These transmissionpeaksshiftlinearlytogetherwiththeBraggwavelengthwhenstrainortemperature changes.Asaresult,theFBG-FPsensorsprovidebettersensingresolution.However,thedynamic rangestilllimitedwithinthespectrumoftheFBGontheorderof200pm.Alsotheperiodicnature ofthefringesarenoteasytodistinguishintermsofequalfreespectralrangeandfringescounter isrequiredtomeasurethespectralshiftcorrectly[13]. Additionally,laserfrequencynoisecannotbeignoredwhenthesharpslopeofthenarrow fringesisusedsincethelaserfrequencynoiseisconvertedtolaserintensityvariationwithalarge factoroftheslope[14,15].Lowfrequencynoise,narrowlinewidthhighperformancelasersource isperfectbutthebulkysizeandhighcostarenotsuitableinpracticalapplications.Highspeed electronicfeedbackcontrolmethodsuchasPound-Drever-Halltechnique[16]canalsobeused tosuppressthelaserfrequencynoise.However,thewavelengthtuningcapabilityislimitedand increasethecomplexity.Low-costlasersourcewithminimallaserfrequencynoiseiscriticalin dynamicstrainmeasurementapplications. Anarrowfringeisalsosensitivetothepolarizationofthelaserbecauseofthebirefringence introducedbytheFBGresultingdi˙erentBraggwavelengthsfortheprincipalaxesofthesensor. TheBraggwavelengthdi˙erencescanbeontheorderofpmwhichisclosetothelinewidthofthe fringe.Eitherapolarizationcontrollerafterthelasertoalignthelaserpolarizationtothesensor [17]orpolarization-maintaining˝berforthesensor[11]isrequiredtoensurethebestperformance. Themisalignmentofthepolarizationbetweenthelaserwavelengthandtheprincipalaxesofthe sensorcanreducethesensingsignalsigni˝cantly. Asthegratingstructureisacylindricalstructurealongthe˝bercore,thesensorexhibitsa uniqueresponsethethedynamicstrainsignal.Itssensitivitytothestrainsignalisdirective.More speci˝city,thesensorismoresensitivetothedynamicstrainsignalthatpropagatealongthe˝ber 4 direction,butnottothosethatpropagateinitstransversedirection[6].Inordertorealizeomni- directionalsensitivity,ametalringstructurewasintegratedwiththeFBGsensortochangeits propertiestothedynamicstrainsignals[18],thesensorbecomesaresonantsensorandsensitive totheout-of-planestrain.Subsequently,thewholesensorstructureisinevitablybulkierandthe signalismorecomplicated. Thisdissertationconsistsofaseriesofstudiesthatallowforthedevelopmentof˝berBragg gratingstructures,demodulationalgorithms,lasernoisereduction,polarizationdependency,and waystosimplifythecontrolsystem.Byapplyingthenew˝ber-opticsensorstructureontovarious dynamicstrainapplications,weintendtoproposenovel˝berBragggratingdesignsandinnovative fabricationprocesstosigni˝cantlyenhancethedynamicrange,resolution,signal-to-noiseratio, laserperformance,andthewholesystemcost. 1.2DissertationOutline Theremainderofthisdissertationisorganizedasfollows;In Chapter2 ,basedonthecoupled modetheory,thetheoreticalanalysisandnumericalsimulationsconductedonthespectraofCFBG andCFBG-FPisprovided.Toimprovethereliability,realizetheabsolutemeasurement,and overcomethedrawbacksoftheFBG-FPsensors,weproposetouseCFBG-FPsensorswithopposite chirpdirectionwhichpossessbothhighsensitivityandhighdynamicrangefordynamicstrain measurement.CFBG-FPsensorsarepromisingcandidatefordynamicstrainmeasurementfor low-cost,multiplexingscenario. Chapter3 presentstheultrasonicwavedetectionwithboththe c -phase-shiftedFBG( c FBG) andtheCFBG-FPsensors.Tominimizetheelectronicfeedbacksystemandthelasernoise, self-injectionlockingdistributedfeedback(DFB)laserwitha c FBGarecombinedforhighsignal- to-noiseratio(SNR)ultrasonicwavedetection;Acousticemissions(AE)aregeneratedandcaptured onthefractionofaaluminumboardwithCFBG-FPsensorbyedge˝lterdetectionmethod. Chapter4 coversalow-˝nesseCFBG-FPsensorwhichrealizesquadraturedemodulationmakes itrespondtoultrasonicsignalallthetimeregardlessthebackgroundenvironmentalvariations.The 5 experimentalresultsshowedthatthesensoriscapableofdetectingultrasonicsignalwhenthesensor spectraexperienceenvironmentaldriftsusingalaserat˝xedwavelength. Chapter5 drawstheconclusions,andsummarizesthecontributionsinthisdissertationand suggestsfutureresearchdirections. 6 CHAPTER2 FABRY-PEROTINTERFEROMETERFORMEDWITHCHIRPEDFIBERBRAGG GRATINGS Partofthematerialinthischapterhasbeenpublishedinabrerotsensorusingcascaded chirped˝berBragggratingswithoppositechirpdirections,"IEEEPhotonicsTechnologyLetters, vol.30,no.16,pp.1431,2018. Inthischapter,weconductanalyticalandnumericalsimulationsonthespectraofchirped˝ber Bragggratings(CFBGs)andCFBG-FPsensors.Thecon˝gurationofchirpdirectionandthee˙ects tothespectrawillbeexplainedindetails.Thegratingspectrumisdescribedbasedonthecoupled modeequations.Thetransformmatrixmethodisappliedtosolvetheseequationstogeneratethe opticalspectrumofgratingwithchirpedstructures.Furthermore,thefreespectralrange(FSR)and thee˙ectivelengthoftheFabry-PerotcavityformedbyCFBGsareprovided.Theanalysiscanbe usedtooptimizethegratingstructuresforsensingapplicationsandtopredictthecharacteristics ofgratingstructuresunderdi˙erentwritingconditions.Therefore,thetheoreticalstudyinthis chaptercanprovideaguidanceforthesensorfabricationandunderstandingthegrating-based sensingbehavior.ThenwedemonstratethedynamicstrainmeasurementwithcascadedCFBG withoppositechirpdirectionsthatcansimultaneouslyachievehighresolutionandlargedynamic range. 2.1CoupledModeTheoryandTransferMatrixMethodforChirpedFiber BraggGrating AsdiscussedinChapter1,ourworkismainlyfocusedontheuseofCFBGsinsingle-mode optical˝bertoovercomethedrawbacksofregularuniformFBGsincludinglowresolutionandsmall e˙ectivebandwidth.Ananalyticalsolutiondoesnotexistformostnonuniformgratingstructures. Inthissection,thetransfermatrixmethod,whichisapplicabletoarbitrarygratingstructures,is usedtonumericallysolvethecoupledmodeequations[19,20,21].ForaCFBGwithlinearperiodic 7 modulationofitse˙ectiverefractiveindexalongthe˝beraxis I [22]: = 455 ¹ I º = = 455 ¸ = 455 » 1 ¸ a cos ¹ 2 c ¹ I º I º¼ (2.1) where = 455 isthee˙ectiverefractiveindexoftheguidedmodeintheunperturbedsingle-mode ˝ber, = 455 isthemodulationdepth, a isthefringevisibility, ¹ I º = 0 ¸ ˘I isthechirpedgating periodwithnominalgratingperiod 0 and ˘ isthechirpratioofthegrating. ForCFBGinasingle-mode˝ber,themodecouplinghappenspredominantlybetweenthe forwardpropagatingmodeandtheidenticalcounter-propagatingmode.However,thecoupling coe˚cientsarenotconstantinchirpedgratingstructure.Therefore,ananalyticalsolutioncould notbederivedfromthe˝rst-orderordinarydi˙erentialcoupled-modeequations.Thetransfer matrixmethod,whichisapplicabletoarbitrarygratingstructures,isusedtonumericallysolvethe coupled-modeequationsforgratinganalysis. Theideaofthetransfermethodistodividethecomplicatedgratingstructureinto # uniform sections.EachsectionistreatedasauniformFBG,andtheoverallspectrumoftheCFBGcan becalculatedbymultiplexingthematrixdescribingeachuniformsectionforwhichananalytical solutionexists. Assumingeachsub-gratingisafourportsystemwithagratingfeaturedasatransfermatrix ) : ,de˝ning = , = tobethe˝eldamplitudesalongthe ¸ I directionand I directionrespectively, thenthetotalstructurecanbederivedbymultiplyingeachtransfermatrixtogether,whichisgiven by[21] 2 6 6 6 6 6 4 0 0 3 7 7 7 7 7 5 = ) " ) " 1 ) : ) 1 2 6 6 6 6 6 4 " " 3 7 7 7 7 7 5 = 2 6 6 6 6 6 4 ) 11 ) 12 ) 21 ) 22 3 7 7 7 7 7 5 2 6 6 6 6 6 4 " " 3 7 7 7 7 7 5 (2.2) Here, 0 , 0 , " ,and " arethe˝eldamplitudesat I = 0 and I = " respectively,andthematrix foreachuniformsection ) : isgivenby[21] ) : = 2 6 6 6 6 6 4 cosh ¹ I º 9 f sinh ¹ I º 9 ^ sinh ¹ I º 9 ^ sinh ¹ I º cosh ¹ I º¸ 9 f sinh ¹ I º 3 7 7 7 7 7 5 (2.3) where f = 2 c= 455 ¹ 1 _ 1 _ º isaDCcouplingcoe˚cientand ^ = c _ = 455 isanACcoupling coe˚cientofthe : C section, = p ^ 2 f 2 .Withtheboundaryconditionthatthelightisinjected 8 from andthegratingstartsat I = ! 2 ,wehave 0 ¹ ! š 2 º = 0 , 0 ¹ ! š 2 º = 0 ,thematrixspeci˝es eachsectionthatcanbeobtained. There˛ectivityofthewholegratingstructurecanbeexpressedas ' = ) 21 ) 11 2 (2.4) Ifthelossisnegligible,asaconsequenceofconservationofenergy,onecan˝ndthetransmitted powersimplyas ) = 1 ' .Inthefollowingnumericalsimulations,onlythetransmission characteristicsareconsidered.Itisworthnotingthatthenumberofsectionsforthetransfermatrix methodshouldbecarefullychosen.Usuallythenumberoftotalpiecesshouldsatisfy[23] " 2 = 455 ! _ (2.5) 2.2Simulation ThestructureofaChirpedFBG(CFBG)isshowninFig.2.1.UnliketheunchirpedFBG,the refractiveindexmodulationhasalinearperiodvariationwithachirprate( )insteadofaconstant period( ).ComparetotheregularFBG,thegratingperiodoftheCFBGincreasesordecreases alongthe˝beraxis,resultingawiderbandwidthofthere˛ectionspectrumthanaregularFBG. ThebandwidthoftheCFBGisproportionaltothechirpratewithacenterwavelengthattheBragg wavelength.ForasingleCFBG,theparametersusedforthenumericalsimulationsarelistedin Table2.1: Table2.1:ParametersoftheCFBGusedinthesimulation. Symbol PhysicalQuantity Value Unit L Gratinglength 5 mm ! Edge-to-edgedistancebetweengratings 0 mm 0 Phasemaskpitchperiod 1067.7 nm C Phasemaskchirpratio 4 nm/cm = 455 E˙ectiverefractiveindex 1.448 - = 455 Refractiveindexmodulationdepth 5 10 4 - M Totalsectionnumber 200 - a Fringevisibilityofindexchange 1 - 9 Figures2.1showsthestructureofasingleCFBGandthesimulatedtransmissionspectrumof theCFBG.SimilartotheuniformFBG,there˛ectivityoftheCFBGcanbeenhancedbyeither theincreasingthegratinglengthorincreasingrefractiveindexmodulationdepththroughmore exposuretotheUVlaser.Thecenterwavelengthwillshiftstowardalongerwavelengthwiththe increasedUVexposureandindependentofthegratinglength.ThebandwidthoftheCFBGis proportionaltothechirprateandgratinglength,whiletheuniformityofthere˛ectionbandis inverselyproportionaltothechirprate.Therefore,dependsontheapplications,chirprateand gratinglengthshouldbecarefullydesignedforoptimalperformanceoftheCFBG. Figure2.1:StructureofasingleCFBG(top)andthesimulatedtransmissionspectrum(bottom). 10 2.2.1CFBG-FPwithsamechirpdirection SimilartoFBG-FPsensors,iftwoidenticalCFBGsareinscribedwithsomespaceapartinan optical˝ber,theyalsoformaFabry-PerotinterferometerwithCFBGre˛ectors(CFBG-FP),the transmissioncharacteristicsoftheCFBG-FPcavityisanideallosslesscavityconstructedbytwo CFBGswiththesamechirpdirectionandalsothesameotherparametersasshownintheTable 2.1.Theedge-to-edgedistancebetweentheCFBGsissetto0. ThetransmissionspectrumoftheCFBG-FPsensorfeaturesanumberofnarrowpeaksthatare approximatelyequal-spacedwithinthebroadtransmissionbandwidth[24].Thespectraldistance betweenadjacentpeaksiscalledfreespectralrange(FSR).Itisdecidedbytherelativeposition betweentwoCFBGs,andthechirpdirection.TheFSRisinverselyproportionaltothegeometrical distancebetweentheCFBGs. ToensureatleastoneinterferencepeaklocateswithintheCFBGspectrum,theFSRshouldbe smallerthanhalfofthefullwidthhalfmaximum(FWHM)ofthebandwidthoftheCFBG.The FSR _ isgivenby: _ = _ 2 2 = 6 ! 2 Œ (2.6) where _ istheBraggwavelengthoftheCFBG, = 6 isthegrouprefractiveindexofthe !% 01 modeof the˝ber.Forconventionalsinglemodeoptical˝ber,grouprefractiveindex = 6 ˇ = 455 ,where = 455 isthee˙ectiverefractiveindex.The = 455 forour˝berisabout1.448. ! 2 isthee˙ectivelength, whichisasumofthee˙ectivelengthsofboththeCFBGsformingthecavityandtheedge-to-edge distancebetweenbetweenthetwoFBGs: ! 2 = ! B ¸ ! 455 1 ¸ ! 455 2 .Thegratinge˙ectivelength ! 455 attheBraggwavelengthisgivenby[12]: ! 455 = ! p ' 2arctanh ¹ p ' º Œ (2.7) where ' isthegratingpeakre˛ectivity.AsshowninFig.2.2,withalowre˛ectivityvalue,the e˙ectivelengthofthegrating ! 455 isaroundhalfofthegratingphysicallength ! ;whileathigh re˛ectivityvaluethee˙ectivelengthisclosetozero.Itcanbephysicallycomprehendedbythe 11 factthatforaweakFBG,there˛ectedlightalongthegratingishomogeneouslydistributed,while ahighre˛ectiveFBGre˛ectsmostofthelightfromitsinitialpart. Figure2.2:Relativee˙ectivelengthofaFBGversusitsre˛ectivity ' . Inournumericalsimulations,therefractiveindexmodulationdepthisabout 5 10 4 which resultingatotalre˛ectivityof60%attheBraggwavelength.Thentherelativee˙ectivelength ! 455 š ! isabout0.4forasingle5-mmCFBGwith60%re˛ectivity.ForapairofCFBGswith thesame60%re˛ectivity, ! 455 1 = ! 455 2 = 2 mm.Theedge-to-edgedistance ! B issettobe0. Therefore,thee˙ectivelength ! 2 is4mm.TheFSRisexpectedtobearound206pm. ThetopofFig.2.3showsthestructureoftheCFBG-FPsensorwiththesamechirpdirectionand thebottomshowsthecorrespondingtransmissionspectrumandtheFSRoftheselectedresonance peaks.AcoupleofCFBGscascadedinthesamechirpdirectionprovidescomb-likeFSR.The intervalsbetweenpeaksareuniformbutnotexactlythesame.Thisschemecanworkasawide- band˝lterforcommunicationsystems.Thesepeakscanalsobeusedforrelativemeasurement bycountingthewavelengthpeaksnumber.However,lostofpreviouscountinginformationcould leadtoenormouserror.Thereare16resonancepeaksinthe3dBtransmissionbandwidthandthe neighboringresonancepeaksintervalsareapproximatelyuniform,ascanseenfromthemarkers fromFig.2.3. 12 Figure2.3:StructureoftheCFBG-FPwiththesamechirpdirection(top)andthesimulated transmissionspectrum(bottom). 2.2.2CFBG-FPwithdi˙erentchirpdirections FortheCFBG-FPsensorconstructedbytwoCFBGswithoppositechirpdirections,asshownatthe topofFig.2.4andFig.2.5,thetransmissionspectraandtheFSRfeaturearedepictedatthebottom ofFig.2.4andFig.2.5,respectively.Obviously,theFSRisalsorelatedtothechirpdirection.If theCFBGshavethesamechirpdirection,theFSRisequallyspacedinthetransmissionbandof theCFBG-FPsensor;Iftheshorter-periodsidesoftheCFBGsarefacetoeachother,theFSRat shorterwavelengthsislargerthanthelongerwavelengths,andviceversa. Itisobvioustheintervalsofneighboringresonancepeaksshownon-uniformityfeature.Ac- cordingtothedi˙erentchirpdirections,thepeakintervalsareincreasedordecreasedwithrespect tothewavelengths.Thatfeaturesarebecausethesignalswithdi˙erentwavelengthsarere˛ectedat di˙erentpositionsalongthelinearlychirpedgratings,whichresultinthedi˙erente˙ectivecavity 13 Figure2.4:StructureoftheCFBG-FPwithlargerpitchperiodsidesclosetoeachother(top)and thesimulatedtransmissionspectrumandtheFSRfeature(bottom). lengthsfordi˙erentwavelength.AsshowninFig.2.4,thelargerpitchperiodsidesclosetoeach other,resultingasmallere˙ectivecavitylengthforlongergratingwavelength.Sincetheneighbor- ingpeakintervaloftheFPcavity(FSR)isapproximatelyinverseproportiontothee˙ectivecavity lengthshowninEq.(2.6),FSRwillbelargeratlongerwavelength.Similarly,fortheshorterpitch periodsidesclosetoeachotherstructureshowninFig.2.5,FSRissmalleratlongerwavelength. TheFSRsinFig.2.4andFig.2.5areingoodagreementwiththetheory.Therefore,byusing CFBG-basedFPcavitiesasaseriesofidealFPcavitieswithdi˙erentlengths,theapparentnon- uniformityofthespectrallinescanbeclearlyseen.Thekeyideatorealizeabsolutemeasurement reliesonthecombinationofinitialreferencewithrecognizabledetectionsignal,i.e.uniqueFSR formedbytheoppositechirpdirection.Reversingonechirpingdirectioncangeneratedi˙erent vityfordi˙erentwavelength.TheuniqueFSRfeatureandthenarrowlinewidthof 14 theresonancepeakscanbeusedforabsolutestrainmeasurementandwillbefurtherdiscussedin Section2.4. Figure2.5:StructureoftheCFBG-FPwithsmallerpitchperiodsidesclosetoeachother(top)and thesimulatedtransmissionspectrumandtheFSRfeature(bottom). 2.3DynamicstraindemodulationoftheFBG-basedsensors FBG-basedpressuresensors,accelerationsensors,vibrationsensors,acousticemissionsensors, andultrasonicsensorscanbecollectivelyreferredtoasdynamicstrainsensors.Thelargedynamic strainssuchaspressure,acceleration,andvibrationcanbedemodulatedbymonitoringthespectral shiftsoftheFBGs.Thedemodulationmethodscanbeclassi˝edasthespectrometricmethod, andthescanningmethod[3].Thespectrometricmethodincludesabroadbandlightsourceand anopticalspectralanalyzerwhichislimitedbythelowresolutionandlowsensitivity,asshown inFig.2.6.Ontheotherhand,thescanningmethodincludesatunablelasersourceandafast 15 respondphotodiodewhichprovideshighresolutionandhighspeed.However,duetothehysteresis e˙ectcausedbythescanninglaser,itlimitsthescanningrangeandscanningspeedwhichcannot comparetothedynamicrangeofthespectrometricmethod. Figure2.6:Schematicinterrogationsetupwithspectrometricmethod. Inthecaseofsmalldynamicstraincausedbysmallvibration,acousticemission,orultrasonic waveisappliedtotheFBG-basedsensor,thedemodulationusinginthisworkiscallededge˝lter detectionmethod,asshowninFig.2.7. Figure2.7:Exampleofexperimentalset-upforedge˝lterinterrogationtechnique. Speci˝cally,narrow-bandlightsuchaslaserlightisusedastheopticalsourceanditswavelength issettotheslopeofthere˛ectancespectrumofthesensor,asshowninFig.2.8.Weassumethe dynamicstrainissmallenoughforthesensorre˛ectancespectrumtobekeptunchangedinshapeas wellasfortheshiftnotoverthelinearregionoftheslope.Therefore,thechangeinthere˛ectance ofthesensorattheoperationwavelengthisproportionaltotheappliedstrain.Asaresult,wecan directlymeasurethevariationofthere˛ectanceintensitytodecodethedynamicstrain. Byusingaphotodetector(PD)toreceivethere˛ectedortransmittedlightpoweroftheFBG sensor,theultrasonicsignalcanberepresentedasavoltagefunction.Withthelinearrangeofthe 16 Figure2.8:Theprincipleoftheedge˝lterdetectioninterrogationtechnique. gratingslope,theamplitudeofthedetectedsignalisproportionaltotheultrasonicsignal.TheAC componentsofthereceivedvoltagesignalcanbeexpressedas[6] + ( = _ ˝' ˇ % (2.8) where + ( isthedetectedACsignalvoltage, _ istheBraggwavelengthshiftcausedbystrain, ˝ istheslopeofthegrating, ' ˇ istheresponsefactorofthePD,and % istheinputlaserpower.Itis clearthatthedetectedvoltageisproportionaltotheslopeofthegratingandtheinputlaserpower, usingasharpslopeofthesensorwithahighpowerlaserbene˝tstheamplitudeofthedetected signal.Ontheotherhand,thenoiselevelofthesystemlimitsthesensitivity,considerablee˙ortsin thisdemodulationtechniquearemadetooptimizethesignal-to-noiseratio.Oneexampletoreduce thefrequencynoiseisusingselfinjectionlockingtechniqueonaDFBlasertoachieveover35dB increaseofthesignal-to-noiseratioforultrasonicsignaldetection. FPinterferometers(FPIs)formedbycascadedchirped˝berBragggratings(CFBGs)show uniquespectralpropertiesthatcanbeexploredtoimprovesensorperformance.Duetothevarying gratingpitchesinaCFBG,di˙erentpositionsoftheCFBGre˛ectlightatdi˙erentwavelengths. 17 Inmostcases,thetwoCFBGshavethesamechirpdirection,resultinginmultiplealmostevenly- spacedspectralnotches.ThemultiplespectralnotchesinaCFBG-FPIhavealsobeenexplored fordetectionofacousticemissionunderlargequasi-staticstrains.Asthetransmissionpeaksof theCFBG-FPIarealmostevenlyspaced,thepeakscannotbeunambiguouslyidenti˝edwithina narrowwavelength-sweepingrange;asaresult,onlyrelativemeasurementispossible.Moreover, achievingincreaseddynamicrangerequirestheaccurateandcontinuouscountingofthepeaksthat enterthesweepingrangethroughoutthemeasurementprocess.Anyerrorincountingthepeaks resultsinaccumulativeandlargeerrorcorrespondingtothespectralspacingofthepeaks.We presenta˝ber-opticFPIsensorformedbycascadedCFBGswithoppositechirpdirection.Forsuch aCFBG-FPI,thecavitylengthoftheFPIiswavelengthdependent,leadingtounevenly-spaced spectralnotches.ThespectrumofsuchFPIshasbeenstudiedtheoreticallyanditsapplicationfor improvingresolutionanddynamicrangehasbeenexplored. 2.4Fabry-PerotSensorUsingCascadedChirpedFiberBraggGratingswith OppositeChirpDirections Inthissection,wedemonstratea˝ber-opticstrainsensorthatcansimultaneouslyachievehigh resolutionandlargedynamicrange.Thesensorisa˝ber-opticFabry-Perot(FP)cavityformedby cascadedhigh-re˛ectionchirped˝berBragggratings(CFBGs)withoppositechirpdirections.The re˛ectionspectrumofthesensorfeaturesaseriesofnarrowspectralnotcheswithunequalspacings. Thesensorisdemodulatedbywavelengthscanningofadistributedfeedbacklaserdiodethrough current-injectionmodulation.Thenarrowspectralnotchleadstohighmeasurementresolution; whiletheunambiguousidenti˝cationofthespectralnotchesthroughtheiruniquespectralspacings resultsinlargemeasurementrangewithouttheneedforfringecounting.Wehavedemonstrateda linearaxialstrainresponseofthesensorwithstrainresolutionof0.033 `Y overarangeof1000 `Y . 18 2.4.1Introduction Fiber-opticsensorsbasedonvariousgratingstructureshavebeenextensivelystudiedformeasure- mentofawiderangeofphysicalandbiochemicalparameters[1,25,26].Inparticular,Fabry-Perot interferometers(FPIs)formedbycascadedchirped˝berBragggratings(CFBGs)showunique spectralpropertiesthatcanbeexploredtoimprovesensorperformance[27,28,29,30].Dueto thevaryinggratingpitchesinaCFBG,di˙erentpositionsoftheCFBGre˛ectlightatdi˙erent wavelengths.Inmostcases,thetwoCFBGshavethesamechirpdirection,resultinginmultiple almostevenly-spacedspectralnotches[24].ThemultiplespectralnotchesinaCFBG-FPIhavealso beenexploredfordetectionofacousticemissionunderlargequasi-staticstrains[17].CFBG-FPIs havealsobeenusedashigh-resolutionsensorsdemodulatedbyadistributedfeedback(DFB)laser diodewhosewavelengthisscannedthroughinjectioncurrentmodulation[29].Althoughthewave- lengthscanningrangeofaDFBlaserislimited(afewhundredpm),multipletransmissionpeaks oftheCFBG-FPIcanbeusedtoincreasethedynamicrangeofthesensor.Asthetransmission peaksoftheCFBG-FPIarealmostevenlyspaced,thepeakscannotbeunambiguouslyidenti˝ed withinanarrowwavelength-sweepingrange;asaresult,onlyrelativemeasurementispossible[29]. Moreover,achievingincreaseddynamicrangerequirestheaccurateandcontinuouscountingofthe peaksthatenterthesweepingrangethroughoutthemeasurementprocess.Anyerrorincounting thepeaksresultsinaccumulativeandlargeerrorcorrespondingtothespectralspacingofthepeaks. Inthissection,wepresenta˝ber-opticFPIsensorformedbycascadedCFBGswithopposite chirpdirection.ForsuchaCFBG-FPI,thecavitylengthoftheFPIiswavelengthdependent,leading tounevenly-spacedspectralnotches.ThespectrumofsuchFPIshasbeenstudiedtheoretically[24] anditsapplicationforimprovingresolutionanddynamicrangehasbeenexplored[27,30].For example,in[30],thedi˙erentspectralwidthsofthenotcheswereusedtotunethesensitivityincase ofintensitydemodulationbyalaser.However,forwavelengthdemodulation,thedemonstration wasstilllimitedtorelativemeasurementandfringecountingwasneededtousemultiplenotches forincreaseddynamicrange.In[27],improvingresolutionanddynamicrangewasachievedby probingthesensorattwodi˙erentwavelengthwindowsthroughawidelywavelength-tunablelaser. 19 Thewavelengthwindowswereseparatedbyover10nmwherethesensorhadvastlydi˙erentfree- spectralranges.Unfortunately,scanningoverthislargewavelengthrangegreatlyreducesthespeed ofthesensorsystemandmakesitunsuitableformeasurementofdynamicparameters.Here,we showthat,throughhigh-speedwavelength-scanningdemodulationusingaDFBlaser,thesensor canachievehighresolution,largedynamicrange,andabsolutemeasurementforbothstaticand dynamicstrainmeasurement.Speci˝cally,theuniquespectralspacingofthere˛ectionnotches rendersthepossibilitytounambiguouslyrecognizeeachofthenotcheswithinthewavelength- sweepingrangethatcoversatleasttwoneighboringspectralnotches.Withtheknowledgeof thewavelengthpositionofaspeci˝cnotch,absolutemeasurementisachieved.Becauseofthe notchisrecognizedduringeachwavelengthsweep,nonotchcountingisneededtoachievelarge dynamicrange.SimilartootherCFBG-FPIs,thenarrowspectralfeaturesallowhighresolution measurement.Thehigh-speedwavelengthscanningachievedthroughinjectioncurrentmodulation oftheDFBlasermakesitpossibleformeasurementofdynamicstrains. 2.4.2Sensorcalibrationandstaticstrainmeasurement ThecascadedCFBGsarewerefabricatedon80- ` msinglemode˝berbyachirpphasemask with4nm/cmchirpingratebasedonthescanningbeamtechnique[31].Thereasontochoose 80 ` msinglemode˝berinsteadofstandard125 ` msinglemode˝berisbecauseofthesmaller diameterandhigherGe-dopedconcentrationwhichleadtoeasiergratingfabricationwiththeUV lasersystem.ThelengthofasingleCFBGis4.5mm,nogapbetweenthecascadedCFBGs.As showninFig.2.4,theoppositechirpdirectionsofthetwoCFBGsisrealizedbychanging˝ber directionbeforefabricatingthesecondCFBG.Onlyonechirpedphasemaskisneeded.During fabrication,thespectrumismonitoredbyanopticalspectrumanalyzer(OSA)withabroadband lightsource.Re˛ectivityofeachCFBGismorethan90%overaspectralwidthof1.6nm.The re˛ectionspectrumofthein-bandpeaks,andthenotchspacingsareshowninFig.2.9.Duetothe limitedresolutionoftheOSA(20pm),thenotchingspacingsweremeasuredbythescanningDFB lasersetupshowninFig.2.10,asdescribedindetaillater. 20 Figure2.9:Re˛ectionspectrumofthesensormeasuredbyanOSAandthespectralspacingof12 spectralnotches StaticstrainmeasurementusingthesetupshowninFig.2.10wasperformedtocalibrate thesensorsensitivitytostrainandstudythesensorperformanceintermsofdynamicrangeand resolution.ThelightfromaDFBlaserwasdirectedtotheCFBG-FPIsensorthroughacirculator. Apolarizationcontrollerwasusedbeforethecirculatortoensurethatlaserpolarizationwasaligned withoneoftheprincipleaxesofthesensor.Throughthesamecirculator,thelightre˛ectedfrom thesensorwasdirectedtothephotodetector(PD)andtheoutputwasrecordedbyadataacquisition (DAQ)deviceatasamplingrateof2.0MS/s.ThecurrentcontrollerfortheDFBlaserwasbiased at225mAandmodulatedwith500Hz,2V(correspondingto100mA)peak-to-peaktrianglewave tocontrolthecenterwavelengthandthescanningrangeofthelaser.Theseparameterswereset sothatthescanningrangeofDFBlaserdiodecoveredatleasttwonotchesofthesensoroverthe designedmeasurementrange. DuetothetuninghysteresisoftheDFBlaserbyinjectioncurrent[32],calibrationofthe relativewavelengthshifttothescanningvoltagerangeisnecessary.AsshowninFig.2.11, triangularscanningwaveformsareusedtodrivetheDFBlaser,upanddownscanningexperience di˙erentpathsandformahysteresisloop.Thescanningrangeandfrequencyareselectedbased onthemeasurementcondition.Thesecalibrationscurveswereusedtoconvertscanningvoltageto 21 Figure2.10:SystemsetupforCFBG-FPIcalibrationandstaticstrainmeasurement.TEC:tempera- turecontroller;LDC:laserdiodecontroller;DFBLD:DFBlaserdiode;PC:polarizationcontroller; PD:photodiode;DAQ:dataacquisition;FG:Functiongenerator. wavelengthshift. Figure2.11:DFBlasercalibrationcurve. Forsensorcalibrationandstaticstrainmeasurement,thesensorisverticallyplacedwitha˝xed topend.Axialstrainisappliedbyincreasingweightonthefreeendofthesensor.Thespectral 22 notchspacingsofthesensorweremeasuredbyapplyingweighttothe˝bertoinduceaxialstrain ontheCFBG-FPIsensor.Byaddingweight,spectralnotchessuccessivelypassedthewavelength scanningrangetomeasuretheirwavelengthpositionsandspectralspacings.Thespectralspacings wereusedforthenotchidenti˝cationinthestrainmeasurement. Figure2.12:Scanningsignaltodrivethecurrentcontrollerforthelaser(uppermost)andthe re˛ectionspectrawhendi˙erentstrainsof(a)0 `Y ,(b)400 `Y ,(c)800 `Y ,and(d)1060 `Y were appliedtoCFBGssensor. 23 Figure2.12showsthescanningsignalthatdrovethecurrentcontrollerfortheDFBlaserand themeasuredre˛ectionspectraofthesensorwhendi˙erentstrainlevelsof0,400,800and1060 `Y wereappliedtothesensor.Althoughboththerisingandfallingedgeofthewavelengthscanning canbeusedforwavelengthshiftdemodulation,hereweonlyshowtheresultsobtainedfromthe risingedge.Whenanarbitrarystrainapplied,theorderofthenotchesinthescanningrangewere identi˝edbymeasuringthespectralintervalbetweenthemandmatchtotheresultsshowninFig. 2.9.Absolutewavelengthshiftcanbecalculatedbymeasuringthepreciselocationofasingle notchinthetuningrangewiththeinitialnotchlocation.Notcheslocationwithinthescanningrange arerecordedandconvertedtorelativewavelengthbasedonthelasercalibrationcurve.Theunique spectralspacingprovidestheorderofeachnotchevenwithonlyonescanningframecaptured bytheDAQandenablesabsolutestrainmeasurement.Speci˝cally,thespectralnotchatlonger wavelengthshowninFig.2.12(a)wassetastheinitialnotchanditswavelengthpositionatzero strainwasrecorded(reddotline).Theorderoftheinitialnotchwasnamedas1forreference.When arbitrarystrainwasappliedonthesensor,notchespositionandspectralspacingsaremeasured. Thewavelengthdi˙erencebetweenNthnotchandthe1stnotchisgivenby ! = # 1 Õ 8 = 1 ( 8 (2.9) where ( 8 isthespectralintervalbetweennotch i andnotch i +1.Asanexample,assumethenotch N isthe˝rstnotch _ 1 locatedatthewavelengthshorterthan _ 0 (e.g.notch4inFig.2.12(b)).The wavelengthinterval _ (seeFig.2.12(b)betweenreference _ 0 and _ 1 canbemeasuredwithhigh resolutionbythiswavelength-scanningmethod,thenthetotalwavelengthshiftcausedbythestrain appliedonthesensorisgivenby ! = ! _ . Astherewere12spectralnotcheswithinaspectralbandwidthof1.6nmavailableformeasure- ment,thestrainmeasurementrangeisover1000 `Y .Fig.2.13showsthemeasuredwavelength shiftasafunctionofappliedstrainwhichvariedfrom0 `Y to1060 `Y inthestepof133.4 `Y .The sensorsystemshowsexcellentlinearresponsewithastrainsensitivityof1.31pm/ `Y . Theresolutionofstrainmeasurementwascharacterizedbycontinuouslymonitoringthewave- 24 Figure2.13:MeasuredwavelengthshiftwithstrainappliedontheCFBG-FPIsensor. lengthpositionofaspectralnotchwhennostrainwasappliedonthesensor.Thewavelength positionofonespectralnotchwascontinuouslymonitoredfor0.6sandtheresults(afterconversion tostrain)areshowninFig.2.14withastandarddeviationof0.033 `Y .Aslowdrifttowardlower strainmayalsobepresent,asindicatedbythelinear˝ttingoftheresults(redcurveinFig.2.14). Thedriftisbelievedtoarisefromthelaserwavelengthdriftfromambienttemperaturevariationof thelaserdiode.Thelaserwavelengthcanbestabilizedbyanexternalwavelengthreference,such asareference˝berBragggratingorareferenceFPI. 2.4.3Dynamicstrainmeasurement Withthehigh-speedwavelengthscanningofDFBlasersthroughcurrentinjectionmodulation,the sensorisalsosuitableformeasurementofdynamicstrains.Thedynamicstrainmeasurementsetup isshowninFig.2.15.Thesensorwasgluedonthecenter-lineofacantileverbeammadefrom aluminum.Thefreeendofthebeamwasexcitedbyanelectromagneticshaker.A20Hzsinusoidal signalisgeneratedbyafunctiongeneratorandampli˝edtodrivetheshaker.Thewavelength sweepingrateoftheDFBlaserwassetto1000Hzwiththesamebiascurrentforhighspeed demodulationwithapeak-to-peakcurrentof150mA(correspondingto3V).Calibrationoflaser 25 Figure2.14:Characterizationofsensorresolution:signal˛uctuationswhensensorwasfreefrom strain. Figure2.15:Systemsetupfordynamicstrainmeasurement.AMP:ampli˝er;TEC:temperature controller;LDC:laserdiodecurrentcontroller;FG:functiongenerator;PC:polarizationcontroller; DAQ:dataacquisition. wavelengthtothelaserinjectioncurrentwasperformedtoobtaintheaccuratewavelengthpositions ofthesensorspectralnotches.EventhoughtheDFBlaserscanningspeedwasover30times largerthantheaveragestrainchangingspeed,thee˙ectofthelaserwavelengthscanningdirection relativetothemovingdirectionsofthespectralnotchesshouldbeconsidered.Thise˙ectisonly presentindynamicstrainmeasurement.Whenstaticstrainisappliedtothesensor,thespectral notchpositionsmeasuredusingthewavelengthupscanninganddownscanningoftheDFBlaser 26 areidentical,asshowninFig.2.16. Figure2.16:MeasuredspectrausingtheupanddownscanningoftheDFBlaserwhenthesensor wasunderstaticstrain. However,underdynamicstraincondition,ifthelaserwavelengthandthespectralnotchesmove inthesamedirection,ittakesextratimeforthelaserwavelengthtorecordthespectralnotch (upscanningcurveinred)comparedtothecaseofstaticstrainwherethenotchesarestationary. Conversely,ifthelaserwavelengthandthespectralnotchesmoveinoppositedirections,ittakes lesstimeforthelaserwavelengthtomeetthespectralnotches(downscancurveinblack).Asa result,thewavelengthpositionofspectralnotchmaybedi˙erentwhendi˙erentdirectionsofthe wavelengthscanningareusedforwavelengthmeasurement,asshowninFig.2.17. Measurementerrorscouldbeintroducedwithoutconsideringthespectralshiftofthenotches duringthedynamicstrainchange.Here,aseachperiodofthewavelengthscanningconsistsofa wavelengthrampupandarampdown,weusetheaveragepositionofeachspectralnotchcalculated frombothupanddownramps.Theaveragingcane˙ectivelyeliminatetheerrorcausedbydynamic strainchange. ThebluesolidlineinFig.2.18showsthedynamicstrainsignalmeasuredbytheCFBG-FPI 27 Figure2.17:MeasuredspectrausingtheupanddownscanningoftheDFBlaserwhenthesensor wasunderdynamicstrain. Figure2.18:MeasureddynamicstrainchangebytheCFBG-FPIsensor.Reddashline:shaker signalforevaluation. sensor,showinga20Hz,768.6 `Y peak-to-peaksinusoidaldynamicstrain.Reddotlineisthe electronicsignalusedtodrivetheshaker.Theaveragestrainchangingrateis30.7 `Y /mswitha maximumstrainchangeratesabouttwiceoftheaveragestrainchangerateforsinusoidalsignal. TheDFBlasertuningrangeis691pm,correspondingtoatuningrateof1055.0 `Y /ms,whichis su˚cienttotrackthedynamicstrainchange.Highertuningfrequencywithlargertuningvoltage 28 canbeusedforhigherstrainchangerate.ThedistortionoftheCFBG-FPIsensorsignalmainly comesfromthejerkingmovementoftheshakeritself. Figure2.19:Zoom-inofthemeasureddynamicstrainchangebytheCFBG-FPIsensor.Reddash line:shakersignalforevaluation. 2.5Summary ThischapterdiscussedtheanalyticalandnumericalsimulationsonthespectraofCFBGsand CFBG-FPsensors.Weintroducedhegratingspectrumisdescribedbasedonthecoupledmode equations.Thetransformmatrixmethodisappliedtosolvetheseequationstogeneratetheoptical spectrumofgratingwithchirpedstructures.Wealsoaddressedthecon˝gurationofchirpdirection andthee˙ectstothespectra. ThenweproposedanddemonstratedanovelabsolutestrainmeasurementsystemusinganFPI formedbycascadedCFBGswithoppositechirpdirectionsdemodulatedbyawavelength-scanning DFBlaser.Duetothedi˙erentanduniquespectralintervalsofthenotchesinthewavelength bandwidthusedformeasurement,thespectralnotchescanbeunambiguouslyrecognizedineach spectralframewithouttheneedforfringecounting.Usingthisprinciple,wedemonstratedhigh- resolutionandabsolutestaticanddynamicstrainmeasurement.Thestaticstrainexperimentresult showsameasurementrangeof1000 `Y withgoodlinearityusing12spectralnotcheswithin1.6nm e˙ectivebandwidth.Thesystemresolutionwas0.033 `Y withasensitivityof1.31pm/ `Y .A20 29 Hz,768.6 `Y peak-to-peaksinusoidalstrainsignalwastrackedsuccessfully.Thelaserwavelength scanningratewas1055.0 `Y /msandcanbeimprovedbyincreasingthefrequencyand/orthe amplitudeofthescanningsignal.TheaboveresultsshowgreatpotentialofutilizingtheCFBG-FP sensorsforvibrationandultrasounddetectionsystem. 30 CHAPTER3 ACOUSTICEMISSIONSENSORSBASEDONHIGH-FINESSESHORT-CAVITYFPI Partofthematerialinthischapterhasbeenpublishedin ‹ "Fiber-opticacousticemissionsensorbasedonachirpedFBGpairforcrackdetectionin aluminumplate."11thInternationalWorkshoponStructuralHealthMonitoring2017:Real- TimeMaterialStateAwarenessandData-DrivenSafetyAssurance,IWSHM2017.DEStech Publications,2017 ‹ "Ultrasensitiveultrasounddetectionusinganintracavityphase-shifted˝berBragggrating inaself-injection-lockeddiodelaser."OpticsLettersvol.44,no.22,pp.5525,2019 ‹ "E˙ectofLaserPolarizationonFiberBraggGratingFabry-PerotInterferometerforUltra- soundDetection,"IEEEPhotonicsJournal,vol.12,no.4,pp.1,2020 3.1Crackdetectionwith˝ber-opticacousticemissionsensorbasedona chirpedFBGpair Inthissection,a˝ber-opticacousticemission(AE)sensorsystemforthedetectionofAE signalsgeneratedfromcrackswithinanaluminumplateisdescribed.Thesensorheadconsistsof apairoftandemchirped˝berBragggratings(CFBGs)thatformaFabry-Perottypeinterferometer (FPI).ThisCFBG-FPIfeaturesaseriesofresonantwavelengthnotchesinthere˛ectionspectrum, whicharesubjecttothesamewavelengthshiftasthesensorisstretchedorcompressedbyAE signals.Bylockingatunablelasertotheslopeofanyindividualnotch,theAEinducedhigh- frequencywavelengthshiftisconvertedintointensityvariation.Usingthesensorsystem,AE signalsgeneratedbythreedi˙erenttypesofsources,i.e.,PZTactuator,pencilbreak,andcracks withinaluminumplates,aredetectedandcompared.Ourexperimentalresultssuggestthatcracks inthealuminumplatesgavebirthtobroadbandAEwithpeakintensityspanningover100kHzto 350kHz. 31 3.1.1Introduction Acousticemission(AE)signalswiththefrequencyrangingfrom100kHzto1MHzarecommonly regardedas˝ngerprintofdamage-relatedstructuralevolution,suchcrackinitiationandgrowth, corrosion,˝berbreakage,etc.Therefore,nondestructiveAEsensorsareattractiveinthe˝eldof structuralhealthmonitoring.Asoneofthemostpromisingtechniques,optical˝berbasedAE sensorsareextremelycompetitiveintermsofsensitivity,size,weight,multiplexingcapability,and immunitytoelectromagneticinterference[33].Amongthem,˝berBragggrating(FBG)basedAE sensorsareattractiveduetotheireasyoperationandmultiplexingcapability[34,35,35,36,37]. TheAEsignalsimpingedontheFBGintroducestrainwithinthe˝berandthusshiftstheBragg wavelength.AFBG-basedAEsenortypicallyrelyonanarrow-linewidthlaserlockedtotheslope ofawavelengthpeakornotchandthewavelengthshiftisconvertedtointensitymodulation.In practice,thetinyAE-inducedwavelengthshiftisoftensuperimposedonalargebackgroundshift causedbytemperatureand/orstrainvariation.Intuitively,ahighperformancelaserwithwide tuningrangecanbeusedtoaccommodatethelargebackgroundwavelengthshift.However,the costwouldbeunacceptableformostofthepracticalapplications.Thus,alowcostlaser,suchas DFBsemiconductorlaser,ismoredesirableinpractice.Inthissituation,thewavelengthtuning rangewouldbetoolimitedtocoverthelargebackgroundwavelengthshift.Totackletheabove problem,werecentlyproposedanAEsensorsystemusingapairoftandemchirpedFBGs(CFBGs) andsmartfeedbackcontrol[17].TheCFBGpairformsaFabry-Perotinterferometerandthus producesaseriesofresonantnotches,anarrowlinewidthlaserislockedtooneofthewavelength notches.Asthebackgroundshiftsthelockednotchoutofthelasertuningrange,anewnotch movesinandthelaserisunlockedfromthepreviousnotchandrelockedtothenewonebyresort toasmartfeedbackcontrolunit.Thus,thelargebackgroundshiftisaccommodatedbythesensor system. Inthissection,usingtheaboveCFBG-basedAEsensorsystem,weinvestigatethedetectionof AEsignalsgeneratedbypencilbreakandcrackswithinanaluminumplate.Acomparisonbetween thesetwodi˙erencesourceswillbegiven. 32 3.1.2Systemandoperationprinciple ThecondensedsystemdemonstratingtheprincipleofoperationisschematicallyshowninFig.3.1. Outputofthelaserdiode,whichismodulatedbyacurrentandtemperaturecontroller,isinjected intothe˝bersensorheadandthere˛ectedsignalisdirectedtoaphoto-detectorviaacirculator.The convertedelectricalsignalfromthephoto-detectorprovidesfeedbacktoaservocontrollerwhich isresponsiblefortheinputofthelasercurrentdriver.Throughanembeddedlow-pass˝lterof theservocontroller,theAEsignal(ACcomponent)fromthephoto-detectoriseliminatedandthe remainingDCcomponentismodulatedbyaproportional-integralcontroller.Usingthisclose-loop feedbacksystem,theoutputwavelengthofthelaserdiodeislockedaroundthequadraturepointon theslopeofanynotchwithinthere˛ectedspectrumoftheCFBGpair. Figure3.1:Schematicofthecrackdetectionsystem.LD:Laserdiode. Asdepictedabove,thesensorheadiscomposedofapairofthesameCFBGs.ForeachCFBG, there˛ectionspectrumspansacoupleofnanometers.ThetwocascadedCFBGsthusformliterally aFabry-Perotcavity,featuringaseriesofresonantwavelengthnotchesinthere˛ectionspectrum, asexhibitedinFig.3.2.AstheAE-inducedstretchingandcompressionareexertedonthesensor head,allthenotchesareshiftedsimultaneouslyandequally.Therefore,nomatterwhichnotchthe laserislockedto,theAEsignalcanbepickedbythesensor.Figure3.3schematicallyshowsthe detectedAEsignalsbytwoneighboringnotches.TheAE-inducedwavelengthshiftisconverted 33 intointensitychangeduetothe˛uctuationofre˛ectivityatthelaserwavelength.Throughan additionalsmartfeedbackcontrolunitaselaboratedindetailinourpreviouswork[17],asone notchisknockedoutofthelasertuningrangebyalargebackgrounddisturbance,anewnotch jumpsinandtakesoverthroughthesmartcontrol.However,withouttheneedtodemonstratethe jumpingagain,thesmartcontrolisnotincorporatedinthissection. Figure3.2:Re˛ectionspectrumoftheCFBG-FPI. Figure3.3:PrincipleofAEsignaldetection. 34 3.1.3Experimentalsetupandresults Schematicrepresentationofthedetailedexperimentalsetupisshownbytheblockdiagramin Fig.3.4.TheLDwasatunablelaserpurchasedfromNewFocus(Model6328-H),andtheLD controllerwasfromthesamevender(Model6300).Theservocontroller(LB1005,NewFocus) usedaproportional-integral(PI)negativefeedbackcontrolwithacon˝gurablecuto˙frequency. ThephotodetectorwaspurchasedfromThorlabs(ModelDET01CFC).TheAEsignalfromthe˝ber sensorwentthroughabroadbandampli˝er(ModelAE2A,PhysicalAcousticsCo.)setatagain valueof26dBandabandpass˝lter(Model3202R,Krohn-Hite)setattherangeof60-1000kHz. TheAEsignalfromthereferencePZTsensorwasampli˝edby40dBviaapreampli˝er(Model 5676,Olympus).BothPZTactuator(HD50)andsensor( ' 15 U )werepurchasedfromPhysical AcousticsCo.ThetwoCFBGswereincontactandtheirspecswerethesamewithalengthof10 mmandspectrumdepthof15dB,thechirprateofthephasemaskwas4nm/cmandthecenter wavelengthwasaround1545nm. Figure3.4:SchematicdiagramdemonstratingthecrackAEdetectionsystem.LD,laserdiode;PD, photo-detector;Cir.,circulator;PC,polarizationcontroller;Amp.,ampli˝er;BPF,band-pass˝lter; Osc.,oscilloscope;FG,functiongenerator. Asdescribedintheprevioussection,thelaserwavelengthwaslockedtooneofthewavelength notchesofthesensorthroughaclose-loopfeedbackcontrol.Apolarizationcontroller(PC)was incorporatedtoselectoneofthepolarizationstates.Thesensorheadwasattachedtoanaluminum 35 sheet.Inthemeantime,onePZTsensorwasplacedinthevicinityofthe˝bersensorforcomparison. InadditiontotheAEsignalsoriginatingfromcrackswithinthesheetasdescribedbelow,AEsignals inducedbyPZTandpencilbreakwerealsoinvestigated.Thus,anotherPZTactuatorwasalso attached. Figure3.5:Photographofthealuminumsheetonwhichaslotwasinitiallyintroduced(left)and thecrackexpandedaspartofthealuminumsheetwasbentdownward(right). Thealuminumsheetwasclampedontheedgeofanopticaltable.Atinyslotwasinitially engravedonthetopsurfaceandthenthesuspendedpartwaspresseddownwardsothatcrackswere generatedduringthebending,asshownbythephotosinFig.3.5.WhenanyAEsignalturned around,theoscilloscopewastriggeredtocapturethewaveform. Becausethesensitivityisproportionaltotheslopeofthenotch,thebandwidthofthenotch isadirectlyrelatedtothesensitivity.Withthesamedepth,thesmallerthebandwidththehigher thesensitivity.Thus,beforethedetectionofAEsignals,thewavelengthnotchthatwasusedfor sensingwas˝rstcharacterized,theresultsareshowninFig.3.6.Itcanbeseenthatthefullwidth athalfmaximumisaround1.3pm.Thenthe˝bersensorwasusedforthedetectionofAEsignals. Firstly,theAEsignalsweregeneratedbyaPZTactuatoroperatinginburstmode(3-cycleexcitation atafrequencyof200kHz),theresultsareshowninFig.3.7.It'sapparentthatboththePZTand ˝bersensorscaughtthesignalsprettywell.Secondly,AEsignalwasgeneratedbyapencilbreak 36 Figure3.6:SpectrumofthewavelengthnotchusedforAEdetection. andthecapturedsignalsareshowninFig.3.8.Again,boththePZTand˝bersensorsworked verywellinmonitoringtheAEsignals.Withthesystemveri˝edforreliableinterrogation,AE signalspossiblygeneratedfromthecrackswithinthealuminumplateweremonitored.Onesuch AEwaveformsuccessfullycapturedbybothPZTand˝bersensorsisshowninFig.3.9. Inordertoexamineindetailthefrequencyrange,fastFouriertransform(FFT)hasbeenapplied totheAEwaveforms,theresultsareshowninFig.3.10-3.12.TheFFTspectrainFig.3.10,3.11, and3.12correspondtothetemporalresponsesinFig.3.7,3.8,and3.9,respectively.Thepeak around200kHzinFig.3.10coincideswiththeexcitationfrequency.Forthepencilbreakshown inFig.3.11,thepeakintensityresidesaround100kHzandthefrequencyextendstoaround600 kHzwithreducedintensityathigherfrequency.Incontrast,forthecrackinducedAEspectrum, thepeakfrequencycoversamuchbroaderrangeof100kHzto350kHzandtheexistingfrequency extendstoaround800kHz.ThecomparisonsuggeststhatthecrackinducedAEcoveredamuch broaderfrequencyrangethanthepencilbreakdidinourcase. 37 Figure3.7:CapturedAEsignalswhenitwasgeneratedbyPZT. Figure3.8:CapturedAEsignalswhenitwasgeneratedbypencilleadbreaktest. 3.2Ultrasensitiveultrasounddetectionusinganintra-cavityphase-shifted ˝berBragggratinginself-injection-lockeddiodelaser Inthissection,wereportahigh-sensitivity˝ber-opticultrasonicsensorsystemusingaself- injection-lockeddistributedfeedback(DFB)diodelaserwherea c -phase-shifted˝berBragggrating ( c FBG)servesasboththelockingresonatorandthesensingelementina˝berringfeedbackloop. 38 Figure3.9:CapturedAEsignalswhenitwasgeneratedbycrackwithinthealuminumplate. Figure3.10:FFTspectrumoftheAEsignalsgeneratedbyPZT. Bycontrollingthedelaytimeofthefeedbacklightthrougha˝berstretcher,thelaserwavelength islockedtoanexternalcavitymodeonthespectralslopeofthe c FBGandtheultrasound-induced wavelengthshiftsofthe c FBGisconvertedtolaserintensityvariation.Theultrasonicsensing schemesimpli˝esthefeedbackcontrolbecausetheself-injectionlockingautomaticallypullsthe laserwavelengthtothe c FBGresonantwavelength.Inaddition,itimprovesthedetectionsensitivity 39 Figure3.11:FFTspectrumoftheAEsignalsgeneratedbypencilleadbreaktest. Figure3.12:FFTspectrumoftheAEsignalsgeneratedbycrackwithinthealuminumplate. becauseofthefrequencynoiseoftheDFBlaserisdrasticallyreduced.Weshowthatthesensor systemachievesastrainsensitivityof78f Y /Hz 1 š 2 ataround200kHz. 40 3.2.1Introduction Ultrasonicsensorsarewidelyusedinanumberofdiverseapplicationsincludingnon-destructive testing[38],structuralhealthmonitoring[39],rangemeasurement[40],andbiomedicalimaging [41].Highsensitivityisoftenneededforperformanceoptimizationinthesesystems.Comparedto traditionalpiezoelectricsensors,˝ber-opticsensors,particularlythosebasedon˝berBragggratings (FBGs),exhibitmanyadvantagessuchassmallsize,lightweight,immunitytoelectromagnetic interference,corrosionresistance,andmultiplexingcapabilities.Duetotherequireddetection speed,thesesensorstypicallyusealaserasthelightsourcewithedge˝lterdetectionmethodto demodulatetheBraggwavelengthshiftforhighsensitivity.Speci˝cally,thelaserwavelengthis lockedtothelinearregionofthespectrumofanFBGsensor.Theslopeofthespectrumconvertsthe ultrasound-inducedspectralshiftintointensityvariationsthatcanbemeasuredbyaphotodetector (PD)[34,42,6].Thesignalstrengthisproportionaltotheslopeinthelinearregionofthespectrum ofanFBGsensor.FBG-basedopticalresonators,suchas c -phase-shiftedFBGs( c FBGs)[43,44] orchirpedFBGFabry-Perotinterferometers[17],providesnarrowspectralfeaturetoincreasethe responsetotheultrasoundsignalandthesystemscanoftenapproachthesignal-to-ratio(SNR) whoselimitissetbythefrequencynoiseofthelaser.Inthesecases,anarrowlinewidthlaserwith minimumfrequencynoiseisthekeyforhigh-sensitivityultrasonicdetection.Externalcavitydiode lasers(ECDL)basedondispersivecomponentso˙ersuperiorperformancerelativetoconventional distributedfeedback(DFB)ordistributedBraggre˛ector(DBR)diodelasersbecauseofthehigh quality-factorthelasercavityresultingfromthelongcavitylength.AlthoughECDLcano˙er superbperformanceintermsoffrequencynoise,thebulksize,thecomplexityofthecavity,and thestringentrequirementontheopticalalignmenthavelimitedtheirapplicationsin˝ber-optic ultrasounddetection. Laserfrequencycanbestabilizedbylockingthelasertoanopticalresonator.Thiscanbe achievedthroughanelectricallockingtechniquewhereanerrorsignalisgeneratedtocorrectthe deviationofthelaserfrequency[45].Complicatedandhigh-speedfeedbackcontrolsystemis neededinthisapproach.Self-injectionlockingtechnique[46]iswidelyacceptedasapowerful 41 yetsimplemethodforlaserfrequency-noisesuppression.Unlikeelectroniclockingschemes,self- injectionlockingisanallopticaloperationwithsigni˝cantlyreducedsystemcomplexity.Ithas beendemonstratedthatlow-costsemiconductorlasers,suchasDFBdiodelasersandFabry-Perot diodelasers,canachieveremarkablynarrowlinewidthbylockingthelaserstostructureslike externalring˝bercavity[47],˝bergrating[48],whisperinggallerymoderesonator[49],confocal Fabry-Perotcavity[50].However,theimplementationofaself-injectionlockedlaserasthelaser sourceina˝ber-opticultrasonicsensorsystemisnottrivialbecausethelaserwavelengthneeds tobetunableinordertobelockedtothespectralslopeofthesensor.Tuningthewavelengthof aself-injectedlockedlaserrequiresthesynchronizedadjustmentoftheresonatorwavelength,the delaytimeoftheopticalfeedback,andthefree-runninglaserwavelength,whichisachallenging taskduepartiallytothedi˚cultyinknowingthefree-runninglaserwavelengthwhenthelaseris underlockedstate. Inthissection,weproposeanddemonstrateanultrasonicdetectionschemewithhighsensitivity usinga c FBGina˝ber-ringfeedbackloopofaself-injection-lockedDFBsemiconductorlaser.The c FBGservesasbothalockingcomponentintheself-injectionoperationandthesensingelement forultrasonicdetection.Byusingarelativelylongdelayline,thelaserwavelengthandtuningthe feedbackdelaytime(usinga˝berstretcher),thelaserwavelengthislockedtoanexternal-cavity modeontheslopeofthe c FBGtransmissionspectrumandultrasound-inducedwavelengthshift ofthe c FBGisconvertedtolaser-intensityvariations.Weshowthatthesensorsystemachievesa sensitivityof78f Y /Hz 1 š 2 around200kHz.Although c FBGshaveservedasself-injectionlocking componentsforDFBlasers[51],thisisthe˝rstreporttousethefeedbackcomponentasthesensing elementforultrasonicdetection.Comparedwithotherultrasonicsensorsystemsbasedon c FBGs orothertypesofFBGs[17,52],thissystemhasthefollowingtwomajoradvantages: 1. Self-injectionlockinge˙ectivelysuppressesthelaserfrequencynoise,allowinghighsensi- tivityultrasonicdetectionwithlow-costsemiconductorlasers. 2. Itsigni˝cantlysimpli˝esthewavelengthlockingsystem,especiallyminimizescomplex 42 electroniclockingsystem. Self-injectionautomaticallylocksthelaserwavelengthtothe c FBGwhenthefree-runninglaser wavelengthissetclosetothelockingregionbyadjustingthetemperatureandcurrentoftheDFB laser.Withtheassistanceofasimple˝berstretcher,thelaserwavelengthcanbe˝xedattheslope ofthesensorspectrumformaximalresponsivity. 3.2.2Principleofoperation Figure3.13:Schematicoftheultrasonicsensorsystemwiththe c FBGsensorinsidetheself- injectionfeedbackloop. TheproposedultrasonicsensorsystemisschematicallyshowninFig.3.13.Thelaseroutput fromadiodelaserisinjectedbacktothelasercavityafterittravelsthrougha˝berringthatconsists ofacirculator,a c FBG,acoupler,anattenuator,anda˝berstretcher.Thefrontmirrorofthe laserdiodeandthe˝berringformsanexternalcavity,whosetransmissionspectrumexhibitsdense sinusoidalfringes(duetotherelativelylongexternalcavitylengthwithanenvelopedetermined bythetransmissionspectrumofthe c FBG,asschematicallyshowninFig.3.14.Bytuningthe attenuatortoobtainappropriatefeedbackcoe˚cient,thelasercanbelockedtoanexternalcavity modearoundthetransmissionpeakofthe c FBGwithsigni˝cantlyreducedlaserlinewidthand 43 goodlockingstability.Thelockingpointcanbe˝ne-tunedbyadjustingthetimedelayofthe feedbacklight(through,e.g.a˝berstretcherintheexternalcavity)toensurethelockingpointis ontheslopeofthe c FBGspectrum.Ultrasoundthatimpingesontothe c FBGcauseswavelength shiftsofthe c FBGbuthaslittlee˙ectonthewavelengthpositionsoftheexternalcavitymodedue tothelongexternalcavitylength( ! 4GC )relativetothe c FBGlength( ! ˙˝ )andtheultrasonic wavelength( ).Morespeci˝cally,the˝berlengthchange( ! )in c FBGregioncausedbythe ultrasoundwouldresultinaspectralshiftof _ 4GC = _ ! š ! 4GC fortheexternalcavitymodeand aspectralshift _ ˙˝ = _ ! š ! ˙˝ forthe c FBG.Because ! 4GC ¡¡! ˙˝ , _ 4GC _ ˙˝ . Inaddition, ! 4GC ¡¡ ,theultrasoundinducesbothcompressiveandtensilestrainsontheexternal cavity˝berwiththeire˙ectsonthecavitylengthcancelingouteachother.Asaresult,thelaser wavelengthremainsunchangedandtheultrasound-inducedspectralshiftofthe c FBGisconverted tolaserintensityvariationsafterthe c FBG,whichistappedoutofthe˝berringviaacouplerand detectedbyaphotodetector. Figure3.14:Illustrationshowingthelaserlineislockedtoanexternalcavitymodeontheslopeof the c FBGtransmissionspectrum.Schematicoftheultrasonicsensorsystemwiththe c FBGsensor insidetheself-injectionfeedbackloop. 44 3.2.3Experiments Theexperimentalsetupfordemonstrationoftheproposedultrasonicdetectionschemeisschemat- icallyshowninFig.3.15.An8-mm c FBGfabricatedin-houseusinga193nmUVlaseranda phasemask[53]wasbondedalongthecenterlineofanaluminumplatetodetecttheultrasonic wavesgeneratedfromacommercialpiezoelectricactuator(HD50,PhysicalAcoustics)gluedata positionontheplate80mmawayfromthe c FBGsensor.Thelasersourceisabutter˛y-packaged DFBdiodelaseroperatingat ˘ 1545.5nmwithoutaninternalisolator.Theisolatorisastandard componentinsidethecommercialDFBlaser.BecauseoftheDFBlaserissensitivetoopticalback re˛ections.Internalisolatorisusedtosuppressbackre˛ectionstoavoidoutput˛uctuationand increasesignaltonoiseratiooftheDFBlaser.Therefore,stablesinglemodeoperationoftheDFB lasercanbeachieved.Hereinourexperiments,aDFBlaserwascustomizedtoremovetheinternal isolator.Withsuchcon˝guration,backre˛ectionscaneasilyreturntothelasercavitytominimize tothefrequencynoiseofthelaser. Figure3.15:ExperimentalsetupforDFBlaserself-injectionlockingandAEsignalmeasurement. TEC:temperaturecontroller;LDC:laserdiodecontroller. ThewavelengthoftheDFBlaserdiodecanbetunedbyadjustingtheinjectioncurrentwithan experimentallymeasuredtuningcoe˚cientof10.9pm/mAat25 C.ThelightfromtheDFBlaser iscoupledtothe˝berringthroughacirculator,wherethelight˝rsttravelsthrougha33:67coupler, usedtotapoutthelightforanalysis,andapolarizationcontroller(PC)beforereachingthe c FBG sensor.ThePCwasusedtoalignthelaserpolarizationwithoneoftheprincipleaxesofthe c FBG 45 asbirefringencewasintroducedfromthe c FBGfabricationprocess.Thetransmittedlightfrom the c FBGwaspartiallycoupledoutoftheringbya50:50coupleranddetectedbyaphotodetector (PD).Thequasi-dccomponentofthesignalfromthePDwasusedforlockingpointanalysis.The acsignalwasampli˝edand˝lteredbya50 500kHzband-pass˝lterforultrasonicsignalanalysis. Theotherhalfthatremainedintheringwasattenuatedbyavariableopticalattenuator(VOA) beforebeinginjectedbacktotheDFBlaserthroughthecirculator.Foroptimallocking,another PCwasplacedbeforethecirculatortocontrolthepolarizationofthelightthatwasinjectedtothe DFBlaser.A˝berstretcherwasplacedbetweentheVOAandPCtotunetheexternal˝ber-ring cavitylength,andconsequentlythefeedbackdelaytime,throughwhichtherelativepositionofthe lockingwavelengthtothepeakofthe c FBGcanbepreciselycontrolled.Compressingthe˝ber causedashifttowardtheshorterwavelength(blueshift)ofthelockedlaser.Conversely,stretching the˝bercausedashifttowardthelongerwavelength(redshift).Theexternalcavitylengthisabout 10m,correspondingtofreespectralrange(FSR)of10MHz. Apiezoelectricactuatorgluedtoontheplatewasusedtogeneratetheultrasonicpulsesfor testing.Itwasdrivenbya˝ve-cyclesinusoidalburstwavecenteredat200kHzwithapeak-to-peak voltageof5Visgeneratedbyafunctiongenerator.Forcomparison,the c FBGsensorwasalso interrogatedbythesameDFBlaserinfreerunningmode.Inthiscase,theself-injectionloopwas openedatthepositionoftheVOAsonolaserwasinjectedbacktothelaser.Thelaserwavelength wastunedtothespectralslopeofthefreerunningbymanuallyadjustingtheelectricalcurrent injectedtolaserthroughthecurrentcontroller. Figure3.16showsthetransmissionspectrumofthe c FBGwithatransmissionpeakat1545.65 nmmeasuredbyanOSAwithaspectralresolutionof20pm.Thedetailedspectralpro˝leofthe centralpeakwasmeasuredbyascanningwavelength-tunablenarrowlinewidth( 300 kHz)laser alongwithaPD,asshowninFig.3.17,whichrevealsthatthecentralpeakhasafull-widthat half-maximum(FWHM)of2.6pm(323MHz)andaspectralslopeof0.39pm 1 inthelinear region. Whenthelaserislockedinthelinearregionofthe c FBG,theacsignal + B aftertheampli˝er 46 Figure3.16:Transmissionspectrumofthe c FBGmeasuredbyanOSA. Figure3.17:Transmissionspectrumofthe c FBGmeasuredbyawavelength-scanninglaser. canbedeterminedby + ( = _( ) + ˇ˘ ˝ (3.1) where _ istheBraggwavelengthshiftofthe c FBGinducedbytheultrasound, ( ) and ) ˇ˘ are, respectively,theslopeandtransmissionofthenormalizedtransmissionspectrumofthe c FBG(Fig. 3.17)atthelockedwavelength, + ˇ˘ isthedetectedDCsignalvoltagefromthePD,and ˝ isthe gainsettingoftheampli˝er. TheBraggwavelengthshiftisproportionaltotheappliedstrain,whichisexpressedas _ = 0Y . 47 0 isthestrainsensitivityoftheBragggrating,theexpectedvalueis ˘ 1.2pm/ `Y whenBragg wavelengthisaround1550nm[54].Therefore,thedetectedstrainisexpressedas: Y = + ( 0( ) + ˇ˘ ˝ (3.2) 3.2.4Resultsanddiscussion Figure3.18:Noisebehaviorofthefree-runningDFBdiodelaser(redline)andtheself-injection lockedDFBdiodelaser(blueline)tothe c FBGsensor. ThenoisecharacterizationoftheDFBdiodelaserisexamined˝rst.Thetypicalnoiseincludes therelativeintensitynoise(RIN)andthefrequencynoise.Inordertoshowfrequencynoise behavior,theslopeofthesensorisusedtoamplifythefrequency˛uctuationofthelaser.Thenoise behaviorismeasuredbysettingthelaserwavelengthatthemaximumslopeofthesensorpeak whichisalsowithinthelockingrange.AnelectricalspectrumanalyzerisconnectedtothePD. Figure3.18showsthenoiseofthefree-runningDFBdiodelaser(redline)andtheself-injection lockedDFBdiodelaser(blueline).Itiscleartoobservea˛attennoise˛oorafterthelaseris self-injectionlocked.Alsoatlowfrequencies( 20MHz)range, 1 š 5 noiseoftheself-injection lockedDFBdiodelaserdropsquicklythanthefree-runningmode. 48 Figure3.19:TemporalAEresponsesobtainedfromtwodi˙erentlasersettingforthe c FBGsensor. Theresponsesofthesensorsystemwiththelaserinself-injectionlockedmodeandinfree- runningmodetotheultrasoundgeneratedbythepiezotransducerontheplateareshowninFig. 3.19and3.20,respectively.Bothcon˝gurationsshowsimilarwaveformswithsimilarpeak-to-peak values( + ?? = 10.2V),However,theself-injectionlockedsystemshowsmuchsmallernoisesas evidencedbylarge˛uctuationsofthesignalleadingtothe˝rstultrasonicpulsepacketinFig. 3.20forbothcases.Tomoreaccuratelycharacterizethenoiseperformanceofthesystems,we turnedo˙thepiezo-transducerandrecordedthesystemoutputs,asshowninFig.3.19and3.20 forthesetwocon˝gurationswithastandarddeviation( + B3 )of8.6mV,and692.0mVforthenoise, respectively.Itshowsthatthecon˝gurationwiththeself-injectionlockedDFBlaserhasmuch bettersignal-to-noise(SNR),whichisover35dBlargerthanthecon˝gurationwiththefreerunning DFBlaser.AccordingtoEq.(3.2),thespectralslopeatthenormalizedtransmissionof0.76is ˘ 49 0.5pm 1 ,V ˇ˘ is1.05V,the10.2Vpeak-to-peakvoltagecorrespondstoa62n Y peak-to-peak strainappliedtothe c FBGsensor.Withthenoiselevelof8.6mVand450kHzsystembandwidth, thethecon˝gurationwiththeself-injectionlockedlasershowsastrainsensitivityof ˘ 78f Y /Hz 1 š 2 . Itismorethan60timessmallerthanthesensitivity.Forcomparison,thethermodynamiclimit ofthephasenoiseforan8mmlongregularoptical˝berat200kHzis 4 Ł 0 10 10 rad/Hz 1 š 2 , correspondingtoastrainlimitof ˘ 12f Y /Hz 1 š 2 . Figure3.20:ThenoiseoutputlevelwithoutAEsignalobtainedfromtwodi˙erentlasersettingfor the c FBGsensor. Theworkingpointtunabilityoftheself-injectionlockedlasersystemisshowninFig.3.21. TheshadowedregioninFig.3.21isthetuningrangeofthelockingpointwhencontrollingthe˝ber stretcher.Tostudythee˙ectofthelockingpositionsonultrasonicdetection,wetunedthelock pointtothreedi˙erentpositions(A,B,andC)onthe c FBGspectrumandrecordedthetemporal 50 responsesofthesensorsystem.Fig.3.22showstheresponsesforlockingpositionsAandC,where theywereclosetotheboundariesofthelockingrangewithmaximumspectralslopesof c FBG. Theirresponsesarewaveformswithsimilaramplitudes(V ?? ˘ 10V)anda180 phasedi˙erence, whichisexpectedbecausespectralslopesatAandChavesimilarabsolutevaluesbutopposite signs.WorkingpointBwaschosentobeclosetothetransmissionpeakofthe c FBGwithminimal spectralslope.ThetemporalresponsestotheultrasoundisshowninFig.3.22and3.23.Compared tooperationatAandC,theresponsewasmuchsmallerwith + ?? reducedfrom ˘ 10Vto 0.3V. AdoublefrequencycomponentwasobservedinFig.3.23,asexpected. Figure3.21:Thelockingrangoftheself-injectionlockinglaserandthreeworkingpointssetby adjustingthe˝berstretcher. Thetolerancerangetothefree-runninglaserwavelengthofthelockedlaserwasalsostudied. Thefree-runninglaserwavelengthwastunedbyadjustingthecurrentinjectedtothelaserthroughthe lasercontroller.Atthebeginning,thecurrentwasaround125mA.Duringthecurrentadjustment, theVOAwasbypassed.Itisfoundthatthelaserbecameunlockedwhenthecurrentwaslessthan 117mAorlargerthan133mAwithalockingrangeof16mA.Basedonthewavelengthtuning 51 coe˚cient10.9 ?< /mA,a16mAcurrentrangecorrespondstoawavelengthrangeof ˘ 174pm forthefreerunninglaser.Thelasercouldbere-lockedbytuningthelasercurrentintotherange between120mAand128mA.Theseexperimentaldemonstrationscon˝rmthattheself-injection lockingsystemisresistanttothe˛uctuationsofthelaserinjectioncurrent. Figure3.22:UltrasonicresponsesatworkingpointsAandC. Figure3.23:UltrasonicresponsesatworkingpointsB. 52 Itisseenthatcontrollingthephaseoftheinjectedlight(throughthe˝berstretchershown inFig.3.15)iscriticaltooptimizethedetectionsensitivity.Ourexperimentshowsthat,without adjustingthe˝berstretcher,thelaserwavelengthunderlockedconditionwasalwayscenteredwithin thehalfofthelinewidthofthe c FBGcentraltransmissionpeak.,thewavelengthofself-injection lockedlaserdriftedrandomlywithinthelockingrange,whichisattributedtotherandomphase shiftoftheinjectedlightfromambientperturbations.Inadditionmodehoppingbetweendi˙erent externalcavitymodesoccurredfromtimetotimeduringthedriftWiththe˝berstretcher,thelaser wavelengthcouldbecontrolledtobelockedatapositionwithamaximalslope,thoughmode hoppingstillcouldoccurduetothedenseexternalcavitymodes.determinedbytheopticallength ofthefeedbackloop.However,thefrequencyofthesignalcausedbymode-hoppingismuchhigher thanthefrequencyoftheultrasoundbeingdetected(tensofMHz EBŁ hundredsofkHz),thesignal fromthemodehoppingcanbeeasily˝lteredoutwithouta˙ectingthedetectedultrasonicsignal. 3.2.5Conclusions Inconclusion,anultrahighsensitivity˝ber-opticultrasoundsensorsystemwitha c FBGsensor insidetheopticalfeedbackloopofaself-injectionlockedDFBdiodelaserwasproposedand demonstrated.Thisintra-cavity c FBGfunctionsasalockingelementandanultrasonicsensing element.Througha˝berstretchertocontrolthephasedelayoftheinjectedlight,thewavelength ofDFBlasersourcewaslockedtotheslopeofthenarrowtransmissionpeakofthe c FBG.with signi˝cantlyreducedlaserfrequencynoise.Thestraininducedtothe c FBGbyultrasoundcause shiftsofthe c FBGtransmissionspectrumbuthaslittlee˙ectonthewavelengthofthelocked laser.Asaresult,theultrasoundsignalisconvertedtolaserintensityvariationsafterthe c FBG. Theexperimentalresultsshowthatthesensitivityoftheproposedsystembasedontheintra-cavity c FBGinaself-injectionlockedlasersystemAchievedastrainof78f Y /Hz 1 š 2 ataround200kHz, whichismorethan35dBhigherthanthatofthesame c FBGinterrogatedbythesamelaserinfree runningmode.Thesystemisresistancetothe˛uctuationsoffreerunninglaserwavelength. 53 3.3E˙ectofLaserPolarizationonFiberBraggGratingFabry-PerotInter- ferometerforUltrasoundDetection Inthissection,wearefocusingononekeyparameterinFBGsensors:Birefringence.During thefabricationoftheFBGsensors,especiallyusingUVlaserbeamsideexposuretechniquewith aphasemasktoperiodicallymodifytherefractiveindexofthe˝bercore,extrabirefringenceis introducedbytheasymmetricalrefractiveindexdistribution.SincetheBraggwavelengthishighly relatedtothepolarization,birefringencecausespolarizationdependentcenter-wavelengthshift (PDCW).Andthepolarizationdependloss(PDL)alsoincreases. 3.3.1Introduction Ultrasonicsensorsarecommonlyusedforstructuralhealthmonitoring[39],nondestructivetest- ing[38],biomedicalimaging[41],andrangemeasurement[40].Fiber-opticultrasonicsensors, especiallythosebasedon˝berBragggratings(FBG),areextremelycompetitivetotraditional piezoelectricsensorsintermsofsize,weight,immunitytoelectromagneticinterference,andmul- tiplexingcapability[34].UltrasonicimpingingontheFBGsenorinducesstraintothe˝berand shiftsthere˛ectionpeakoftheFBG.Thesensorisusuallydemodulatedbysettingthewavelength ofalasertotheslopeofspectrumofanFBGsensor.Therefore,thewavelengthshiftisconverted tointensityvariationsthatcanbemeasuredbyaphotodetector(PD)[34].Inordertoachievehigh sensitivity,largespectralslopeinthelinearregionofthespectrumofthesensorisrequired[55]. Highre˛ectiveFBG-basedopticalresonators,suchas c -phase-shiftedFBG( c FBG)[55,56],FBG Fabry-Perotinterferometer(FPI)[57],orchirpedFBG-FPI[17,58],canprovidenarrowspectral featureswithwidthontheorderofpicometertoincreasethesensitivity.Apotentialissueinpracti- calapplicationsthathasbeenoverlookedinthepastisthe˝berbirefringenceinducedduringFBG fabrication.Althoughregularsingle-modeoptical˝bershavelittlebirefringence,laserillumination involvedinFBGfabrication,eitherUVlasersorNIRultrafastlasers,caninducebirefringenceto the˝ber[59,60].Duetothe˝berbirefringence,theshapeofthere˛ectionspectrumofthesensor seenbythelaserwillbedependentonthestateofpolarizationofthelaser.Asaresult,thelaser 54 polarizationcangreatlya˙ectthedetectionsensitivityofthesensor.Typically,thelaserpolariza- tionismanuallycontrolledtobelinearandalignedtooneoftheprincipalaxesusingapolarization controller(PC)toachieveoptimizedultrasounddetectionsensitivity[17].Thiscon˝gurationis su˚cientforrelativelyshort˝bersinlaboratoryenvironment,wherethelaserpolarizationcanbe stableoverextendedtime.However,forpracticalapplicationswherethe˝bercouldbelongand undergovariousmechanicalperturbationandambienttemperaturechanges,laserpolarizationmay experiencerandomandlargechanges[61],whichcanleadtoreducedorevenvanishingsensor sensitivity.Tacklingthisproblemisdi˚cultbecauseofthelackofeconomicallypracticalwaysin boththedetectionandtheautomaticcontroloflaserpolarization. InweakrefractiveindexmodulationFBGsensor,asmallamountofthebirefringenceis expectedtobenegligibleinlowsensitiveapplications.Ontheotherhand,high˝nessefeature istypicalrequiredforhighsensitive˝beropticultrasoundsensor,thatmeansstrongrefractive indexmodulationisrequired,multipleFBGsinseriesarenecessary,whichfurtherintensifythe birefringencewiththeconventionalone-sideUVlaserbeamexposurefabricationmethod.Inorder tousethesetypesofsensors,polarizationmanagementisrequiredintheultrasounddetection system.Typically,atleastonepolarizationcontroller(PC)isplacedbeforethesensortoalignthe polarizationofthelightsourcetooneoftheprincipalaxesofthesensortoreachthemaximum responsetotheultrasoundsignal.Forlong-termoperation,thelaserdriftandalsoambient environmentsuchastemperature,strain,bendingcouldcausemisalignmentbetweenthelaser polarizationandtheprincipalaxisofthesensor.Therefore,theresponsetotheultrasoundsignal willbedegraded.Frequentpolarizationalignmentisrequiresforlong-termstabilityandlimitsthe practicalimplementationofthesensors. Inordertodecreasethepolarizationdependencytothelaser,thebirefringenceofthesensorcan bereducedbythe90-degreerotationmethodduringthefabricationofthesensor.Hanawa etal. proposedthebirefringencereductiontechniqueforcascadedFBGs[62]andtheexperimentalresults ofthepolarizationdependencyisreportedin[63].ThesensorconsistsapairofFBGscascaded toformanFPIstructure.BothFBGshaveverysimilarre˛ectivity,thereforetherefractiveindex 55 distributionintroducedbyeachFBGisthesame.Inordertoreducethebirefringence,the˝ber isrotated90degreesbeforethefabricationofthesecondFBG.Asexpected,theoverallindex distributionsfortwoorthogonalpolarizationstatesarethesamefortheFBG-FPI.Thus,thesensor isinsensitivetothepolarizationstateofthelaser.Thistechniquedidnotdrawmuchofattention whiletheapplicationscenariowaslimited.Whileinhigh˝nesseresonancespectralfeaturesfor ultrasonicdetection,thebirefringencereductioniscritical. Inthissection,wedevelopedatheoreticalmodeltoanalyzethee˙ectoflaserpolarizationonthe sensitivityofhigh-˝nesseFBG-PFIultrasonicsensorswithrefringence.Theresultshighlightthe importanceofminimizingthebirefringenceofsuchsensorsforpracticalapplicationsinultrasonic detection.Experimentally,wefabricatedanFBG-FPIsensorformedbytwocascadedhigh- re˛ectivityFBGsthathasreducedoverallbirefringence.Byintroducinga90 rotationtothe˝ber betweenthefabricationofthetwoindividualFBGs,thebirefringenceintroducedduringtheFBG fabricationcancelouteachother.There˛ectionspectralnotchofthefabricatedFBG-FPIhas anarrowwidthof2.0pmandtheoverallbirefringenceofthesensorisreducedtoanegligible level.Thispolarization-insensitiveFBG-FPIsensorischaracterizedandtestedforultrasonic detection.Forcomparison,aregularFBG-FPIwithoutbirefringencecontrolwasalsofabricated andtested.TheexperimentalresultsshowthattheregularFBG-FPIexhibitedlargevariationsin thesensorresponseasthelaserpolarizationwasvaried,whilethepolarization-insensitiveFBG-FPI showslittledegradationinthesensitivitywithpolarization.Asaresult,nocontrolonthelaser polarizationisneededduringtheoperationofthepolarization-insensitiveFBG-FPIforultrasonic detection,whichisasigni˝cantsteptowardsthepracticalapplicationsofsuchsensors. 3.3.2TheoreticalAnalysis Wedevelopedatheoreticalmodeltoanalyzethee˙ectoflaserpolarizationand˝berrefringence onthedetectionsensitivityoftheultrasonicsensor.Weassumethatthe˝ber-opticultrasonic sensorismadefromahigh-˝nesseFPI,suchasanFBG-FPIformedbytwohighlyre˛ectiveFBGs. Thetransmissionspectrumofahigh-˝nesseFPIcanbeapproximatedbyaLorentzianfunction 56 Figure3.24:Schematicsof(a)anFBG-FPIwithxandybeingthetwoprincipalaxesofthe sensorandtheredarrowindicatingthepolarizationoftheprobelaser,and(b)there˛ectionspectra measuredbylightpolarizedalongitstwoprincipalaxesaswellasalonganarbitrarydirectionfor thecasesof E¡ 0 and E 0 . (narrow-peakapproximation)[64].AsshowninFig.3.24(a)let G and H bethetwoprincipal axesofthebirefringentFBG-FPI;thenthenormalizedre˛ectionspectraoftheFPIprobedbylight polarizedalong G and H axes, ' GŒH ,andtheircorrespondingspectralslope, ( GŒH ,can,respectively, beexpressedas ' GŒH ¹ E " º = 1 ¹ E š 2 º 2 ¹ E E GŒH º 2 ¸¹ E š 2 º 2 Œ (3.3) and ( GŒH ¹ E º = m' GŒH mE = 2 ¹ E E GŒH º¹ E š 2 º 2 »¹ E E GŒH º 2 ¸¹ E š 2 º 2 ¼ 2 Œ (3.4) where E denotesopticalfrequency, E G and E H arethecenterfrequenciesofthecorresponding spectralnotches,and E isthefull-width-at-half-maximum(FWHM)ofthenotches.Wefurther assumethatthelaserlineforsensordemodulationissetatthemaximumslopeofthespectrum foroneofthepolarizations.Thisassumptionisconsistentwiththecommonpracticeinwhichthe laserpolarizationisadjustedusingaPCtobealignedwithoneoftheprincipalaxesandthelaser wavelengthissettoapointonthespectralnotchwithmaximumslopeforoptimizeddetection sensitivity.Withoutlossofgenerality,weassumethelaserlineissetontherisingedgewith positiveslopeofthere˛ectionspectrumcorrespondingtothe G polarization( ' G ).Thefrequency atwhich ' G hasthemaximumslope, E " ,canbefoundbysolving m 2 ' G š mE 2 = 0 andtheresultis 57 E " E # = p 3 6 E ˇ 0 Ł 29 EŁ (3.5) Substituting E inEq.3.4with E " ,weobtainthemaximumslopeas ( GŒH ¹ E " º = 3 p 3 6 E ˇ 1 Ł 30 E Ł (3.6) Asdiscussedabove,laserpolarizationcanvaryasitpropagatesalongthe˝berduetoenviron- mentalperturbations.Theoverallre˛ectionspectrumofthesensorisasuperpositionofthespectra measuredbythe G and H componentsofthelightanditsexactshapeisdependentontheexact stateofpolarizationofthelightarrivingatthesensor.Forsimplicity,weconsiderthecasewhere thepolarizationofthelaserarrivingatthesensorissimplyrotatedbyanangleof \ fromitsoriginal linearpolarizationalong G axis,asshowninFig.3.24(a).Theoverallre˛ectionspectrumandthe correspondingspectralslopeseenbythelaserisgiven,respectively,by ' ¹ E º = ' G ¹ E º cos 2 \ ¸ ' H ¹ E º sin 2 \ (3.7) and ( ¹ E º = ( G ¹ E º cos 2 \ ¸ ( H ¹ E º sin 2 \Ł (3.8) Thespectralslopeforthepolarization-rotatedlaseratthepreviouslysetfrequencyisevaluated byplugging E = E " intoEq.3.8,and,aftersomealgebra,weobtainthenormalizedspectrumslope, de˝nedby B = , ( ¹ E " ºš ( G ¹ E " º ,as B = = 1 sin 2 \ ( 1 16 ¹ 1 2 p 3 E š E º »¹ 1 2 p 3 E š E º 2 ¸ 3 ¼ 2 ) Œ (3.9) where E = E H E G isthespectralseparationoftheFPIfringescausedbythebirefringence oftheFPI.Notethat E cantakebothpositiveandnegativevalues,dependingonwhetherx- axisistheslowaxisorthefastaxisofthesensor,asillustratedinFig.3.24(b).Alsonotethat 1 B = 1 ,whereanegative B = meansthatthespectralslopebecomesnegativeunderthat 58 particularpolarizationangle.Eq.3.9isthemainresultofthetheoreticalmodelthatcanbeused toanalyzehowthepolarizationangle( \ )andthespectralseparationoffringescorrespondingto thetwopolarizationsrelativetothespectralwidth( E š E )a˙ectthedetectionsensitivityofthe sensor. Figure3.25:Minimumnormalizedsensitivityobtainedbyvaryinglaserpolarizationanglevs. normalizedsensorbirefringence. Inpracticalapplications,bothpositiveandnegativeslopescanbeusedforsensordemodulation andthelightpolarizationintheoptical˝bermayexperiencelargechangesoveranextended time.Therefore,itismeaningfultovarythepolarizationangle( \ )and˝ndtheminimumofthe absolutevalueof B = ¹j B = jº ,whichisusedforcharacterizingtheoverallsensitivityofthesensorto laserpolarizationatdi˙erentbirefringencevalues( E š E ).TheresultisshowninFig.3.25. When E š E 0 ,whichmeansthat E H E G ,theminimumsensitivitygraduallydecreases andeventuallyvanishesasthesensorbirefringence( j E j )increases.Inthiscase,theminimum sensitivityoccurswhenthepolarizationisrotatedby90 fromthe G axistothe H axis.When E š E ˇ 0 Ł 41 ,theminimumsensitivityisreducedto0.5,representinga6-dBreductionin sensorsensitivity.When E š E¡ 0 ,theminimumsensitivitydecreasesmorerapidlyasthesensor 59 birefringenceincreases.The6-dBsensitivityreductionoccursat E š E ˇ 0 Ł 20 ,approximately halfofthebirefringencerequiredforthesamereductionforthecasewhere E š E 0 .To maintainthesensitivityabovehalfofitsmaximum,thespectralnotchseparationcausedbysensor birefringence( E )shouldbelessthan ˘ 61% ofthespectralwidthofthenotch.Theminimum sensitivityreducesto0when E š E ˇ 0 Ł 29 .Inthiscase,thenotchvalleyforthe H polarization coincideswiththelaserwavelength( E H = E " ),wherethespectralslopevanishesforthisspeci˝c polarization.Theminimumsensitivityremainstobe0asthesensorbirefringencecontinuesto increasebeyond E š E ˇ 0 Ł 29 .Fig.3.26showsthesensitivityvs.polarizationangleforseveral valuesof E š E .Itisworthnotingthatfor E š E 0 Ł 29 ,theminimumsensitivityisnon-zero andalwaysoccursat \ = 90 orthelaserpolarizationisrotatedtothe H axis.For E š E¡ 0 Ł 29 , thesensitivityisreducedto0atananglethatdependsonthesensorbirefringenceandislessthan 90 .Forexample,thesensitivitydecreasesto0atangle \ = 46 for E š E = 0 Ł 5 ;whileit decreasesto0at \ = 55 Ł 3 for E š E = 1 .Thenthesensitivitychangestonegativevaluesasthe polarizationanglecontinuestoincrease. Figure3.26:Normalizedsensitivityvs.polarizationangelforseveralsensorbirefringencelevels. Inordertoresponsetoalargefrequencybandoftheultrasonicsignal,thetotallengthofthe 60 sensorshouldkeepasshortaspossible.Ingeneral,thelengthofthesensorshouldbelessthan halfoftheultrasonicwavelength.Ifthesensorlengthislongerthantheultrasonicwavelength,the tensilestrainandcompressivestraincausedbytheultrasonicsignalwouldpartiallyaverageout eachother.Therefore,inourdesign,twoFBGsshouldbeshortaswellasthedistancebetween them. ThedepthoftheFBGisdesignedas16dB,correspondingtoare˛ectivityof97.5%.Thefull widthathalf-maximum(FWHM)oftheFBGisabout0.35nm.Toensureatleastoneinterference peaklocateswithintheFBGspectrum,theFSRshouldbesmallerthanhalfoftheFWHM.The FSRisgivenby: _ = _ 2 2 = 6 ! 2 Œ (3.10) where _ istheBraggwavelengthoftheFBG, = 6 isthegrouprefractiveindexofthe !% 01 modeof the˝ber.Forconventionalsinglemodeoptical˝ber,grouprefractiveindex = 6 ˇ = 455 ,where = 455 isthee˙ectiverefractiveindex.The = 455 forour˝berisabout1.446. ! 2 isthee˙ectivelength, whichisasumofthee˙ectivelengthsofboththeFBGsformingthecavityandtheedge-to-edge distancebetweenbetweenthetwoFBGs: ! 2 = ! B ¸ ! 455 1 ¸ ! 455 2 .FromEq.(3.10),forapair of5-mmFBGwithanFSRsmallerthan0.17nm,thee˙ectivelengthofthegrating ! 2 shouldbe largerthan4.89mm. Thegratinge˙ectivelength ! 455 attheBraggwavelengthisgivenby: ! 455 = ! p ' 2arctanh ¹ p ' º Œ (3.11) where ' isthegratingpeakre˛ectivity.AsshowninFig.3.27,withalowre˛ectivityvalue,the e˙ectivelengthofthegrating ! 455 isaroundhalfofthegratingphysicallength ! ;whileathigh re˛ectivityvaluethee˙ectivelengthisclosetozero.Itcanbephysicallycomprehendedbythe factthatforaweakFBG,there˛ectedlightalongthegratingishomogeneouslydistributed,while ahighre˛ectiveFBGre˛ectsmostofthelightfromitsinitialpart. 61 Figure3.27:Relativee˙ectivelengthofaFBGversusitsre˛ectivity ' . 3.3.3StructureandFabricationofPolarization-InsensitiveFBG-FPISensor Inourdesign,therelativee˙ectivelength ! 455 š ! isabout0.195forasingle5-mmFBGwith 97.5%re˛ectivity.ForapairofFBGswiththesame97.5%re˛ectivity, ! 455 1 = ! 455 2 = 0 Ł 975 mm.Therefore,theedge-to-edgedistance ! B shouldbelargerthan2.94mm. Figure3.28:Fabricationofpolarization-insensitiveFBG-FPIsensoranditstransmissionspectrum. WefabricatedanFBG-FPIsensoron125- ` msinglemode˝berthatisinsensitivetolaser polarizationusingaphasemaskandaUVlaser.Thefabricationprocedureisschematicallyshown 62 inFig.3.28.The˝berwasclampedbetweenapairof˝berrotators(Thorlabs,HFR007)through whichthe˝bercouldberotatedwithaprecisecontroloftherotationangle.First,oneofFBGs thatformtheFPIwasfabricatedandacertainamountof˝berbirefringencewasinducedtothe ˝ber.Assumetheindexmodi˝cationsalongthe G and H directionsare,respectively, = G = = 1 and = H = = 2 ,where = 1 < = 2 duetotheinduced˝berbirefringence.Thenthe˝berwas manuallyrotatedby90 towritetheotherFBG.Assumingthewritingconditionswerethesame asforthepreviousFBG,thesameamountofbirefringencewasinduced.However,duetothe 90 ˝berrotation,theindexmodi˝cationsalongthe G and H directionsforthisFBGbecome, respectively, = G = = 2 and = H = = 1 .Notethatthewavelengthpositionofthespectralnotches ofanFPIisdeterminedbytheopticallengthoftheFPI.Inthiscase,theopticallengthsfor G and H polarizationdirectionsarethesame,bothbeing ¹ 2 = 0 ¸ = 1 ¸ = 2 º ! ¸ = 0 ! 0 ,where = 0 is theunmodi˝ede˙ectiverefractiveindexofthe˝ber, ! isthegratinglength,identicalforboth FBGs,and ! 0 istheseparationofthetwoFBGs.Asaresult,thespectralnotchesfor G and H polarizationdirectionsoverlapandthesensorisinsensitivetolaserpolarizationvariations.It isnotedthatasimilarstructureintendedforapplicationin˝ber-opticcommunicationsystemshas beenreported[62,63].However,itsapplicationaspolarization-insensitiveultrasonicsensorshas notbeendemonstrated.Duringthefabricationprocess,transmissionspectrumwasmonitoredby anopticalspectrumanalyzer(OSA)withawhite-lightsourcetodeterminethere˛ectivityofthe FBG.Re˛ectivityofeachFBGwasmorethan97.5 % .Thepitchofthephasemaskwas1071.5nm, resultingaBraggwavelengthataround1550nm.ThelengthofeachoftheFBGswasL=5mm withagapof ! 0 = 3 << betweenthem,resultinginatotallengthof13mmfortheFBG-FPI.The transmissionspectrumoftheFBG-FPIisshowninFig.3.29(a). DuetothelimitedresolutionoftheOSA(20pm),theinterferencepeakswithintheFPB- FPIspectrumweremeasuredbyawavelength-scanninglaseralongwithaphotodetector(PD)as schematicallyshowninFig.3.30.Notethatthesamesetupwasalsousedfortestingofthesensor forultrasounddetection,asdescribedlater.Witha3-paddlemanual˝berPC,thelaserpolarization couldbetunedrandomly,whichalsoallowedustostudythesensitivityoftheFBG-FPItolaser 63 Figure3.29:(a)measuredbyanOSAandthere˛ectionspectrum(b)measuredbyawavelength- scanninglaser.(c)and(d)arethere˛ectionspectraofaregularFBG-FPIfabricatedwithout˝ber rotationmeasuredbythewavelength-scanninglaserattwodi˙erentpolarizationstates. polarization.Thedetailedre˛ectivespectralpro˝leofthere˛ectionnotchusedforultrasound detectionisshowninFig.3.29(b),whichrevealsthatthenotchhasaFWHMof E = 2 Ł 0 ?< .Then thepolarizationofthelaserwaschangedbyrotatingthethreepaddlesofthePCandthere˛ection spectrumwasmonitored.Novisiblechangeintheshapeofthenotchorthesplittingofnotchwas observed,indicatinganegligibleoverallbirefringenceoftheFBG-FPIsensorwithrespecttothe spectralwidth( E š E ˇ 0 ). Forcomparison,aregularFBG-PFIsensorwasfabricatedwithout˝berrotatingandcharacter- izedwiththesameexperimentalsetupandprocessasdescribedabove.TheUVilluminationduring theFBGfabricationinducedsigni˝cantbirefringencetothe˝berandthere˛ectionspectrumofthe FBG-FPIshowsalargedependenceonthepolarizationstateoftheprobinglaser.Figure3.29(c) isthere˛ectionspectrumrecordedwhenasinglenarrownotchwasobtainedbytuningthelaser polarization.Inthiscase,itisexpectedthatthelaserpolarizationwasalignedwithoneoftheprin- 64 cipalaxesoftheregularFBG-FPI.ThenotchhasaFWHMof E = 3 Ł 1 ?< .Thisincreasedspectral widthcomparedwiththepolarization-insensitiveFBG-FPIisbelievedtoarisefromthedi˙erences inthealignmentoffocusedUVbeamandthe˝bercorethatresultedinaslightdi˙erenceinthe gratingstrength.Figure3.29(d)isanothercasewherethespectrumsplitintotwovalleyswiththe samedepth.Inthiscase,thelaserwaspolarizedinsuchwaythatthelaserpowerwasequally distributedbetweenthetwoprincipalaxesoftheFBG-FPIandthespectrumwasasuperimposition ofthetwospectraprobedbythelasercomponentsatthetwoprincipalpolarizationdirections.The twovalleyswereseparatedby2.7pm.Notethatthisseparationofthetwovalleyscannotbesimply treatedastheseparationofthenotchescorrespondingtothetwoindividualpolarizations( E ). UsingthemodelforthespectrumdescribedbyEq.3.3,the2.7pmvalleyseparationcorrespond toarelativebirefringenceof j E š E jˇ 0 Ł 97 with E = 3 Ł 0 ?< .AsshowninFig.3.25,such levelofbirefringencewouldmaketheFBG-FPIhighlysensitivetolaserpolarizationwithrelative sensitivitythatcanbereducedto0forthecaseof E š E¡ 0 andtotheminimumvalueof0.15 forthecaseof E š E 0 atcertainpolarizationangles. 3.3.4SensorTestingforUltrasonicDetection Figure3.30:Experimentalsetupforsensorpolarizationdependencymeasurementandultrasound detection.PC:polarizationcontroller,PD:photodetector. Theexperimentalsetupusedforstudyingthedependenceonlaserpolarizationofthesensorfor 65 ultrasounddetectionisshowninFig.3.30.Thelightfromawavelength-tunablenarrowlinewidth diodelaserwasdirectedtotheFBG-FPIsensorthroughacirculator.Afterthecirculator,thelight ˝rstpassedthrougha3-paddlePCbeforereachingthesensor.ThePCallowedustomanually changethelaserpolarization.Theendofthe˝berwiththesensorwascoveredwithindexmatching geltoeliminatethelightre˛ectionfromthe˝berend.Thelightre˛ectedfromthesensor,after passingthroughthePC,wasroutedtoaPDthroughthesamecirculator.ThesignalfromthePD wasthenampli˝edand˝lteredbya50-500kHzbandpass˝lterforultrasonicsignalanalysis.A piezoelectricactuatorgluedtotheplatewasusedtogenerateultrasonicpulsesfortesting.Itwas drivenbyafour-cycle5Vpeak-to-peaksinusoidalburstwavecenteredat200kHzgeneratedbya functiongenerator.Thesensor˝berwasbondedwithScotchtapetoanaluminumplateataposition closetobutawayfromthesensorposition.Throughthisremote-bondingcon˝guration[65,66], theultrasonicwavetravelingontheplatewas˝rstcoupledtothe˝berinthebondingregion,then traveledalongthe˝bertothesensorfordetection.Thisso-calledcon˝guration cane˙ectivelypreventthepotentiallylargequasi-staticstrainoftheplatefrombeingappliedtothe sensor.ThecentertothecenterseparationbetweenthebondingregionandtheFBG-FPIwas2cm. Thedistancebetweenthepiezoelectricactuatorandthebondingcenterwas18cm.Otherthanthe bondingarea,otherpartsofthe˝berwereisolatedfromthealuminumboardtoavoidundesirable ultrasoundcoupling. First,thepolarization-insensitiveFBG-FPIsensorwastested.Todeterminetheoperatingpoint, there˛ectionspectrumwasmonitoredbyscanningthelaserwavelengthasthelaserpolarization waschangedbyrandomlyrotatingthethreepaddlesofthePC.Asdescribedabove,theshapeofthe spectralnotchdidnotshowobservablechanges.Thenthelaserwaschangedtosingle-frequency operationandultrasonicpulsesweregeneratedbythepiezotransducer.Thelaserwavelength wastunedtoapositionthatyieldedmaximumresponsetotheultrasonicpulsesobservedonthe oscilloscope.Oncethelaseroperatingpointwasset,thesensitivitytolaserpolarizationwastested bymonitoringthesensorresponsetotheultrasonicpulsesasthelaserpolarizationwasagain changedrandomlyusingthePC.Avideodisplayingthesensorresponseasthelaserpolarization 66 wasrandomlychanged.Itisseenthatthesensorresponseshowedonlyslightchanges.Theblack andredcurvesinFig.3.31are,respectively,theresponseswithmaximumandminimumresponses asthepolarizationwaschanged.Bothofthemhavesimilarpeak-to-peakamplitudeof ˘ 2 Ł 2 + . Theslightdi˙erencebetweenthemisattributedtothechangesintheattenuationofthePCasthe paddlesofthePCwererotated. Figure3.31:Ultrasonicresponsesofthepolarization-insensitiveFBG-FPIsensor. Next,theregularFBG-FPIsensorwiththetwoFBGsfabricatedwithoutrotatingthe˝berwas tested.Again,there˛ectionspectrumofthesensorwasmonitoredaslaserpolarizationwaschanged untilthespectralnotchreacheditsnarrowestwidth,whichindicatesthatthelaserpolarizationwas alignedwithoneoftheprincipalaxesofthesensor.Then,followingthesimilarprocessused forpolarization-insensitivesensor,thelaserwavelengthwastunedtothepointwithmaximum response,asshownbytheblackcurveinFig.3.32withapeak-to-peakoutputof ˘ 1 Ł 2 + .Note that,comparedwiththepolarization-insensitiveFBG-FPI,thereductionofthemaximumresponse oftheregularFBG-FPI(1.2Vvs.2.2V)isconsistentwithitssmallermaximumspectralslope duetoitswiderspectralnotch(3.1pmvs.2.0pm).Thesensorresponsetotheultrasonicpulses wasmonitoredasthelaserpolarizationwasrandomlychanged.Clearly,thesensorresponseshows 67 largevariationswithpolarization.Itisalsoseenthataroundcertainpolarizationstates,thesensor responsevanishedcompletelyandthenincreasedbutwitha180 phasechange.Theredcurvein Fig.3.32istheresponseofthesensorwhenthelaserwastunedtoanarbitrarypolarizationstate. Thepeak-to-peakvoltagewas0.05V,a30dBreductionfromitsmaximumresponse. Figure3.32:Ultrasonicresponsesoftheconventionalone-sideexposedFBG-FPIsensor. 3.3.5Conclusions Inconclusion,wehavedevelopedamodeltoanalyzethee˙ectoflaserpolarizationonthe sensitivityofhigh-˝nesseFBG-FPIsensorsforultrasonicdetection.Theanalysisshowsthat,to maintainthesensitivityabovehalfofitsmaximum,thespectralnotchseparationcausedbythe sensorbirefringenceshouldbelessthan ˘ 61% ofthefull-width-at-half-maximumofthenotch oftheFBG-FPI,highlightingtheimportanceincontrollingthebirefringenceofthesensorin practicalapplications.WehavefabricatedanFBG-FPIwithreducedoverallbirefringencebya 90 rotationofthe˝berbetweenthefabricationofthetwoFBGs.Duetothis90 rotation,the birefringenceinducedduringthefabricationofthetwoFBGscancelsouteachother.Thefabricated FBG-FPIshowsanarrownotchwidthof2.0pmandnegligiblebirefringence.Forcomparison,a 68 regularFBG-FPIwasalsofabricatedwithout˝berrotation,whichexhibitsanotchwidthof3.1 pmthatsplitintotwopeakswitha2.7pmseparationatcertainpolarizationstatesoftheprobe laser.Bothsensorsweretestedforultrasonicdetection.Theexperimentalresultsshowthatthe regularFBG-FPIexhibitedlargevariationsinthesensorresponseasthelaserpolarizationwas varied,whilethepolarization-insensitiveFBG-FPIshowslittledegradationinthesensitivitywith polarization.Asaresult,nocontrolonthelaserpolarizationisneededduringtheoperationofthe polarization-insensitiveFBG-FPI,representingasigni˝cantsteptowardsthepracticalapplications ofsuchsensors. 3.4Summary ThischapterpresentsthestudyofvariousultrasonicwavedetectionsystembasedonFBG- basedresonators.Weinvestigatedahigh-sensitivity˝ber-opticultrasonicsensorsystemusinga self-injection-lockeddistributedfeedback(DFB)diodelaserwherea c -phase-shifted˝berBragg grating( c FBG)servesasboththelockingresonatorandthesensingelementina˝berring feedbackloop.FBG-FPIshaveshowngreatpromiseassensitiveultrasonicsensors.However,the fabricationprocessofthesensorsusuallyintroducesbirefringencetothe˝ber,whichmakesthe sensoroperationsensitivetothepolarizationoftheprobelaser.Here,wetheoreticallystudythe e˙ectoflaserpolarizationonthesensitivityofthesensorwithbirefringence.Thenwestudied thepolarizationinsensitiveFBG-FPsensorwith90 rotationfabricationmethodtorealizestable ultrasonicresponsetoarbitrarypolarizationstateofthelasersource.Asaresult,thebirefringence introducedduringthefabricationofthetwoFBGscancelsouteachother.Nocontrolonthelaser polarizationisneededduringtheoperationofthepolarization-insensitiveFBG-FPIforultrasonic detection,animportantattributerequiredinmanypracticalapplicationsofthesensor.Atlast, anAEdetectionsystembasedonaCFBGpairhasbeendescribed.Byintroducingcrackson thealuminumplate,realAEsignalsareexamined,whicharealsocomparedwiththosefrom pencilbreaktests.Ourexperimentalresultssuggestthatthecrack-inducedAEspansoverabroad ultrasonicfrequencyrange,withapeakintensityrangingfrom100kHzto350kHz. 69 CHAPTER4 ACOUSTICEMISSIONSENSORSBASEDONLOW-FINESSEFIBER-COILFPI Partofthematerialinthischapterhasbeenpublishedin ‹ assivequadraturedemodulationofbirefringentlow-˝nesse˝ber-opticFabrerotinter- ferometricsensors,"OpticsLetters,vol.45,no.13,pp.3419,2020 ‹ "Polarization-insensitive,omnidirectional˝ber-opticultrasonicsensorwithquadraturede- modulation,"OpticsLetters,vol.45,no.15,pp.4164,2020 4.1Passivequadraturedemodulationofcoiledpolarizationmaintaining ˝berFabry-Perotinterferometerforultrasonicsensing Inthissection,weproposeanddemonstratea˝ber-opticultrasonicsensorusingcoiledpolar- izationmaintaining(PM)˝berwithlow-˝nesseFabry-Perotinterferometerformedbytwochirped ˝berBragggratings(CFBG).Bycontrollingthebendingradius,thebendinglength,andthetwistof thecoilstructure,extrabirefringenceisintroducedbetweenthegratingsandresultingatotalphase delaycloseto90 betweenthefastandslowpolarizationsofthePM˝ber.Thenthelasersignal passthroughapolarizationbeamsplitterandmeasuredbytwophotodetectors.Combiningthecoil structure,widespectralrange,andquadraturedemodulation,astrainandtemperatureinsensitive ˝ber-opticultrasonicdetectionisrealized.Theultrasonicsensingschemeisimmunetothelaser wavelengthdrift,thereforenowavelengthlockingmechanismisneeded. 4.1.1Introduction Ultrasounddetectionusing˝beropticresonatorshasbeenwidelyinvestigatedasasubstitute topiezoelectrictransducers.Asmentionedbefore,comparetopiezoelectrictransducer,˝ber- opticsensoriscommonlyimmunetoelectromagneticinterference,lightweight,andresistanceto corrosion.Inordertoachievehighresponsetothedisturbancetothe˝berBragggratingtypeof 70 sensor,edge˝lterdetectionmethodisusuallyusedtodemodulatetheultrasonicsignal.Speci˝cally, probinglaserwavelengthislockingtotheslopeofthespectrumofthesensor.Forultrasonicsignal detectionapplication,thedynamicstraincausedspectrumshifttranslatestolaserintensitychange. Theatrically,thevariationsofthedetectedlaserintensityareproportionaltothemagnitudeofthe ultrasonicsignal.Thesensitivityisproportionaltotheslopeofthespectrumoftheresonator.To maximizesensitivity,highQ-factorsarerequiredfor˝beropticresonators.Contradictory,high Q-factorleadtosmalllinearrangewhichlimitsthedetectablesignalstrengthandvulnerableto externaldisturbances.Inpractice,laserwavelengthshouldbelockedtothesensitiveregionofthe resonatorspectrum. Fiber-opticFabry-Perot(FP)interferometricsensors[67]possessseveralfavorablecharacter- isticsincludinghighsensitivity,simplestructure,easyfabrication,andcapabilitytowithstand harshenvironment.Theyarebecomingattractiveoptionsformeasurementofavarietyofphysical parameterssuchaspressure,temperature,strain,andacousticandultrasonicwaves.Sensorde- modulationhasbeenalong-recognizedchallengeinthepracticalapplicationsofthesesensorsfor measuringsmallandhighlydynamicsignalssuchasacousticandultrasonicwaves.Laser-based demodulationwherethewavelengthofthelaserissetonthespectralslopeofthesensorsfringes toconvertthemeasurand-inducedphasechangesintolaserintensityvariationsistypicallyusedto achievetherequireddetectionsensitivityandspeed.However,theoperatingpointcanchangefrom theoptimalpositionsduetothelaserwavelengthdriftand/orspectralshiftofthesensorfromenvi- ronmentalperturbations,leadingtosignalfadingatthefringevalleysorpeakswherethesensitivity vanishes.Astraightforwardsolutionistolockthelaserwavelengthtothelinearrangeofthesensor spectrum[68,17].However,thestringentrequirementonthetuningrangeandtuningspeedof thelaserandthecomplexelectronicsystemforlockingmakesitimpracticalinmanyapplications. Forlow-˝nesseFPsensorswhosespectrumfeaturessinusoidalfringes,quadraturedemodulation providesanelegantsolutiontotheissueofsignalfading.Theessenceofquadraturedemodulation istogenerateapairofsignalsorfringeswhosephasesarequadratureshifted.Environmental perturbationsshiftthebothfringessimultaneouslybythesameamountsothatthequadraturephase 71 shiftismaintained,andsensitivedetectionispossibleforatleastoneofthemregardlesstherelative positionofthelaserwavelengthonthespectralfringesofthesensor.Inparticular,phase-generated carrierdemodulation[69]isawell-knownactivequadraturedemodulationtechniquewherethe quadraturesignalsaregeneratedbyactivelymodulatingthelaserfrequencyorthesensoritself.A drawbackofthemethodistherequirementofawavelength-tunablelaserorasensorwhosecavity lengthcanbemodulatedinoperationwithhighspeed. Passivequadraturedemodulationmethodsthatdoesnotrequiretuningthelasersourceorthe sensor,whichsigni˝cantlysimpli˝esthewavelengthlockingsystem,especiallyminimizescomplex electroniclockingsystem.Manypassivequadraturedemodulationmethodshavebeenproposed anddemonstrated.OneofthemistouseapairofFPcavitieswithquadraturephaseshifted fringesthatworkintandem[70].However,producingsuchpairofFPcavitiesrequiresprecise controloverthecavitylengths,whichisanon-trivialtask.Anothermethodistousemultiple laserswhosewavelengthsareinquadraturepositionsofthesensorfringes[71,72,73].Theuseof multiplelasersmaysigni˝cantlyincreasethesystemcomplexityandcost.Inaddition,forsensors withdensespectralfringes,thelaserwavelengthsareclose,causingdi˚cultyinmaintainingthe quadraturephaseshiftduetothelaserwavelengthdriftaswellasdi˚cultyinseparatingthetwo lasersignals.Recently,wedemonstratedanotherpassivequadraturedemodulationmethodinwhich thetwowavelengthsatthequadraturepointsaregeneratedbyalaserandafrequencyshifter[52]. However,themethodisonlyapplicabletosensorswithlongFPcavitiesbecauseofthelimited frequencyshiftthatcanbegeneratedbythefrequencyshifter. Therefore,weproposeanddemonstrateadi˙erentpassivequadraturedemodulationmethod wherequadraturephase-shiftedfringesaregeneratedbylightofthetwoorthogonalpolarizations inthe˝berandtheFPcavity.Themethodisenablebyanew˝ber-opticFPsensordesignthathas abirefringentFPcavitywithpreciselycontrollablebirefringence. 72 4.1.2Sensordesignandtheoreticalanalysis 4.1.2.1FPcavitywithlinearbirefringence Figure4.1:Schematicsof(a)asensorwithabirefringentFPcavityand(b)spectralfringeswith quadraturephaseshiftprobedbylightlinearlypolarizedalongtwoprincipalaxesofthecavity. TheprincipalofoperationcanbemoreclearlyillustratedusingFig.4.1asanexample,which depictsanFPcavityformedbyashortsectionof˝berwithlinearbirefringence.Assumingthe refractiveindicesofthe˝bercorrespondingtothetwoprincipalaxesoftheFPcavityare = G and = H ,thespectralfringesprobedbythelightatthesetwopolarizationsaregivenby ˚ G = » 1 ¸ 1 cos ¹ 4 c= G ! š _ ¸ \ º¼ ˚ H = » 1 ¸ 1 cos ¹ 4 c= H ! š _ ¸ \ º¼ Œ (4.1) where _ isthewavelengthofoperation, ! isthephysicallengthoftheFPcavity, and aretwo constantsdeterminedbytheopticalpowerofthelightattwopolarizations,and 1 and \ denote, respectively,thefringevisibilityandtheinitialphaseofthefringes.Forsimplicity,band \ are assumedtobeidenticalforbothpolarizations.Thephaseshiftbetweenthetwofringesaregiven by \ = 4 c =! š _Œ (4.2) where = = = G = H isthecavitybirefringence.FromEq.(4.2),aroundasmallrangeofagiven operatingwavelength,aquadraturephaseshiftbetweenthetwofringes,asshowninFig.4.1(b),can beobtainedbycontrollingthecavitybirefringence ¹ = º and/orthecavitylength ¹ ! º .Speci˝cally, 73 letting \ = ¹ < ¸ 1 š 2 º c ¹ < = 0 Œ 1 Œ 2 ŒŁŁŁ º Œ (4.3) gives =! = ¹ < š 2 ¸ 1 š 8 º _Ł (4.4) Ifthetwopolarizationsarebothexcitedandseparatelydetected,atleastoneofthepolarizations willgiveasignalthatissensitivetothemeasurand-inducedspectralshiftoftheFPsensor. Figure4.2:TheCFBG-FPsensorstructure. ThestructureofthesensorisshowinFig.4.2.Thesensorcontainsapairofchirped˝berBragg gratings(CFBG)withthesamechirpingrateanddirection.TheCFBGsareweaklywrittenonthe polarizationmaintaining(PM)˝ber.TwoCFBGsfunctionastwomirrorsandformalow-˝nesse Fabry-Perotinterferometer(FPI),asschematicallyshowninFig.4.3.Inordertogeneratesharp spectralslope,thefringesshouldbedense.Therefore,theseparationbetweenthetwoCFBGs shouldbelargeenough.Toachieveresponsivetoultrasonicsignalwhosewavelengthismuch shorterthanthe˝berlengthbetweenthetwoCFBGs.The˝berbetweentheCFBG-FPIiscoiled inonelayertightloops.Thediameteroftheouterloopisshorterthantheultrasoundwavelength. Thenthecoiledloopsisgluedtothealuminumplateforultrasounddetection. 4.1.2.2Quadraturedemodulation Thekeyideaforquadraturedemodulationisthata90-degreephasedi˙erencebetweenthetwo channels.Inourdesign,thequadraturephasedi˙erenceisformedbycontrollingthebirefringence inthePM˝ber.Speci˝cally,thebirefringenceinthePM˝bercontainsthreecomponents: 1. OriginalbirefringenceofthePM˝beritself; 74 Figure4.3:SimulatedCFBG-FPItransmissionspectrumwithlow-˝nesseFPIfeaturessinusoidal fringes. 2. CFBGintroducedbirefringence; 3. Bendingintroducedbirefringence. The˝rsttwocomponentsare˝xedandhardtotunesincetheCFBGfabricatedontoaspeci˝ctype ofPM˝ber.However,thebirefringenceintroducedbythebendingcanbetunedbycontrollingthe coildiameterandthetwiststatus.Therefore,aquadraturephasedi˙erenceisachievablebetween thefastandslowaxesofthePM˝ber. InordertoformsinusoidalfringeswithaCFBG-FPIstructure,there˛ectanceoftheCFBG shouldbesmall.Thefreespectralrange(FSR)isde˝nedasthewavelengthseparationbetween adjacenttransmissionpeaks _ andgivenby: _ = _ 2 0 2 = 6 ; Œ (4.5) where _ 0 isthewavelengthwithinthebandwidthoftheCFBG, = 6 isthegrouprefractiveindex, ; istheseparationbetweenthetwoCFBGs. IfbothCFBGhaveare˛ectance ' ,thetransmittancefunctionoftheCFBG-FPIisgivenby: ) = ¹ 1 ' º 2 1 ¸ ˙ sin 2 ¹ i š 2 º Œ (4.6) 75 where ˙ = 4 ' ¹ 1 ' º 2 (4.7) isthecoe˚cientof˝nesse.The˝nesseisde˝nedastheFSRdividedbythebandwidth(full-width half-maximum)ofthetransmissionpeak: ˙ = _ X_ (4.8) where X_ isthefull-widthhalf-maximum(FWHM)ofthetransmissionpeak. The˝nesseisonlydeterminedbythere˛ectanceoftheresonatorandisindependentofthe cavitylength. Sincetheshapeofthespectrumisnotperfectsinusoidal,a90 phasedelaybetweenthefast andslowpolarizationsisnotoptimalforquadraturedemodulation.AsshowninFig.4.6,when thelaserwavelengthlocatesatthespectrumvalleyofthefastpolarization,themagnitudeofthe slopeoftheslowpolarizationisnotreachingthemaximum.Besides,theminimumresponseto theultrasonicsignalisdeterminedbytheminimummagnitudeoftheintersectionpointsofthe slopecurvesbetweenthefastandslowpolarizations.Inordertoachievemaximumandfull-time responsetotheultrasonicsignal,themagnitudeoftheintersectionpointsshouldaslargeaspossible. Therefore,thephasedelaybetweenthefastandslowpolarizationsshouldlargerthan90 .Basedon theanalysisabove,simulationresults(Fig.4.7)showthata104 phasedelayprovidestheoptimal responsetotheultrasonicsignal.Theminimummagnitudeoftheslopeisabout0.1rad 1 foran FPsensorwith10%re˛ectanceofeachCFBG. 4.1.3Experimentaldemonstration 4.1.3.1Systemsetup Wedemonstratedthepolarimetricquadraturedemodulationmethodforultrasonicdetectionona metalplateusinganexperimentalsetupshownschematicallyinFig.4.4.Thesensorstructure, depictedinFig.4.5,isalow-˝nesseFPinterferometerformedbytwochirped˝berBragggratings 76 Figure4.4:Schematicsofthesensorsystemwithpolarimetricpassivequadraturedemodulation forultrasonicdetection. (CFBGs)attheendsofacoiledpolarizationmaintaining(PM)˝ber.ThepurposeofthePM˝ber istomaintainthepolarizationstatesofthelightintheFPcavity.TheCFBGsprovideoptical re˛ectionsoverarelativelywidebandwidththathasthepotentialtoaccommodatealargespectral shiftofthefringesfromenvironmentalperturbations.Thereareseveralbene˝tsofusingthe˝ber- coilFPcavityasthesensingelementforultrasonicdetection.Comparedwithultrasonicsensors withstraight˝berswhoseresponseisdependentonthedirectionoftheultrasonicsignal,a˝ber coilsensor[74]isomnidirectionalduetoitscircularlysymmetricstructure. Figure4.5:ThePM˝ber-coilFPsensor. A˝bercoilwithmultipleloopscanincorporatealongspanof˝berintoasmallsensorfootprint. Along˝berlengthresultsindensespectralfringeswithlargespectralslopesforsensitivedetection ofspectralshift;whileasmallsensorsizecanminimizethephasecancellatione˙ect,whichis importantfordetectingofhigh-frequencyultrasound.The˝bercoilalsoprovidesaconvenientway topreciselyadjustthetotalbirefringenceoftheFPcavityevenaftertheCFBGsarefabricatedand 77 the˝berlengthoftheFPisdetermined.Bycontrollingthebendingradiusandthelengthofthe coiled˝berandtwistingthe˝ber,extrabirefringenceandphaseshiftcanbeintroducedtothe˝ber intheFPcavitytoachieveatotalphasedi˙erencecloseto90 ofthetwofringescorrespondingto thetwopolarizations.Speci˝cally,bending-inducedbirefringenceofa˝berisdeterminedbythe bendingcurvatureradius ¹ ' º andthe˝berdiameter ¹ 2 A º andisgivenby[75] = = 0 Ł 25 = 3 ¹ ? 11 ? 12 º¹ 1 ¸ E º A 2 š ' 2 Œ (4.9) where ? 11 and ? 12 aretheelasto-opticcoe˚cients,and E isthePossion'sratioofthe˝ber. Foraregularsilica˝berwithadiameterof 2 A = 125 `< , = = 1 Ł 45 , ? 11 ? 12 = 0 Ł 15 , E = 0 Ł 17 , thebending-inducedbirefringenceofa˝bercoilwithadiameterof 2 ' = 1 Ł 2 cm,whichisthe diameterofthe˝bercoilusedintheexperiment,is = = 1 Ł 8 10 5 .Intheworstscenario,a maximumphaseshiftof c š 2 needstobeprovidedby˝berbendingtoachieveaquadraturephase shiftbetweenthefringesofthetwopolarizations.Letting < = 0 inEq.(4.4),weobtainthelength ofthecoiled˝bercorrespondingtothis c š 2 phaseshift,whichis ! = _ š 8 = = 1 Ł 1 cmat wavelength _ = 1550 nm. Then,regardlessoftheinitialphasedi˙erenceofthetwofringes,ifnecessary,weonlyneed tostraightenashortaspan(atmost1.1cm)of˝berfromthe˝bercoiltoachieveaquadrature shiftbetweenthefringes.Notethatiftheprincipalaxesofthebending-inducedbirefringencedo noalignwiththoseoftheinherentbirefringenceofthe˝ber,thebendingmaycausearotation oftheprincipalaxesoftheoverallbirefringenceofthe˝bercoilwithrespecttotheuncoiled PM˝ber.Becausethebending-inducedbirefringenceismuchsmallerthanthatofthePM˝ber ( = = 3 10 4 foraPM˝berwithabeatlengthof5mmat1550nm),therotation,ifexists,is expectedtobesmallandslightlytwistingthePM˝bermayaligntheprincipalaxesofthe˝bercoil withthestraightPM˝ber[76]. DuetothebirefringenceintroducedbyCFBGfabrication,thecoilandtwistofthePM˝ber, atotalphasedelayof90 betweenthefastandslowpolarizationsofthePM˝berisgenerated withinthesensorspectrumandthesimulatedtransmissionspectraareshowninFig.4.6.The magnitudeslopesofthefastandslowpolarizationspectraareshownatthebottomofFig.4.7. 78 Forultrasonicsensingwithedge˝lterdetectionmethod,thesignalstrengthisproportionaltothe slopeinthelinearregionofthespectrumofanFBG-basedopticalresonator.Asaresult,the ultrasound-inducedspectralshiftoftheCFBG-FPIisconvertedtolaserintensityvariationsafter theCFBG-PFI.Intheproposedscheme,ultrasoundthatimpingesontothecoiled˝bercauses fringesshiftsoftheCFBG-FPIbuthaslittlee˙ectonthephasedi˙erencebetweenofthefast andslowpolarizations.Hence,thefastandslowpolarizationsspectraoftheCFBG-FPIshift simultaneously.Theslopecurvesabovecrosssectionbetweenfastandslowpolarizationscanbe selectedforhighlysensitiveultrasonicsignaldetection.Sincetheslopecurvesabovecrosssection betweenfastandslowpolarizationsarenon-zero,thesensorisalwaysresponsetoultrasonicsignal bycombiningthefastandslowpolarizationsignalwitharbitrarylaserwavelengthandinsensitive toenvironmentchangestothesensor.Therefore,thereisnoneedforlaserwavelengthlockingnor temperature/straincompensationtothesensorwhichgreatlyreducethecomplexityofthesystem. Figure4.6:Spectralfringesattwopolarizationsandthecorrespondingslope(absolutevalue)when thephaseshiftofthefringesis90degree. ThesensorwasdemodulatedinthetransmissionasshowninFig.4.4.Linearlypolarizedlight fromanarrow-linewidthlaserwithasingle-mode˝ber(SMF)pigtailpassedthroughapolarization controller(PC)andthe˝ber-coilFPsensor.Thetransmittedlightfromthesensorwasthendirected toapolarizationbeamsplitter(PBS)sothatthelightpolarizedatthetwoprincipalaxesofthe 79 Figure4.7:Spectralfringesattwopolarizationsandthecorrespondingslope(absolutevalue)when thephaseshiftofthefringesis104degree. PM˝berwereseparatedintotwo˝bersandreceivedbytwophotodetectors(PDs).Theoutputs formthePDswereampli˝edinthefrequencyrangeof 50 500 kHzwithidenticalampli˝ersand bandpass˝ltersforultrasonicdetection,whiletheun-ampli˝eddccomponentsoftheoutputswere usedtoanalyzetheoperatingpoints.ThePCwasadjustedtocontrolthepolarizationoflightso thatapproximatelyequalopticalpowerwasdistributedbetweenthetwopolarizationstates.The ˝ber-sensorwasgluedtoaaluminumplatefordetectingtheultrasonicpulsesontheplategenerated byapiezoelectrictransducer(HD50,PhysicalAcoustics)gluedclosetothe˝bersensor. Apairof5-mmCFBGswerefabricatedonaPM˝ber(PM1550-XP,Nufern)in-houseusing193 nmUVlaserandachirpedphasemask.ThebeatlengthofthePM˝berislessthan5mmat1550 nm.TheBraggwavelengthofthephasemaskis1067.7nmwithachirpingrateof4nm/cm.The center-to-centerseparationbetweenthetwoCFBGswasapproximately29cm.Thetransmission spectra(normalizedtothepeaktransmission)ofthe˝rstCFBGandtheCFBG-FPsensor,measured byanopticalspectrumanalyzer(OSA)witharesolutionof0.02nm,aredisplayedinFig.4.8, showingare˛ectionwindowof ¡ 2nmcenteredat1545nm.Notethatthe˝nesinusoidal-like fringesoftheFParenotvisibleonthemeasuredspectrumbecauseofthelowwavelengthresolution oftheOSA.Thesystemisoperatedataroundat1545nmaroundthecenteroftheCFBGbandwidth 80 wherethere˛ectivityforeachoftheCFBGsisestimatedtobe ˘ 10% . Figure4.8:NormalizedtransmissionspectraofoneCFBGandtheFPsensormeasuredbya whitelightsourceandanOSA. The10%re˛ectivityoftheCFBGscausedthefringestohaveasmallbutnoticeabledeviation fromaperfectlysinusoidalformduetothenon-negligiblemultipathinterference.Asaresult, anexactphasedelayof90 betweenthetwopolarizationsmaynotbeoptimalforquadrature demodulation.Simulationwascarriedoutto˝ndtheoptimalphaseshift.Figure4.6and4.7 show,respectively,thesimulatedfringeswitha90 phaseshiftand104 phaseshiftandtheir correspondingabsolutevaluesofthespectralslopeforanFPcavityformedbytwomirrorswith 10%re˛ectivity.Duetothedeviationofthefringesfromaperfectlysinusoidalwaveform,the absolutevaluesofthespectralslopeforonepolarizationdidnotreachthemaximumatfringe valleysorpeaksoftheotherpolarizationforthecaseof90 phaseshift.Theminimumresponseof thesensorisdeterminedbytheminimummagnitudeoftheintersectionpointsoftheslopecurves forthetwopolarizations,whichis0.07rad 1 forthecaseof90 phaseshift.Anopticalphaseshift betweenthetwofringesshouldmaximizetheminimumresponse,whichoccurswhenthephase shiftis104 basedonoursimulation.Inthiscase,theminimumresponseofthesensorincreases toitsmaximumvalueof0.1rad 1 ,asshowninFig.4.7. Toobtainthedesirablephaseshiftofthefringes,the˝berbetweenthetwoCFBGswerecoiled 81 Figure4.9:3Dprintedstructureofthemold. withadiameterof ˘ 12 mmwiththehelpofa3Dprintedmold(Fig.4.9).Atotalopticalloss of0.3dBwasintroducedwiththe˝bercoil.Thephasedi˙erencebetweenthefringesofthetwo polarizationswascontinuouslymonitoredduringthecoilingprocessusingawavelength-scanning laseralongwiththetwoPDsthatgaveenoughresolutiontoresolvethe˝nefringes.Thelaserwas scannedoverarangeof10spmcenteredaround1545nm.Bycontrollingthe˝berlengthinthe coiledregionandtwistingthePM˝ber,weobtainedaphasedi˙erencecloseto104 forthetwo fringes. Thenthe˝bercoilwassurfacebondedontothealuminumplatewithsuperglue.Notethatthe CFBGswereprotectedwithametaltubeandlaidfreelyontheplate.Figure4.10isapictureof the˝ber-coilsensorontheplate,anHD50isgluedontherightastheactuator,whilean ' 15 U isattachedtotheplatewithcouplingagentontheleftasareferencesensor.Figure4.11shows thetwotransmissionfringesofthe˝ber-coilFPsensoratthetwopolarizationsmeasuredafter itwasbondedontheplate.Bothfringeshaveasimilarfree-spectralrangeof ˘ 3 Ł 0 pm,which agreereasonablywellwiththetheoreticalvaluesof2.8pmforanFPcavitywith29-cmoptical ˝berassumingthee˙ectiveindexofthe˝beris1.45.Thesmalldiscrepancymayarisefromthe inaccuracyofthescanningrangeofthelaserusedforthefringemeasurement.Aspectralshiftof approximately0.9pmwasobservedbetweenthefringesofthetwopolarizationscorrespondingto 108 phasedi˙erence,whichagreewellwiththetheoreticaldesign.Inpractice,bothenvironmental 82 Figure4.10:PictureofthesensorbondedontheplatewiththeCFBGsprotectedandlaidfreelyon theplate. perturbationsandlaserwavelengthdriftcanchangetheoperatingpoint.Weperformedaquick checkonthefringesbyintentionallybendingtheplatetointroducebackgroundstraintothe˝ber. Weobservedthatthetwofringesexperiencedlargespectralshiftbutmaintainedtheirrelativephase di˙erence. Figure4.11:Measuredspectralfringesatthetwopolarizationsafterthesensorwasbondedonthe plate. 83 4.1.3.2Ultrasounddetection Thenwedemonstratedtheproposedpassivequadraturedemodulationforultrasounddetection usingtheproposedsystem.Thepiezoelectrictransducerwasdrivenbya5-cyclesinusoidalburst wavecenteredat250kHzwithapeak-to-peakvoltageof20V.Thelaserwasfreerunningwith constantinjectioncurrentandtemperature.Tensilestrainwasappliedtothe˝bercoilbybending theplatetochangethepositionoftheworkingpointonthefringes,whichcausedthespectralshift ofthefringes.NotethattheCFBGswerenotbondedontheplatesurfaceandwerefreefromthe strain. Theresponsesofthesensorsystemtotheultrasoundandthecorrespondingpositionofthe operatingpointrelativetothefringesareshowninFig.4.12.ThedccomponentsofthePDsignals wereusedforworkingpointsanalysis(Fig.4.12(a-d))andthecorrespondingaccomponentswere ampli˝edand˝lteredwithbandpass˝lters(Fig.4.12(e-h)).Thesensorsystemwasabletodetect theultrasonicsignalwithgoodsignal-to-noiseratio(SNR)regardlessofthebackgroundstrainor theworkpointposition.Speci˝cally,Fig.4.12(a)istheinitialcasewherethelaserwavelength wasonfringevalleyofthex-axispolarizationbutontheslopeofthey-axisfringes.Figure4.12(e) showsthecorrespondingresponsesofthetwopolarizationchannels.Asexpected,thechannel ofthex-axisexhibitedlittlesensitivity,butthechannelofthey-axishadalargeresponsetothe ultrasonicsignal.Thenthetensilestrainwasincreasedontheboard,sothatthefringesofbothaxes wereshiftedtowardtothelongerwavelengthtochangetheoperatingpointofthesensor.Figure 4.12(b)isthecasewherethelaserwavelengthreachedtothepointwithzero-slopeofthey-axisbut alargeslopeofthex-axis.Figure4.12(f)showsthatthechannelofthex-axishadalargeresponse totheultrasonicsignal,whilethechannelofthey-axisbarelycapturedtheultrasonicsignal.When wecontinuedtoincreasethetensilestrain,theoperatingpointswerenowonthespectralslopeof bothchannelswiththesameslopedirections(Fig.4.12(c)),bothchannelscapturedtheultrasonic signalswithconsistentin-phasewaveforms.Asthetensilestrainwasfurtherincreasedtothe situationshowninFig.4.12(d),thelaserwavelengthwasonthemaximumabsoluteslopesofboth axesbutwithoppositeslopedirection.Inthiscase,bothchannelsdeliveredmaximumamplitude 84 Figure4.12:(a)-(d)Operatingpoints(indicatedbythegreenlines)relativetothetransmission spectraofsensoratthetwopolarizations.(e)-(h)Correspondingdetectedultrasonicsignalsfrom bothpolarizationchannels. oftheultrasonicsignal.Notethatthedetectedultrasonicwaveformsbythetwochannelswereout ofphase,consistentwiththeoppositeslopedirectionsofthetwofringesattheoperatingpoint. 4.1.4Conclusions Inconclusion,weproposedanddemonstratedapassivequadraturedemodulationmethodusing linearlypolarizedlaserandasensorwithabirefringentlow-˝nesseFPcavity.Withprecisely controlledbirefringenceintheFPcavity,thefringesprobedbylightpolarizedalongthetwo 85 principalaxescanhaveaquadraturephaseshiftandcanbeseparateddetected.Asaresult, sensitivedetectioncanbeachievedbyatleastoneofthepolarizationchannelsregardlessofthe laserwavelengthrelativetothefringes.Wedemonstratedtheconceptfor˝ber-opticultrasonic sensorusingalowFPcavityformedbytwolow-re˛ectivityCFBGsattheendsofacoiledPM˝ber. Atotalphasedelayof108 betweenthefringesofthetwopolarizationsofthePM˝ber,optimized fortheFPsensorwithnon-sinusoidalfringes,wasobtainedbycontrollingthelengthofthecoiled ˝berandtwistingofthe˝ber.Quadraturespectrawereextractedbyapolarizationbeamsplitter andmeasuredbytwophotodetectors.Theexperimentalresultsshowedthatthesensoriscapable ofdetectingultrasonicsignalwhenthesensorspectraexperienceenvironmentaldriftsusingalaser at˝xedwavelength.AlthoughtransmissionmodeoftheFPsensorwasusedinthedemonstration, thedemodulationmethodproposedherecanalsobeusedforthere˛ectionmodeoftheFPsensor orsensorsbasedonothertypesofinterferometers. 4.2Polarization-insensitive,omnidirectional˝ber-opticultrasonicsensor withquadraturedemodulation Inthissection,anultrasonicsensorsystembasedonalow-˝nesseFabry-Perotinterferometer (FPI)formedbytwoweakchirped˝berBragggratings(CFBGs)onacoiledsingle-mode˝ber isproposed.Thesensorsystemhasseveraldesirablefeaturesforpracticalapplicationsinnon- destructiveevaluationandstructurehealthmonitoring.Bycontrollingthebirefringenceofthe˝ber coilduringthesensorfabrication,thesensorismadeinsensitivetothepolarizationvariationsof thelasersource.Thecircularsymmetricstructureofthe˝bercoilalsorenderstheomnidirectional responseofthesensortoultrasound.Whilethe˝bercoilisbondeddirectlytothestructure,the CFBGsaresuspendedfromthestructureandfreefromlargebackgroundstrainswithlittlereduc- tiontothesensitivityofthesensor.Thelow-˝nesseFPIfeaturessinusoidalre˛ectionspectrum. Liketheconventionalphasegeneratedcarriedtechnique,aphasemodulatorisutilizedtoimple- mentquadraturedemodulation.Therefore,thesensingsystemisadaptivetolargebackground perturbationsexperiencedbythe˝bercoil. 86 4.2.1Introduction Although˝ber-opticultrasonicsensors,particularlythosebasedon˝berBragggratings(FBGs), havebeenwidelyenvisionedasanattractivetechnologyfornon-destructiveevaluationandstructure healthmonitoring[6,33],severalchallengesmakefewofthesesensorscommerciallysuccessful. Firstly,thesensorsystemshouldhaveahighsensitivitytoultrasoundandbeabletoaccommodate largebutusuallyslowlyvaryingbackgroundstrainfromenvironmentalperturbations,suchas structuraldeformationandambienttemperaturevariations.Secondly,thesensoroperationshould beindependentonthelaserpolarizationvariationswhicharedi˚culttomeasureandcontrolin practice.Thirdly,anomnidirectionalresponseofthesensorisoftendesirablesothattheultrasonic signalsfromanydirectionscanbedetectedwithgoodsensitivity. Thereareafewreportsregardingthedevelopmentofsensitivesensorsand/orsensorsadaptive tobackgroundstrain.Detectionsensitivitycanbeimprovedbyopticalresonatorssuchas c -phase- shiftedFBGsandFBGFabry-Perotinterferometers(FPIs)thathavenarrowspectralfeatureswith largespectralslopes[11,55,17].Astraightforwardmethodtocombatthespectraldriftfrom environmentalperturbationsistolockthelaserwavelengthtothelinearrangeofthespectralslope [17,77,78,44].Themethodishinderedbythecomplicatedlockingsystemandlimitedavailability oflaserswithsu˚cienttuningrangeandspeed.Remotebonding,wheretheFBGisfreefrom thestructureandtheultrasoundiscoupledtothe˝beratapointawayfromtheFBGregion,isa uniquetechniquethataimsatisolatingthesensorfrombackgroundstrainexertedbythestructure [79,80].However,thesensorspectrumstillexperiencesthermaldriftduetoambienttemperature variations.Therearefewstudiestoaddressthechallengesinsensorbirefringenceanddirectivity. Manualpolarizationcontrollers(PCs)areoftenusedtocontrolthelaserpolarization.However, suchapproachisnotdesirableinpracticalapplicationswherethelaserpolarizationcanbechanged overalargerangeandinarandomwaybyenvironmentalperturbationssuchas˝berbending, twisting,andtemperaturevariations.Automaticcontroloflaserpolarizationthroughafeedback loopischallengingduetothelackofa˙ordableandportabledevicesforpolarizationmanagement. MostoftheFBGsensorshasalargedirectivityfordetectingultrasoundonasolidsurfacebecause 87 theyaremostsensitivetothestrainalongthe˝berandshowlittlesensitivitytostraintransverseto the˝ber[81]. 4.2.2Principleofoperation Inthissection,anadaptiveultrasonicsensorsystemwithapolarization-insensitiveandomnidirec- tionalsensorisproposedanddemonstrated.TheproposedsystemisconceptuallyillustratedbyFig. 4.13.Thesensorheadisalow-˝nesseFPIwithlongcavitylengthformedbyapairofweakchirped FBGs(CFBGs)writtenonabend-insensitive˝ber.The˝berismadeintoatightcoiltoreducethe footprintofthesensorandincreasetheultrasonicfrequencyrange.Thelongcavitylengthofthe FPIresultsin˝nefringeswithlargespectralslopes,givingrisetothehighdetectionsensitivity. Thecircularsymmetryofthe˝bercoilendowsthesensorwithomnidirectionalresponse.Theexact lengthofthecoiled˝beriscontrolledsothatthebend-inducedbirefringencegeneratesaround-trip phasedi˙erenceof 2 #c (N=0,1,...)betweenthefastandslowaxes,sothatthefringesatthetwo principalpolarizationstatesoverlap,whichmakesthesensoroperationindependentonthelaserpo- larization.Meanwhile,thetwoCFBGsaresuspendedfromthestructuretoisolatethebackground strainstransferredfromthestructure.CFBGshaverelativelywidere˛ectionspectralwindowsto accommodatethespectralshiftfromambienttemperaturevariations.Similartotheconventional phase-generatedcarrier(PGC)demodulationscheme[69],passivequadraturedemodulationfor thissensorcanberealizedbythesystemshowninFig.4.13. Outputofthelasergoesthroughaphasemodulatorandistheninjectedtothesensorviaan opticalcirculator.Thephasemodulatorisdrivenbyasinusoidalwaveformdeliveredbyafunction generator.Thereturnedopticalsignalisreceivedbyaphotodetector(PD)whoseoutputissplit intotwopaths.Onepathgoesthroughaband-pass˝lterwhichrejectsallthecomponentsoutside thefrequencybandoftheultrasoundbeingdetected,directlyleadingtotheextractedultrasonic signals.ThispathisherereferredtoastheDCchannel.Usinganelectronicmixer,theotherpath ismultipliedbyaharmonicfunctionwiththesamefrequencyappliedtothephasemodulator.The mixedsignalpassesthroughanotherbandpass˝lterwhichretainsonlythefrequencycomponentsof 88 Figure4.13:Schematicillustrationofthesystemcon˝gurationforconceptdescription.TheFBGs aresuspendedfromthestructuretoisolatelargebackgroundstrain.Pha.Mod.,phasemodulator; Ch.,signalchannel;Ult.Sig.,ultrasonicsignal;BPF,band-pass˝lter;FSR,freespectralrange. interest,leadingtoanotherultrasonicsignal.Thesecondpathisherereferredtoasthe1stharmonic channel.Thesetwochannelswillbeshownlater,boththeoreticallyandexperimentally,toprovide quadraturedemodulationcapability.Wenotethatalthough˝ber-coilswithregularFBGshave beenpreviouslystudiedforultrasonicdetection[74,52],theylackthekeyfeatureofpolarization insensitivitypossessedbythesensorhere.Additionally,westudiedthesensordirectivityand presentedamorepracticalmethodforsensordemodulation. Tobetterillustratethesystem,abrieftheoreticalanalysisisgiven.Thephasemodulatedlaser hasaseriesofsidelobesorharmoniccomponents(Fig.4.13(a)).Sincethemodulationdepthis shallowinourexperiments,asshownlater,theelectric˝eldafterphasemodulation, ˆ 8 ,canbe expressedas[82] ˆ 8 = ˆ 0 4 9 ¹ l 0 C ¸ V sin l < C º ˇ ˆ 0 » ˜ 0 ¹ V º 4 9l 0 C ¸ ˜ 1 ¹ V º 4 9 ¹ l 0 ¸ l < º C ˜ 1 ¹ V º 4 9 ¹ l 0 l < º C ¼ (4.10) 89 Figure4.14:(a)sensorspectrumandphasemodulatedlaser,and(b)signaldemodulationchannels. where ˆ 0 isamplitudeofthelaser˝eld, l 0 and l < are,respectively,theangularfrequencyofthe laserandthephasemodulation, ˜ 0 and ˜ 1 are,respectively,the0th-orderandthe1st-orderBessel functionsofthe˝rstkind, V ismodulationdepth,and C denotestime.There˛ectioncoe˚cient A ¹ l º ofalow-˝nesseFPIsensorisgivenby[82] A ¹ l º = A 1 ¸ A 2 4 9 2 l=! š 2 (4.11) where A 1 and A 2 are,respectively,there˛ectioncoe˚cientofthefrontandbackmirrors, = is e˙ectiverefractiveindexofthe˝ber, ! isthecavitylength, 2 isspeedoflightinvacuum.Here, A 1 and A 2 areassumedtobethesameforboththeoriginallaserlineandthesidelobes.Then,the totalre˛ectedelectric˝eldisgivenby ˆ A = ˆ 0 » ˜ 0 ¹ V º 4 9l 0 C A ¹ l 0 º¸ ˜ 1 ¹ V º 4 9 ¹ l 0 ¸ l < º C A ¹ l 0 ¸ l < º ˜ 1 ¹ V º 4 9 ¹ l 0 l < º C A ¹ l 0 l < º¼ (4.12) Theopticalpower % receivedbythePDisgivenby % / ˆ A ˆ A (4.13) where denotescomplexconjugate.Inthefrequencydomain,thesignaloutputfromthePD consistsofdiscretechannelswithaseparationofthemodulationfrequency,asillustratedinFig. 90 4.14(b).TheultrasonicsignalintheDCchannelcanbeextracteddirectlybyabandpass˝lter, whiletheultrasonicsignalintheharmonicchannelsisobtainedbythecombinationofamixerand abandpass˝lter.Inpractice,onlytheultrasonicsignalsintheDCandthe1stharmonicchannels areextracted.Theotherhigherorderharmonicchannelsareignored. Usually, A 1 and A 2 arecomplexnumberswhichincludeaphaseshiftuponre˛ectionfroman FBG[21].However,forsimplicityandwithoutlosinggenerality,thephaseshiftisignoredhere. Infact,considerationofthephaseshiftonlyleadstoanextraconstantphasebesidesthe q 0 shown laterinEqs.4.14and4.15.Withsuchsimpli˝cation, A 1 and A 2 arerealandpositivenumbers. Aftersomealgebra,thevoltageoutputfromtheDCchannelreads + ˇ˘ / 2 % 0 A 1 A 2 » ˜ 2 0 ¹ V º¸ 2 ˜ 2 1 ¹ V º cos q < ¼ cos q 0 (4.14) andthevoltageoutputfromthe1stharmonicchannelreads + 1 BC / 8 % 0 A 1 A 2 ˜ 0 ¹ V º ˜ 1 ¹ V º sin q < 2 sin q 0 (4.15) where % 0 isthelaserpowerbeforethephasemodulator, q 0 = 2 l 0 =! š 2 ,and q < = 2 l < =! š 2 .In thepresenceofultrasound,both q 0 and q < aremodulated.However, q < isvirtuallyaconstant sincetheopticalfrequencyismuchhigherthanthatoftherfmodulationfrequency,i.e., l 0 ˛ l < . Therefore,theultrasonicsignalsareonlyincludedimplicitlyin q 0 .Equations4.14and4.15 representtheoutputsofthetwochannelswithquadraturephaseshiftsothattheultrasoundsignal canbeextractedregardlessofthespectralshiftscausedbyenvironmentalperturbations.Notethat thesignalamplitudeisafunctionofboththephasemodulationdepthandfrequency.Itisworth mentioningthat,inderivingEq.4.15,aphaseshiftisneededinthesinusoidalfunctionsenttothe mixersothatamplitudeoftheextractedultrasonicsignalismaximized.Thisphaseshiftisalso dependentonthefrequencyofphasemodulation. 91 4.2.3Sensorstructureandexperimentsetup Toexperimentallydemonstratethesystem,two5-mmlongCFBGswithre˛ectivityofaround 20% centeredaround1550nmwerefabricatedin-houseonabend-insensitive˝ber(F-SBC,Newport). Thelengthofthe˝berbetweentheCFBGswasabout39cm.Assemblyofthe˝bercoilwas facilitatedbyadevised3-Dprintedmold.Diametersoftheinnermostandoutermostloopswere 8mmand10mm,respectively,resultinginanaveragebend-inducedbirefringenceof 5 Ł 18 10 5 [75].Therefore,abendinglengthofaround37.4cmproducedaround-tripphasedi˙erenceof 50 c betweenthefastandslowaxesat1550nm.Asaforementioned,aphasedi˙erenceofaninteger multipleof 2 c wouldmakethesensoroperationindependentonthelaserpolarization.Thebending lengthwas˝ne-tunedbymonitoringtheFPIspectrumasthelaserpolarizationwasrandomlyvaried (seeFig.4.15)formoredetails).Whenapolarization-insensitiveFPIwasreached,the˝bercoil was˝xedusingfast-curedglue. Figure4.15:Experimentalsetuptostudythesensitivityofthesensortolaserpolarizationandan imageofthe˝bercoil. Thespectralresponseofthesensortopolarizationvariationwasstudiedusingthesetupshown inFig.4.15.Again,polarizationofthelaserwasmanuallyandrandomlytunedusingaPC.After thePC,thelaserwassplitintotwopathsusinga50/50coupler.Usingacirculator,thelightin 92 onepathwassenttoareferencesensorwhichwaspolarizationsensitive,whiletheotherpath wasconnectedtothepolarization-insensitivesensor.Wavelengthofthelaserwasscannedusinga trianglewaveform,andthereturnedspectrumwasseparatelyreceivedbyaPDanddisplayedonan oscilloscopeforbothsensors.Thisarrangementgaveadirectcomparisonbetweentheresponses ofthetwosensors.Thespectrainthetop,middleandbottompanelsofFig.4.16wererecorded forthreedi˙erentpolarizationstatesofthelaser.Apparently,whilethespectrumofthereference sensorshoweddi˙erentphasesorshapesforthethreepolarizationstates,thespectrumofthe maintaineditssinusoidalshapewithnovisiblechangesinbothitsamplitudeandphase. Figure4.16:SpectraoftheFPIsprobedbythelaseratdi˙erentpolarizations. 93 4.2.4Directivityofthesensor ThedirectivityofthesensorwasexaminedusingthesetupshowninFig.4.17.Thesensorwas gluedtoan0.8mmthickaluminumplate.Apiezotransducerwasmovedtodi˙erentangular positionsaroundthesensorwithastepsizeof30 (seetheinsetofFig.4.17).Wavelengthofthe laserwastunedtoapointonthefringeswithmaximumslope.Thepeak-to-peakamplitudewas usedastheresponse.Threecyclesofmeasurementswereperformedtoensurebetterreliability. TheresultsaresummarizedinFig.4.18.Thesensorshowsratherconsistentresponsesfordi˙erent angularpositions.Thesmalldeviationfromaperfectlyomnidirectionalresponsemightarisefrom theslightlydi˙erentultrasoundcouplinge˚ciencyfromthepiezotransducertotheplate. Figure4.17:Experimentalsetupandanimageofthesensorgluedontothealuminumplate. 94 Figure4.18:Demonstrationofsensordirectivity,sensorresponsesatdi˙erentincidentangles. 4.2.5Ultrasounddetectionwithquadraturedemodulation Finally,wedemonstratedthequadraturedemodulationforultrasounddetectionusingthesetup showninFig.4.19.Polarizationofthelasersource(6328-H,NewFocus)wasadjustedtomatch thephasemodulatorviaaPC.Adual-channelfunctiongeneratorwasusedtodrivethephase modulator.Thephasemodulatedlightwassplitintotwoarmsusinga50/50coupler.Inonearm, thelaserlinesweremonitoredbyahigh-˝nessescanningFPIwithabuilt-inPD.Notethatthis armwasmerelyforoptimizingthedrivingsignalofthephasemodulatorandisnotneededin practicalapplications.Inanotherarm,thelightpropagatedthroughacirculatorandreachedthe sensorandthereturnedopticalsignalwasdividedintotwochannelsusinganother50/50coupler. Inonechannel(dcCh.),theoutputformthePDpassedsuccessivelythrougha40-dBampli˝erand 95 a30-500kHzbandpass˝lter.Intheotherchannel(1stCh.),thePDoutputwassenttoamixerto mixwithasinusoidalwaveatthephasemodulationfrequencyandwithappropriatephasebefore passingthroughanothersetofsimilarampli˝erandbandpass˝lter. Figure4.19:Experimentalsetupforthequadraturedemonstrationofthesensor.Amp.,ampli˝er. Thelaserlinesmeasuredbythecanning-FPIareshowninFig.4.20.Therewasonlyonelaser linewithoutphasemodulation(blackcurveinFig.4.20).Whenthephasemodulationwasturned on,twosidelobesshowedup(redcurveinFig.4.20).Therelativeintensitybetweentheoriginal laserandthesidelobessuggestsamodulationdepth( V inEq.4.10)ofaround0.97.Thissmall modulationdepthleadstoarelativelystrong1stharmoniccomponentandnegligiblehigher-order harmonics. Finally,thequadraturedemodulationwasdemonstrated,andtheresultsaredisplayedinFig. 4.21,inwhichallthewaveformsweretheaverageoffourmeasurements.Thetop˝gureinFig.4.21 showsthe˝vedi˙erentoperatingpoints(depictedbythedi˙erentrelativepositionsoftheoriginal laserlineonthespectralfringes)atwhichtheultrasoundwaveformswerecapturedbythetwo 96 Figure4.20:Spectrumofthephasemodulatedlasermeasuredbythescanning-FPI. channelsandthecorrespondingchanneloutputsareshowninthebottomofFig.4.21.PositionsP1 andP5werethecaseswherethelaserlinewasatthepeakandvalleyofthefringes,respectively.As expected,theDCchanneldidnotrecordanyultrasoundsignals(seetheaccordingblackcurves)and the1stharmonicchannelregisteredtheultrasoundsignalwiththelargestamplitude.Thesituation forpositionP3,whichwasaroundthemiddlepointofthere˛ectionspectrum,wasopposite.In thiscase,the1stharmonicchanneldidnotrecordtheultrasound,whiletheDCchannelcaptured theultrasound.AttheintermediatepositionsP2andP4,bothchannelswereabletodetectthe ultrasound,butwithreducedamplitude.Alsonotethatsignalsfrombothchannelswereoutof phaseatpositionP2butinphaseatpositionP4.Asareference,theultrasoundwaveformdetected byacommercialpiezosensorisalsoshown(bluecurveatthebottomofFig.4.21). 4.2.6Conclusions Insummary,westudiedanultrasonicsensorsystempromisingforpracticalapplications.The sensorheadconsistsofapairofidenticalweakCFBGsinscribedinabending-insensitive˝ber, formingalow-˝nesseFPIwith˝ne,sinusoidal-likespectralfringes.The˝berbetweenthetwo 97 Figure4.21:Ultrasoundwaveformscapturedbythetwochannels(bottom)whenthelaserisat di˙erentoperatingpoints(upper). FBGsiscoiledtightly,whichendowsthesensorwithomnidirectionalresponse.Inthemeantime, lengthofthecoiled˝beriscontrolledsothatthephaseshiftofthetwofringescorresponding tothetwoprincipalaxesisanintegermultipleof 2 c .Satisfactionofthisconditionmakesthe sensorinsensitivetothelaserpolarization,adesirablefeatureinpracticalapplications.Asignal demodulationsystemsimilartoPGCmethodisutilizedtorealizepassivequadraturedemodulation, leadingtoanultrasonicsensorsystemadaptivetoenvironmentalperturbations. 98 CHAPTER5 CONCLUSIONANDFUTUREWORK 5.1Summary Thisdissertationpresentedaseriesofstudieswhichexploredtheuseofthe˝berBragggrating basedoptical˝bersensorsfordynamicstrainmeasurement.Regular˝berBragggratingsprovidea smallre˛ectionbandwidthwithgentleslopes,areverydi˚cultandine˚cienttomeasuredynamic strainvariations.Therefore,newsensorstructureanddemodulationtechniquesmustbedeveloped andoptimized.Throughoutthisdissertationthenewsensorstructureisdevelopedbasedonchirped ˝berBragggratingswhichprovidesarelativelargere˛ectionbandwidthcomparetoregular˝ber Bragggratings.AnFabry-Perotcavityisformedwithapairofchirped˝berBragggratings.Then resonancepeaksformedwithinthere˛ectionbandwidthwhichgreatlyenhancetheresolutionand sensitivity.Thedynamicstrainmeasurementwithproposedsensorsisextensivelystudied.We˝rst demonstratedanovelhighresolution,largedynamicrangestrainsensorwithFabry-Perotcavity usingcascadedchirped˝berBragggratingswithoppositechirpdirections.Thenweproposedand demonstratedahigh-˝nesseshortcavitysensorsforacousticemissionandultrasonicdetectionin structurecrackandfrompiezoelectricactuator.Atlast,westudiedlow-˝nesselongcavitysensor withcoilstructuretomeasureultrasonicwaveswithoutlaserwavelengthlockingandimmuneto thebackgroundenvironmentalchanges. 5.2FutureWork Inthisdissertation,wehavebuiltanultrasensitiveultrasounddetectionplatformusinganintra- cavityphase-shifted˝berBragggratinginself-injection-lockeddiodelaser.Theself-injection lockingtechniqueisconvenientandpowerfulregardingtothelaserfrequencynoisereduction. However,itisnoteasytotunethelasingwavelengthafterlockingthelaser,duetotherandom driftingwithinthelockingrange.ChangingtheinjectioncurrentofthelaserandtheBragg 99 wavelengthofthesensorareeasyandstraightforward.Butwe˝rsthavetogaintheknowledge ofthelaserwavelengthrelativetothelockingrangebeforewemakeanychange.Onepotential solutionisarapidscanningofthelaserinjectioncurrentundertheweakself-injectionlocking condition.Thenthecenterofthelaserinjectioncurrentcanbechangedtoexaminethe"error" signaloftheDCoutputofthephotodiode.The"error"signalshouldhavesigni˝cantdi˙erenceat theedgesofthelockingrange.AndtheDCsignalwilldroptozeroifthelaserisunlocked.Bythis way,thelaserwavelengthcanbeextractedwithoutbreakingtheself-injectionlockingstatus. Regardingtothecoiled˝berlow-˝nesselongcavitysensorwithphasegeneratedcarriertech- nique,thepotentialofthehigherordermodecanbefurtherexploredtoextracttheultrasoundsignal thatdoesnotfadewiththeenvironmentalperturbations. 100 BIBLIOGRAPHY 101 BIBLIOGRAPHY [1] A.D.Kersey,M.A.Davis,H.J.Patrick,M.LeBlanc,K.Koo,C.Askins,M.Putnam,and E.J.Friebele,ibergratingsensors, JournalofLightwaveTechnology ,vol.15,no.8,pp. 1997. [2] Y.-J.Rao,D.J.Webb,D.A.Jackson,L.Zhang,andI.Bennion,bragg-gratingtem- peraturesensorsystemformedicalapplications, JournalofLightwaveTechnology ,vol.15, no.5,pp.1997. [3] C.E.Campanella,A.Cuccovillo,C.Campanella,A.Yurt,andV.Passaro,ibrebragg gratingbasedstrainsensors:reviewoftechnologyandapplications, Sensors ,vol.18,no.9, p.3115,2018. [4] Y.ZhuandA.Wang,˝ber-opticpressuresensor, IEEEPhotonicsTechnology Letters ,vol.17,no.2,pp.2005. [5] J.Mora,A.Diez,J.Cruz,andM.Andres,Amagnetostrictivesensorinterrogatedby˝ber gratingsfordc-currentandtemperaturediscrimination, IEEEPhotonicsTechnologyLetters , vol.12,no.12,pp.2000. [6] Q.Wu,Y.Okabe,andF.Yu,structuralhealthmonitoringusing˝berbragg grating, Sensors ,vol.18,no.10,p.3395,2018. [7] J.LengandA.Asundi,on-destructiveevaluationofsmartmaterialsbyusingextrinsic fabryinterferometricand˝berbragggratingsensors, NDT&EInternational ,vol.35, no.4,pp.2002. [8] S.Liang,C.Zhang,W.Lin,L.Li,C.Li,X.Feng,andB.Lin,iber-opticintrinsicdistributed acousticemissionsensorforlargestructurehealthmonitoring, OpticsLetters ,vol.34,no.12, pp.2009. [9] R.Kashyap, Fiberbragggratings .Academicpress,2009. [10] G.MeltzandW.W.Morey,gratingformationandgermanosilicate˝berphotosensi- tivity,in Internationalworkshoponphotoinducedself-organizatione˙ectsinoptical˝ber , vol.1516.InternationalSocietyforOpticsandPhotonics,1991,pp. [11] A.Rosenthal,D.Razansky,andV.Ntziachristos,compactultrasonicde- tectorbasedonapi-phase-shifted˝berbragggrating, OpticsLetters ,vol.36,no.10,pp. 2011. [12] Y.O.Barmenkov,D.Zalvidea,S.Torres-Peiró,J.L.Cruz,andM.V.Andrés,e lengthofshortfabry-perotcavityformedbyuniform˝berbragggratings, OpticsExpress , vol.14,no.14,pp.2006. 102 [13] A.Wada,S.Tanaka,andN.Takahashi,˝bervibrationsensorusingfbgfabry interferometerwithwavelengthscanningandfourieranalysis, IEEESensorsJournal ,vol.12, no.1,pp.2011. [14] L.Hu,G.Liu,Y.Zhu,X.Luo,andM.Han,frequencynoisecancelationinaphase- shifted˝berbragggratingultrasonicsensorsystemusingareferencegratingchannel, IEEE PhotonicsJournal ,vol.8,no.1,pp.2016. [15] G.Cranch,L.Johnson,M.Algren,S.Heerschap,G.Miller,T.Marunda,andR.Holtz,k detectioninrivetedlapjointsusing˝berlaseracousticemissionsensors, OpticsExpress , vol.25,no.16,pp.19467,2017. [16] R.Drever,J.L.Hall,F.Kowalski,J.Hough,G.Ford,A.Munley,andH.Ward,phase andfrequencystabilizationusinganopticalresonator, AppliedPhysicsB ,vol.31,no.2,pp. 1983. [17] Q.Zhang,Y.Zhu,X.Luo,G.Liu,andM.Han,Acousticemissionsensorsystemusinga chirped˝ber-bragg-gratingfabryinterferometerandsmartfeedbackcontrol, Optics Letters ,vol.42,no.3,pp.2017. [18] V.Giurgiutiu,C.Roman,B.Lin,andE.Frankforter,piezo-opticalringsen- sorforenhancedguidedwavestructuralhealthmonitoring, SmartMaterialsandStructures , vol.24,no.1,p.015008,2014. [19] A.Yariv,theoryforguided-waveoptics, IEEEJournalofQuantumElec- tronics ,vol.9,no.9,pp.1973. [20] W.-P.Huang,theoryforopticalwaveguides:anoverview, JOSAA ,vol.11, no.3,pp.1994. [21] T.Erdogan,ibergratingspectra, JournalofLightwaveTechnology ,vol.15,no.8,pp. 1997. [22] V.MizrahiandJ.E.Sipe,propertiesofphotosensitive˝berphasegratings, Journal ofLightwaveTechnology ,vol.11,no.10,pp.1993. [23] M.YamadaandK.Sakuda,Analysisofalmost-periodicdistributedfeedbackslabwaveguides viaafundamentalmatrixapproach, AppliedOptics ,vol.26,no.16,pp.1987. [24] X.Dong,W.Liu,D.Wang,andM.Wu,tudyonfabrycavityconsistingoftwo chirped˝berbragggratings, OpticalFiberTechnology ,vol.18,no.4,pp.2012. [25] S.Zheng,Y.Zhu,andS.Krishnaswamy,iberhumiditysensorswithhighsensitivityand selectivitybasedoninteriornano˝lm-coatedphotoniccrystal˝berlong-periodgratings, SensorsandActuatorsB:Chemical ,vol.176,pp.2013. [26] S.Zheng,M.Ghandehari,andJ.Ou,crystal˝berlong-periodgratingabsorption gassensorbasedonatunableerbium-doped˝berringlaser, SensorsandActuatorsB: Chemical ,vol.223,pp.2016. 103 [27] K.Koo,M.LeBlanc,T.Tsai,andS.Vohra,iber-chirpedgratingfabry-perotsensorwith multiple-wavelength-addressablefree-spectralranges, IEEEPhotonicsTechnologyLetters , vol.10,no.7,pp.1998. [28] Y.Rao,Z.Ran,andC.Zhou,iber-opticfabry-perotsensorsbasedonacombination ofspatial-frequencydivisionmultiplexingandwavelengthdivisionmultiplexingformedby chirped˝berbragggratingpairs, AppliedOptics ,vol.45,no.23,pp.2006. [29] A.Wada,K.Ikuma,M.Syoji,S.Tanaka,andN.Takahashi,ide-dynamic-rangehigh- resolution˝berfabryinterferometricsensorwithchirped˝berbragggratings, Journal ofLightwaveTechnology ,vol.31,no.19,pp.2013. [30] K.Ikuma,A.Wada,S.Tanaka,K.Omichi,andN.Takahashi,˝bersensingwith chirpedfbgfabry-perotinterferometer:vibrationmeasurement,in OFS201222ndInterna- tionalConferenceonOpticalFiberSensors ,vol.8421.InternationalSocietyforOpticsand Photonics,2012,p.84213R. [31] W.Loh,M.Cole,M.N.Zervas,S.Barcelos,andR.Laming,xgratingstructureswith uniformphasemasksbasedonthemoving˝berbeamtechnique, OpticsLetters , vol.20,no.20,pp.1995. [32] K.Numata,J.R.Chen,andS.T.Wu,andfastwavelengthtuningofadynamically phase-lockedwidely-tunablelaser, OpticsExpress ,vol.20,no.13,pp.14243,2012. [33] G.WildandS.Hinckley,Acousto-ultrasonicoptical˝bersensors:Overviewandstate-of- the-art, IEEESensorsJournal ,vol.8,no.7,pp.2008. [34] D.C.Betz,G.Thursby,B.Culshaw,andW.J.Staszewski,Acousto-ultrasonicsensingusing ˝berbragggratings, SmartMaterialsandStructures ,vol.12,no.1,p.122,2003. [35] I.M.Perez,H.Cui,andE.Udd,Acousticemissiondetectionusing˝berbragggratings,in SmartStructuresandMaterials2001:SensoryPhenomenaandMeasurementInstrumentation forSmartStructuresandMaterials ,vol.4328.InternationalSocietyforOpticsandPhotonics, 2001,pp. [36] M.Vidakovic,C.McCague,I.Armakolas,T.Sun,J.S.Carlton,andK.T.Grattan,ibrebragg grating-basedcascadedacousticsensorsforpotentialmarinestructuralconditionmonitoring, JournalofLightwaveTechnology ,vol.34,no.19,pp.2016. [37] H.Tsuda,K.Kumakura,andS.Ogihara,sensitivityofstrain-insensitive˝ber bragggratingsensorsandevaluationofultrasound-inducedstrain, Sensors ,vol.10,no.12, pp.11258,2010. [38] B.W.DrinkwaterandP.D.Wilcox,arraysfornon-destructiveevaluation:A review, NDT&EInternational ,vol.39,no.7,pp.2006. [39] J.L.Rose,guidedwavesinstructuralhealthmonitoring,in KeyEngineering Materials ,vol.270.TransTechPubl,2004,pp. 104 [40] M.Parrilla,J.Anaya,andC.Fritsch,signalprocessingtechniquesforhighaccuracy ultrasonicrangemeasurements, IEEETransactionsonInstrumentationandMeasurement , vol.40,no.4,pp.1991. [41] M.TanterandM.Fink,astimaginginbiomedicalultrasound, IEEETransactionson Ultrasonics,Ferroelectrics,andFrequencyControl ,vol.61,no.1,pp.2014. [42] M.Majumder,T.K.Gangopadhyay,A.K.Chakraborty,K.Dasgupta,andD.K.Bhattacharya, ibrebragggratingsinstructuralhealthmonitorstatusandapplications, Sen- sorsandActuatorsA:Physical ,vol.147,no.1,pp.2008. [43] T.LiuandM.Han,Analysisof c -phase-shifted˝berbragggratingsforultrasonicdetection, IEEESensorsJournal ,vol.12,no.7,pp.2012. [44] G.LiuandM.Han,avelengthlockingofadiodelasertothemaximalslopeofa c -phase- shifted˝berbragggratingforacousticemissiondetection, IEEESensorsJournal ,vol.18, no.22,pp.2018. [45] D.Gatti,G.Galzerano,D.Janner,S.Longhi,andP.Laporta,iberstrainsensorbasedona c -phase-shiftedbragggratingandthepound-drever-halltechnique, OpticsExpress ,vol.16, no.3,pp.2008. [46] B.Dahmani,L.Hollberg,andR.Drullinger,uencystabilizationofsemiconductorlasers byresonantopticalfeedback, OpticsLetters ,vol.12,no.11,pp.1987. [47] J.B.Escobedo,V.Spirin,C.López-Mercado,P.Mégret,I.Zolotovskii,andA.Fotiadi, injectionlockingofthedfblaserthroughanexternalring˝bercavity:Polarizationbehavior, ResultsinPhysics ,vol.6,pp.2016. [48] Y.ZhaoandC.Shu,operationcharacteristicsofaself-injectionseededfabry- perotlaserdiodewithdistributedfeedbackfroma˝bergrating, IEEEPhotonicsTechnology Letters ,vol.9,no.11,pp.1997. [49] W.Liang,V.Ilchenko,A.Savchenkov,A.Matsko,D.Seidel,andL.Maleki,ing- gallery-mode-resonator-basedultranarrowlinewidthexternal-cavitysemiconductorlaser, OpticsLetters ,vol.35,no.16,pp.2010. [50] W.Lewoczko-Adamczyk,C.Pyrlik,J.Häger,S.Schwertfeger,A.Wicht,A.Peters,G.Erbert, andG.Tränkle,rowlinewidthdfb-laserwithopticalfeedbackfromamonolithic confocalfabry-perotcavity, OpticsExpress ,vol.23,no.8,pp.2015. [51] J.-F.Cliche,Y.Painchaud,C.Latrasse,M.-J.Picard,I.Alexandre,andM.Têtu,row bragggratingforactivesemiconductorlaserlinewidthreductionthroughelectricalfeedback, in BraggGratings,Photosensitivity,andPolinginGlassWaveguides .OpticalSocietyof America,2007,p.BTuE2. [52] G.Liu,Y.Zhu,Z.Liu,andM.Han,assivequadraturedemodulationofanultrasonic˝ber- opticinterferometricsensorusingalaserandanacousto-opticmodulator, OpticsLetters , vol.44,no.11,pp.2019. 105 [53] Q.Zhang,N.Liu,T.Fink,H.Li,W.Peng,andM.Han,iber-opticpressuresensorbasedon ?8 -phase-shifted˝berbragggratingonside-hole˝ber, IEEEPhotonicsTechnologyLetters , vol.24,no.17,pp.2012. [54] A.Othonos,iberbragggratings, ReviewofScienti˝cInstruments ,vol.68,no.12,pp. 1997. [55] Q.WuandY.Okabe,ultrasonicphase-shifted˝berbragggratingbalanced sensingsystem, OpticsExpress ,vol.20,no.27,pp.28362,2012. [56] Y.Zhu,L.Hu,Z.Liu,andM.Han,eultrasounddetectionusinganintracavity phase-shifted˝berbragggratinginaself-injection-lockeddiodelaser, OpticsLetters ,vol.44, no.22,pp.2019. [57] F.Wei,F.Yang,X.Zhang,D.Xu,M.Ding,L.Zhang,D.Chen,H.Cai,Z.Fang,andG.X¼ia, tzlinewidthreductionofadfbdiodelaserusingself-injectionlockingwitha˝ber bragggratingfabry-perotcavity, OpticsExpress ,vol.24,no.15,pp.17415,2016. [58] Y.Zhu,Q.Zhang,G.Liu,X.Luo,andM.Han,abrysensorusingcascadedchirped ˝berbragggratingswithoppositechirpdirections, IEEEPhotonicsTechnologyLetters , vol.30,no.16,pp.2018. [59] T.ErdoganandV.Mizrahi,izationofuv-inducedbirefringenceinphotosensitive ge-dopedsilicaoptical˝bers, JOSAB ,vol.11,no.10,pp.1994. [60] P.Lu,D.Grobnic,andS.J.Mihailov,izationofthebirefringencein˝berbragg gratingsfabricatedwithanultrafast-infraredlaser, JournalofLightwaveTechnology ,vol.25, no.3,pp.2007. [61] S.Rashleigh,iginsandcontrolofpolarizatione˙ectsinsingle-mode˝bers, Journalof LightwaveTechnology ,vol.1,no.2,pp.1983. [62] M.Hanawa,T.-Y.Kim,T.Yamada,S.-J.Kim,C.-S.Park,andK.Nakamura,in- gencereductiononcascaded˝berbragggratings, Proceedingsofthe2006IEICEGeneral Conference,C-3-107 ,2006. [63] M.Hanawa,T.Yamada,T.-Y.Kim,C.-S.Park,andK.Nakamura,olarizationdependency measurementsonbirefringence-reducedcascadedfbgs, Proceedingsofthe2006IEICE ElectronicsSociety,C-3-44 ,2006. [64] L.L.Sánchez-Soto,J.J.Monzón,andG.Leuchs,Themanyfacetsofthefabry EuropeanJournalofPhysics ,vol.37,no.6,p.064001,2016. [65] J.-R.LeeandH.Tsuda,Acousto-ultrasonicsensingusingcapsular˝brebragggratingsfor temperaturecompensation, MeasurementScienceandTechnology ,vol.17,no.11,p.2920, 2006. [66] J.Wee,B.Wells,D.Hackney,P.Bradford,andK.Peters,signalamplitudein ˝berbragggratingdetectionoflambwavesusingremotebonding, AppliedOptics ,vol.55, no.21,pp.2016. 106 [67] M.Islam,M.M.Ali,M.-H.Lai,K.-S.Lim,H.Ahmad etal. ,offabry-perot interferometer˝ber-opticsensorsandtheirapplications:areview, Sensors ,vol.14,no.4, pp.2014. [68] J.F.Dorighi,S.Krishnaswamy,andJ.D.Achenbach,tabilizationofanembedded˝ber opticfabry-perotsensorforultrasounddetection, IEEETransactionsonUltrasonics,Ferro- electrics,andFrequencyControl ,vol.42,no.5,pp.1995. [69] A.Dandridge,A.B.Tveten,andT.G.Giallorenzi,demodulationschemefor ˝beropticsensorsusingphasegeneratedcarrier, IEEETransactionsonMicrowaveTheory andTechniques ,vol.30,no.10,pp.1982. [70] K.A.Murphy,M.F.Gunther,A.M.Vengsarkar,andR.O.Claus,phase-shifted, extrinsicfabryoptical˝bersensors, OpticsLetters ,vol.16,no.4,pp.1991. [71] I.Read,P.Foote,andS.Murray,˝breacousticemissionsensorfordamagedetection incarbon˝brecompositestructures, MeasurementScienceandTechnology ,vol.13,no.1, p.N5,2001. [72] B.Dong,M.Han,andA.Wang,Two-wavelengthquadraturemultipointdetectionofpartial dischargeinpowertransformersusing˝berfabry-perotacousticsensors,in FiberOptic SensorsandApplicationsIX ,vol.8370.InternationalSocietyforOpticsandPhotonics, 2012,p.83700K. [73] H.Liao,P.Lu,L.Liu,S.Wang,W.Ni,X.Fu,D.Liu,andJ.Zhang,demodulation ofshort-cavityfabryinterferometricacousticsensorswithtwowavelengths, IEEE PhotonicsJournal ,vol.9,no.2,pp.2017. [74] R.Pappu,Acousticemissiondetectionusingoptical˝bresensorsforaerospaceapplications, Ph.D.dissertation,AstonUniversity,2012. [75] R.Ulrich,S.Rashleigh,andW.Eickho˙,birefringenceinsingle-mode ˝bers, OpticsLetters ,vol.5,no.6,pp.1980. [76] R.UlrichandA.Simon,olarizationopticsoftwistedsingle-mode˝bers, AppliedOptics , vol.18,no.13,pp.1979. [77] N.Stan,D.Bailey,S.Chadderdon,S.Webb,M.Zikry,K.Peters,R.Selfridge,andS.Schultz, dynamicrangeofa˝brebragggratingedge-˝lteringinterrogatorwithapro- portionalcontrolloop, MeasurementScienceandTechnology ,vol.25,no.6,p.065206, 2014. [78] H.Wei,C.Tao,Y.Zhu,andS.Krishnaswamy,iberbragggratingdynamicstrainsensor usinganadaptivere˛ectivesemiconductoropticalampli˝ersource, AppliedOptics ,vol.55, no.10,pp.2016. [79] H.Tsuda,E.Sato,T.Nakajima,H.Nakamura,T.Arakawa,H.Shiono,M.Minato, H.Kurabayashi,andA.Sato,Acousticemissionmeasurementusingastrain-insensitive ˝berbragggratingsensorundervaryingloadconditions, OpticsLetters ,vol.34,no.19,pp. 2009. 107 [80] J.Wee,D.Hackney,P.Bradford,andK.Peters,imentalstudyondirectionalityofultra- sonicwavecouplingusingsurface-bonded˝berbragggratingsensors, JournalofLightwave Technology ,vol.36,no.4,pp.2018. [81] Q.Wu,Y.Okabe,K.Saito,andF.Yu,distributionpropertiesofaphase-shifted ˝berbragggratingsensortoultrasonicwaves, Sensors ,vol.14,no.1,pp.2014. [82] E.D.Black,Anintroductiontoverlaserfrequencystabilization, American JournalofPhysics ,vol.69,no.1,pp.2001. 108