University, Shenyang, China b State Key Laboratory of Synthetical Automation for Process

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1 This article was downloaded by: [University of Montana] On: 06 April 2015, At: 21:00 Publisher: Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: Registered office: Mortimer House, Mortimer Street, London W1T 3JH, UK Instrumentation Science & Technology Publication details, including instructions for authors and subscription information: Characterization of Temperature and Strain Using a Tilted Fiber Bragg Grating Qi Wang ab, Xue Li a, Xuxing Zhao a & Chengwu Zhao a a College of Information Science and Engineering, Northeastern University, Shenyang, China b State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China Accepted author version posted online: 07 Nov 2014.Published online: 20 Jan Click for updates To cite this article: Qi Wang, Xue Li, Xuxing Zhao & Chengwu Zhao (2015) Characterization of Temperature and Strain Using a Tilted Fiber Bragg Grating, Instrumentation Science & Technology, 43:2, , DOI: / To link to this article: PLEASE SCROLL DOWN FOR ARTICLE Taylor & Francis makes every effort to ensure the accuracy of all the information (the Content ) contained in the publications on our platform. However, Taylor & Francis, our agents, and our licensors make no representations or warranties whatsoever as to the accuracy, completeness, or suitability for any purpose of the Content. Any opinions and views expressed in this publication are the opinions and views of the authors, and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content should not be relied upon and should be independently verified with primary sources of information. Taylor and Francis shall not be liable for any losses, actions, claims, proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or howsoever caused arising directly or indirectly in connection with, in relation to or arising out of the use of the Content. This article may be used for research, teaching, and private study purposes. Any substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing, systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &

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3 Instrumentation Science and Technology, 43: , 2015 Copyright # Taylor & Francis Group, LLC ISSN: print/ online DOI: / CHARACTERIZATION OF TEMPERATURE AND STRAIN USING A TILTED FIBER BRAGG GRATING Qi Wang, 1,2 Xue Li, 1 Xuxing Zhao, 1 and Chengwu Zhao 1 1 College of Information Science and Engineering, Northeastern University, Shenyang, China 2 State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China & The simultaneous measurement of multiple parameters by tilted fiber Bragg grating is an emerging area of research. The tilted fiber Bragg grating is a special short-period fiber grating in which the plane of the grating is intentionally tilted with respect to the fiber axis. The angle between the grating plane and fiber axis enables the transmission spectrum of the fiber to contain both core and cladding mode information which is a unique advantage. This article describes simultaneous measurements of temperature and strain using a tilted fiber Bragg grating. Keywords fiber optic sensors, strain, temperature, tilted fiber Bragg grating INTRODUCTION The demand for multiple parameter measurements has grown rapidly. In industrial processes, multiple parameters usually exist simultaneously, so sensors for simultaneous measurement of these parameters need to be developed. At present, the methods to measure multiple parameters use multiple sensors. After the corresponding data are recorded and integrated, the desired results are achieved. Alternatively, through a complex treatment process on some devices, such as a fiber Bragg grating, multiple parameter measurements can be achieved. However, these methods have disadvantages such as complicated operation, high cost, heavy workload, and other unfavorable factors. This article reports a method to simultaneously measure temperature and strain using a single tilted fiber Bragg grating. The difficulties in operation and costs using such a device would be greatly reduced. Address correspondence to Qi Wang, College of Information Science and Engineering, Northeastern University, Shenyang , China. wangqi@ise.neu.edu.cn Color versions of one or more of the figures in the article can be found online at com/list.

4 Characterization of Temperature and Strain Using a TFBG 245 Theoretical and experimental researches on tilted fiber Bragg gratings were first carried out in [1] Erdogan used coupled-mode theory to deduce mode propagation characteristics on the tilted fiber Bragg grating to calculate the influence of the grating angle on the grating reflectivity and analyzed cladding mode resonant modes on a tilted fiber Bragg grating. In 2001, Li [2] applied a volume=current method to analyze outcoupled radiation from tilted fiber gratings. Compared with coupled-mode theory, the results provided by the volume current method were more explicit and allowed direct simple physical interpretation. In 2000, Liu [3] conducted theoretical research on the reflective properties of the tilted fiber Bragg grating and deduced the influence of tilt angle of the grating planes upon the grating reflectivity. In 2002, Jauregui [4] studied the phase mask angle and the tilt angle of the grating planes in the production of tilted fiber Bragg grating. In 2004, Zhao [5] produced a particular reflection spectrum grating, which had a flat reflection peak between 1551 nm and 1555 nm, by writing multiple angles on the same tilted fiber Bragg grating. In 2006, Huy [6] tested samples, whose tilt angles were 0, 4,8,12, and 16 using a single-mode fiber tilted fiber Bragg grating. In 2006, Zhou [7] increased the angle to 81.3 to obtain high refractive index sensitivity and low thermal cross sensitivity, and the refraction sensitivity was three times the value of a liquefied petroleum gas sensor. In 2008, Lu [8] conducted numerical simulation of coupled-mode theory and found that within 1 45 the radiation coupling wavelength had polarization dependent properties and showed the larger the tilt angle, the stronger the grating dependence. This work showed that the excellent characteristics of tilted fiber Bragg grating may be used for sensing. In 2014, Gu [9] proposed a simple and compact reflective refractometer based on a tilted fiber Bragg grating inscribed in thin-core fiber. In 2014, Yang [10] realized magnetic field sensing based on a tilted fiber Bragg grating coated with nanoparticle magnetic fluid. In 2014, Melo [11] proposed and demonstrated a concentration sensor based on a tilted fiber Bragg grating for monitoring anions. This article presents a sensor that allows simultaneous temperature and strain measurement based on a tilted fiber Bragg grating. The temperature and strain at the same position can be measured simultaneously relying on different temperatures and strain sensitivities of core peaks and cladding peaks in the transmission spectrum of tilted fiber Bragg grating. THEORY The tilted fiber Bragg grating possesses unique sensing properties since its core peaks and cladding peaks have different sensing characteristics for parameters because of its special physical structure. The transmission

5 246 Q. Wang et al. characteristics of the tilted fiber Bragg grating vary due to changes in the external environment; the temperature is one of these important influences. When the ambient temperature changes, thermal expansion causes the grating period change. In addition, thermo-optic effects also have an impact on the refractive index of the fiber grating. The changes of the reflection wavelength of the tilted fiber Bragg grating caused by temperature variations can be expressed as: Dk B ¼ða þ fþdt k B ; ð1þ where a ¼ is thermal expansion coefficient of fiber, which describes the relationship between the pitch of grating and temperature and f ¼ 1 n is the thermo-optic coefficient of fiber, which describes the relationship between temperature and refractive index of fiber. For a tilted fiber Bragg grating, core modes are coupled with core modes and cladding modes with core modes coupled with reverse transfer cladding mode. The grating period and effective refractive index of core mode and cladding mode changes are a function of temperature. The temperature sensitivity of the core mode resonance wavelength can be expressed as: dk Bragg dt ¼ 2 dn eff ;core dt K g cos h þ n eff ;core cos h dk g dt : ð2þ The temperature sensitivity of the cladding mode resonance wavelength can be expressed as: dk i clad dt ¼ dn! eff ;core þ dni eff ;clad Kg dt dt cos h þ 1 dk g cos h dt n eff ;core þ neff i ;clad : ð3þ Thus, the difference between Bragg resonance wavelength shift and each order cladding mode resonance wavelength shift caused by small changes in temperature can be expressed as: "! dk dt ¼ dk B dt dki clad dt ¼ 1 cosh K dn eff ;core g dt dni eff ;clad þ dk # g dt dt n eff ;core neff i ;clad ð4þ where k B and k i clad are the core fundamental mode resonant wavelengths and the i-th cladding mode resonant wavelength and n eff, core and neff i ;clad are the effective refractive indices of the core fundamental mode and the i-th effective refractive index of the cladding mode.

6 Characterization of Temperature and Strain Using a TFBG 247 If a tilted fiber Bragg grating is placed on the substrate whose thermal expansion coefficient is a s, the changes of the reflected wavelength of tilted fiber Bragg grating caused by the temperature changing through Equation (1) can be expressed as: Dk B k B ¼½ða s aþð1 p e ÞþfŠDT ; ð5þ where p e ¼ n 2 eff ½p 12 lðp 12 þ p 11 ÞŠ=2 is effective elastic coefficient of the fiber, p 11 and p 12 are elastic coefficients of fiber, and l is Poisson s ratio of fiber. When the fiber is subjected to longitudinal strain, the grating period K changes and the other two directions perpendicular to the fiber axis will generate strain, whose transverse strain is le z. The fiber is an isotropic material and can be considered to have no shear strain. Under strain De, the Bragg wavelength and the i-th cladding mode central wavelength shift can be expressed as: Dk B ¼ 2n eff ;core cos h Dk 0 þ 2K cos eff De ¼ k B ð1 p e ÞDe ðni eff ;core þ ni eff ;clad cos þ K ð@neff i ;core þ ni eff ;clad Þ! cos De ¼ k i clad ð1 pi cld ÞDe; where p e and pcld i are the effective elastic coefficients of the fiber and of the i-th cladding mode. The effective elastic coefficient of the corresponding core and the i-th cladding mode may be calculated by changes of the effective refractive index of core mode and cladding mode: Dn ¼ 1 2 n3 ½p 12 lðp 11 þ p 12 ÞŠe z ¼ p e ne z ; ð6þ ð7þ ð8þ where p e ¼ 1 2 n2 ½p 12 lðp 11 þ p 12 ÞŠ is the effective elastic coefficient of fiber. The fiber grating center wavelength shift caused by the longitudinal strain can be expressed as: Dk ¼ 2nDK þ 2KDn ¼ k 0 ð1 p e Þe z : ð9þ The effective elastic coefficients of respective modes are different, so in the case of the same strain, the wavelength shifts of the respective modes are different.

7 248 Q. Wang et al. PARAMETER OPTIMIZATION The main difference between a tilted fiber Bragg grating and a common Bragg fiber is there is a tilt angle h between the grating plane and the fiber axis, which is the most important factor that makes the spectral characteristics different from an ordinary grating. The effects of tilted fringes to the spectrum can be described by the effective fringe visibility s (h): RR s ðþ h ¼ s core exp i 2p K tanðþet h ðx; yþet ðx; yþdxdy RR e T ðx; yþet ðx; yþdxdy : ð10þ core FIGURE 1 Transmission spectra with h ¼ 1. FIGURE 2 Transmission spectra with h ¼ 4.

8 Characterization of Temperature and Strain Using a TFBG 249 FIGURE 3 Transmission spectra with L ¼ 10 mm. The transmission spectra of different tilt angles of tilted fiber Bragg grating were simulated. The impact of tilt angles can be seen visually through its spectrum. Figures 1 and 2 show the transmission spectra of tilted fiber Bragg grating, whose tilt angles changes from 1 4. As shown in Figures 1 and 2, with an increase in tilt angle, more light in the fiber core is coupled to the cladding and converted to the radiation mode. When the tilt angle is 3, the phenomenon reaches a maximum value, and decreases at higher angles. The transmittance increases above 3, because a decrease of the coupling coefficient reduces light coupled into cladding or converted to radiation mode. When the angle is 3, the FIGURE 4 Transmission spectra with L ¼ 22 mm.

9 250 Q. Wang et al. FIGURE 5 Transmission spectra with D ¼ core peak and cladding peaks in the spectrum is relatively clear, which is the optimum for the peak wavelength detection. The grating length is one of the main parameters to affect spectral characteristics. The grating length not only affects its spectral characteristics, but also is decided by the production process, the application environment, and other factors. Figures 3 and 4 show the transmission spectra of different grating lengths of the tilted fiber Bragg grating. With an increase in grating length, more light in the fiber core is coupled into the cladding, so the transmission is smaller. The tilt angle of grating plane and modulation depth of refractive index determine the coupling efficiency and the bandwidth of light leakage. Therefore, the modulation depth of the FIGURE 6 Transmission spectra with D ¼

10 Characterization of Temperature and Strain Using a TFBG 251 refractive index is also an important parameter to affect the spectral characteristics. As can be seen from Figures 5 and 6, with an increase of refractive index modulation depth, the transmissivity is smaller, which shows more light transmitted in the fiber core is coupled to the cladding and converted to the radiation mode. EXPERIMENTAL MEASUREMENTS The simultaneous measurement of temperature and strain experimental system based on tilted fiber Bragg grating was constructed, as shown in Figure 7. The tilted fiber Bragg grating is fixed to the cantilever, whose left side is fixed and right side provides strain by a micrometer fixed in the experimental apparatus. The tilted fiber Bragg grating is placed in a water bath and a platinum resistance thermometer monitors the temperature. During the experiment, light is emitted from an Amplified Spontaneous Emission (ASE) source and is received by Optical Spectrum Analyzers (OSA) to obtain a signal spectrum after passing the tilted fiber Bragg grating. The temperature and strain is measured by the changes of the tilted fiber Bragg grating transmission spectra. After the tilted fiber Bragg grating was attached to the cantilever, a transmission spectrum of tilted fiber Bragg grating was obtained, as shown in Figure 8. Data were extracted from the near wavelength of the core peak FIGURE 7 Experimental schematic.

11 252 Q. Wang et al. FIGURE 8 Transmission spectrum of tilted fiber Bragg grating measured after bonding to the cantilever. and ghost peak, and then filtered separately before using a Gaussian fitting method for spectral data processing. The peak points of the core peak and ghost peak were obtained to monitor changes in the spectrum. The experimental setup in Figure 7 can be used to perform temperature measurements. The micrometer is fixed at a predetermined position and remains constant while monitoring temperature in order to eliminate the influence of strain. During these measurements, only the temperature changes and the other parameters remain the same, so their effects can be eliminated. A water sample was heated to approximately 80 C and added to the tank of the experimental device, guaranteeing the cantilever was not impacted during the water injection. The platinum resistance thermometer was then placed near the tilted fiber Bragg grating so it did not contact other objects. The water was allowed to cool; data were collected at 1 C intervals. When the temperature changed, the core peak and the ghost peak had significant movements. According to the experimental results, the fitted curve of ghost peak wavelength versus temperature is shown in Eq. (11): y ¼ 0:03818x þ 1561: ð11þ The fitted curve of core peak wavelength versus temperature is shown in Eq. (12): y ¼ 0:03719x þ 1563: ð12þ

12 Characterization of Temperature and Strain Using a TFBG 253 When the temperature changed, the slopes of the core peak and the ghost peak were and , respectively, which denote the temperature sensitivity of the core peak and ghost peak. Therefore, the temperature characteristic of cladding mode and core mode of tilted fiber Bragg grating are almost the same. To measure strain, the other conditions remained the same; the strain was generated only by changing values of the micrometer. First, the micrometer was placed at one end, and then gradually moved to the other end and data were recorded every 0.5 mm. According to the experimental results, the fitted curve of ghost peak wavelength versus strain is shown in Eq. (13): y ¼ 0:06085x þ 1563: ð13þ The fitted curve of core peak wavelength versus strain is shown in Eq. (14): y ¼ 0:05282x þ 1565: ð14þ It is obvious that when strain changes, the slopes of the ghost peak and the core peak are and , which demonstrates the sensitivity of the core peak and ghost peak. For a different slope of the core peak and a ghost peak for strain, the strain characteristics of cladding mode and core mode of tilted fiber Bragg grating are different. These two factors caused drift of the core mode and the cladding mode denoted as Dk core and Dk cladding. The relationship is expressed in a matrix as follows: Dk core ¼ Dk cladding e T K core;e K cladding;e K core;t K cladding;t ; ð15þ where e is the strain, T is the temperature, K core,e and K cladding,e are the strain sensitivity coefficients of core mode and cladding mode, and K core,t, K core,e, and K cladding,e are the temperature sensitivity coefficients of the core mode and cladding mode. Once the sensitivity of each factor and the wavelength shift were measured, the size of temperature and strain were calculated. CONCLUSIONS The structural characteristics of the tilted fiber Bragg grating were studied to simultaneously measure temperature and strain. Based on numerical simulation, analysis of spectral characteristics, and temperature and strain characteristics, a tilt angle of 3 is the best for simultaneous temperature

13 254 Q. Wang et al. and strain measurements. The transmittance was smaller with an increase in the length of the grating, and the transmittance decreased with an increase in the modulation depth of refractive index. Combined with the production process and other factors, a tilt angle of 3, grating length of 20 mm, and a refractive index difference of of tilted fiber Bragg grating were selected. The cantilever and water bath conditions were designed to measure strain and temperature and the two parameters were measured and analyzed simultaneously. FUNDING This work was partly supported by the National Natural Science Foundation of China ( , ), the Fundamental Research Funds for the Central Universities (N ), the Specialized Research Fund for the Doctoral Program of Higher Education of China ( ), the China Postdoctoral Science Foundation funded project ( , 2013T60293), the State Key Laboratory of Synthetical Automation for Process Industries (2013ZCX09), and the Natural Science Foundation of Hebei Province (F ). REFERENCES 1. Erdogan, T.; Sipe, J.E. Tilted Fiber Phase Gratings. J. Opt. Soc. Amer. A 1996, 13(2), Li, Y.; Froggatt, M.; Erdogan, T. Volume Current Method for Analysis of Tilted Fiber Gratings. J. Lightwave Technol. 2001, 19(10), Liu, C. A Study on Ref Lection Property of Fiber Tilted-Grating. Study Opt. Commun. 2000, 4, Jauregui, C.; Quintela, A.; Echevarria, J.; Conde, O.M.; Lopez-Higuera, J.M. Experimental Characterization of Tilted Fiber Bragg Gratings. Optical Fiber Sensors Conference Technical Digest, Portland, OR, May 6 10; IEEE: New York, Zhao, Z.; Zhang, S.; Yu, Y.; Zhuo, Z.; Zhang, J.; Zheng, W.; Zhang, Y. Fabrication of a Tilted Fiber Bragg Grating with a Designed Ref Lection Spectrum Profile. Opt. Lett. 2004, 29(3): Huy, M.C.P.; Laffont, G.; Dewynter, V.; Ferdinand, P.; Labonté, L.; Pagnoux, D.; Roy, P.; Blanc, W.; Dussardier, B. Tilted Fiber Bragg Grating Photowritten in Micro Structured Optical Fiber for Improved Refractive Index Measurement. Optics Express. 2006, 14(22), Zhou, K.; Zhang, L.; Chen, X., Bennion, I. Optic Sensors of High Refractive-Index Responsivity and Low Thermal Cross Sensitivity that Use Fiber Bragg Gratings of >80 Tilted Structures. Opt. Lett. 2006, 31(9), Lu, S.; Xu, O.; Feng, S.; Dong, X.; Jian, S. Effects of Tilt Angle on Blazed Fiber Grating Radiation Mode Coupling Wavelength. Opt. Dev. 2008, 5, Gu, B.B.; Qi, W.L.; Zheng, J.; Zhou, Y.Y.; Shum, P. P.; Luan. F. Simple and Compact Reflective Refractometer Based on Tilted Fiber Bragg Grating Inscribed in Thin-Core Fiber. Opt. Lett. 2014, 39(1), Yang, D.X.; Du, L.; Xu, Z.Q.; Jiang, Y.J.; Xu, J.; Wang, M.R.; Bai, Y.; Wang, H.Y. Magnetic Field Sensing based on Tilted Fiber Bragg Grating Coated with Nanoparticle Magnetic Fluid. Appl. Phys. Lett. 2014, 104(6), Melo, L.B.; Rodrigues, J.M.M.; Farinha, A.S.F.; Marques, C.A.; Bilro, L.; Alberto, N.; Tome, J.P.C.; Nogueira, R.N. Concentration Sensor Based on a Tilted Fiber Bragg Grating for Anions Monitoring. Opt. Fiber Technol. 2014, 20(4),

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