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Simultaneous pressure and temperature measurement using Hi-Bi fiber Bragg gratings
Optics Communications 228 (2003) 99–105 www.elsevier.com/locate/optcom
Simultaneous pressure and temperature measurement using Hi-Bi fiber Bragg gratings Guanghui Chen a,c, Liying Liu a, Hongzhi Jia b, Jimin Yu c, Lei Xu a, Wencheng Wang a,* a
State Key Lab for Advanced Photonic Materials and Devices, Department of Optical Science and Engineering, Fudan University, 220 Handan Road, Shanghai 200433, China b College of Optics and Electronics Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China c No. 23 Research Institute of China Electronics Technology Group Corporation, Shanghai 200437, China Received 22 June 2003; received in revised form 25 September 2003; accepted 26 September 2003
Abstract The fiber Bragg grating has been written in a novel high birefringence (Hi-Bi) fiber by phase-mask method. The temperature and gas pressure characteristics of the fiber Bragg grating were analyzed and demonstrated quantitatively. Two Bragg wavelengths corresponding to the fast-axis mode and slow-axis mode shift linearly with temperature change and gas pressure change. Experimental results showed that this Hi-Bi fiber Bragg grating could be used to measure temperature and gas pressure simultaneously with a deviation of less than 1 °C and 0.5 MPa from the set values respectively. Ó 2003 Elsevier B.V. All rights reserved. PACS: 42.81.Pa Keywords: Hi-Bi fiber; Fiber Bragg grating; Bragg wavelength; Sensors; Pressure measurement; Temperature measurement
1. Introduction Fiber Bragg grating (FBG) sensors have generated great interests in recent years because of their many industrial applications [1]. They are particularly suitable for monitoring the high gas pressure or fluid pressure in hostile environments
*
Corresponding author. Tel.: +86-21-65642961; fax: +86-2165641344. E-mail address: [email protected] (W. Wang).
due to being passive and intrinsically safe [2,3]. As a kind of wavelength-encoding optical fiber sensor, FBG sensors have many significant advantages, such as simplicity in fabrication, independent of overall system light level. But, in general, the Bragg wavelength shift in a FBG comes from two different effects, i.e., temperature and strain induced by pressure. It is hard to distinguish these two effects of the parameters when only the wavelength shift is measured. Many works to discriminate the strain and temperature effects have been carried out, such as superimposed
0030-4018/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2003.09.079
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G. Chen et al. / Optics Communications 228 (2003) 99–105
gratings [4], hybrid FBG/long-period gratings [5], and different polymer-coated fiber Bragg gratings [6]. Bragg gratings written in Hi-Bi optical fibers can play an important part in this area. Bragg gratings written in Hi-Bi optical fibers have been demonstrated [7] and used to compose some kinds of optical fiber devices, such as optical fiber lasers [8,9], compensators of polarization mode dispersion [10] and sensors [11,12]. In this letter, we introduce a Bragg grating written in a novel Hi-Bi optical fiber and demonstrate a grating sensor being capable of simultaneous measurement of gas pressure and temperature using this Hi-Bi optical fiber Bragg gratings.
2. Principle of Hi-Bi fiber Bragg grating sensor When a grating is formed in a Hi-Bi fiber, because of the slight difference of effective refractive indices for the two orthogonal polarization modes, there will be two reflective peaks at slight different wavelengths, while the shapes of two reflective spectra are similar. Their Bragg wavelengths can be written as kFB ¼ 2nF K;
ð1Þ
kSB ¼ 2nS K;
ð2Þ
It has a GeO2 -doped silica core and a circular silica cladding. This fiber has much higher birefringence (7.2 104 ) comparing with other kinds of fibers such as PANDA fiber (4.5 104 ) and bow-tie fiber (5.5 104 ) [11–13], because its two stress-inducing elements are closer to the core (see Fig. 1). In this case, the BG and the BSo can be neglected. Therefore, when there is no extra radial force applied on the fiber, the total birefringence at the core center is expressed by BS ¼ a T G E C ðTS T Þ=½2 ð1 tÞ;
ð4Þ
where aT is the difference of thermal coefficient between cladding and stress-inducing elements, G is a coefficient related to the shapes and positions of the two stress-inducing elements, E is the YoungÕs modulus, C is the photo-elastic constant, t is the PoissonÕs ratio, TS is the softening temperature of the fiber core, and T is the surrounding temperature of the fiber. From (1), (2) and (4), it can be inferred that two Bragg wavelengths of the Hi-Bi fiber grating would have different temperature sensitivities. According to [14], when the ambient temperature is changed by an amount DT , the birefringence is changed by
where kFB and nF ; kSB and nS are the Bragg wavelengths and the effective refractive indices corresponding to the fast-axis mode and slow-axis mode, K is the period of grating. The modal birefringence B ¼ nS nF of Hi-Bi fibers, produced by internal origins, is described as [13] B ¼ BG þ BSo þ BS ;
ð3Þ
where BG is the geometrical component induced by the shape difference of the core, BSo is the component induced by the thermal expansion difference of the asymmetrical core, and BS is the component induced by the stress-inducing elements. The Hi-Bi optical fiber we used is a new kind of Hi-Bi fiber called ‘‘quasi-rectangle’’ (China patent no. ZL95243466) because of the shapes of two stress-inducing elements of B2 O3 -doped silica glass. This fiber was fabricated by MCVD method.
Fig. 1. The cross-section of the ‘‘quasi-rectangle’’ Hi-Bi fiber. Two dark spots are stress-inducing elements.
G. Chen et al. / Optics Communications 228 (2003) 99–105
DBT ¼ ðDT =ðT TS ÞÞ B:
ð5Þ
In the temperature range we used for the experiments (from )50 to 80 °C), DBT is estimated to be )0.14B. The birefringence of the Hi-Bi fiber will also be changed by the hydrostatical pressure applied on it. However, for the fiber we used, the pressureinduced birefringence would be far less than that induced by the stress during the fabrication if the pressure is not too high. This conclusion can be verified by the result of previous analysis [14,15], for a bare fiber, the pressure-induced birefringence DBp can be expressed by DBp ¼ ½E2 ð1 þ t1 Þð1 2t1 Þ E1 ð1 þ t2 Þð1 2t2 Þ þ E2 ðt2 t1 Þð1 2t1 ÞP B =½E1 E2 ðTS T Þ aT ;
ð6Þ
where t1 and t2 , E1 and E2 are the PoissonÕs ratios, YoungÕs moduli of the cladding and the stress-inducing elements, P is the hydrostatical pressure applied on the fiber. For our fiber, the typical data are t1 ¼ 0:17, t2 ¼ 0:22, E1 ¼ 72:5 103 MPa, E2 ¼ 50.75 103 MPa, TS T ¼ 900 K and aT ¼ 15:6 107 K1 . When the pressure applied on the fiber is 10 MPa as in our experiments, the pressure-induced birefringence DBp was estimated to be about 1:7 102 B, less than that induced by temperature. This means the two Bragg wavelengths of Hi-Bi fiber grating would have slightly different sensitivities to the hydrostatical pressure at a fixed temperature. Based on the above analyses, we proposed a sensor using Hi-Bi fiber Bragg gratings, which can measure temperature and hydrostatical pressure simultaneously. According to the wavelength sensing principle of fiber Bragg gratings and ignoring the cross-sensitivities between two parameters, the shifts of two Bragg wavelengths, DkFB and DkSB , subjected to the applied pressure and temperature are given by DkFB ¼ KFT DT þ KFP DP ;
ð7Þ
DkSB ¼ KST DT þ KSP DP ;
ð8Þ
where KFT and KST are the temperature sensitivities of the two Bragg wavelengths corresponding to the fast-axis mode and slow-axis mode, KFP and KSP are the hydrostatical pressure sensitivities. It can
101
be seen from the above two equations that the applied hydrostatical pressure and temperature were uniquely determined if the shifts of two Bragg wavelengths in Hi-Bi fiber were measured.
3. Experiments and results Fiber Bragg gratings had been written in a new kind of Hi-Bi fiber that was fabricated by MCVD method. This novel fiber has a GeO2 -doped silica core and a circular silica cladding. Its birefringence results from two borosilicate elements (referred as stress-inducing element) beside the fiber core (see Fig. 1). The two elements have a different coefficient of thermal expansion from their surroundings, so that when they cool down to room temperature after manufacturing process ends, anisotropic stress is set up across the core of the fiber. The fiber we used has a birefringence as large as 7:2 104 . Before written Bragg gratings, the fiber was loaded with H2 under about 100 bars at room temperature for 30 days in order to increase its photosensitivity. The H2 loaded Hi-Bi fiber was exposed to the KrF excimer laser beam (248 nm, 200 mJ/cm2 ) through a nulled-zero-order phase mask (Km ¼ 1075:4 nm). Fig. 2 shows the reflection spectrum of the FBG, which was recorded with an optical spectra analyzer (ADVANTEST Q8384). It can be seen from Fig. 2 that the FBG has two similar reflection peaks corresponding to the fast-axis mode and slow-axis mode respectively. Their wavelengths were measured to be 1556.82 and 1557.59 nm at 20 °C. The difference of the wavelengths is 0.77 nm. The temperature characteristics of the FBG were studied experimentally. The light from a broad-band source was launched into the FBG through a coupler with a normal single-mode fiber. An optical spectrum analyzer (ADVANTEST Q8384) was used to measure the reflection spectra. The FBG was first placed in a temperature-circulate box and cooled to )50 °C. Then the grating temperature was increased successively to different temperature and left it at the temperature for about 10 min for the measurements. The optical spectra analyzer recorded two Bragg wavelengths at
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G. Chen et al. / Optics Communications 228 (2003) 99–105
Fig. 2. The reflection spectrum of a FBG written in the ‘‘quasi-rectangle’’ Hi-Bi fiber. The left peak, kFB ¼ 1556:82 nm, is corresponding to the fast-axis mode, the right one, kSB ¼ 1557:59 nm, is corresponding to the slow-axis mode.
different temperature. When the temperature rose from )50 to 80 °C, both Bragg wavelengths redshifted linearly, but the difference of the two Bragg wavelengths decreased (see Fig. 3). The temperature sensitivities of these two Bragg wavelengths,
corresponding to the fast-axis mode and slow-axis mode, were measured to be KFT ¼ 0:0093 nm/°C and KST ¼ 0:0088 nm/°C, respectively. The experimental set-up for the hydrostatical pressure measurement with the FBG was shown in
Fig. 3. The temperature dependence of the two Bragg wavelengths under a normal atmosphere. (d) Slow-axis mode, (N) fast-axis mode, lines are the linear fittings. Inset: Bragg wavelength difference kSB kFB dependence on the surrounding temperature.
G. Chen et al. / Optics Communications 228 (2003) 99–105
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the errors of the barometer. The pressure sensitivities of both Bragg wavelengths were almost the same, KPF ¼ KSF ¼ 0:020 nm/MPa. From the above equations and data, it is found that for the FBG written in the Hi-Bi fiber, the applied gas or fluid pressure (in MPa) and temperature (in °C) could be obtained from the following equations:
Fig. 4. The FBG was loosely sheathed in a glass capillary in order to avoid bending under the gas flow. Then the FBG with the glass capillary was put in a gasproof steel pipe, which was filled with high-pressure nitrogen. The pressure of the gas surrounding the FBG was changed through a pressure reducer. The reflection spectra were recorded for the pressure change from 0 to 10 MPa, see Fig. 5 for the measurement results. The two curves showed good linearity and the linear fit error was less than 0.3%, which mainly came from
DT ¼ 2000ðDkFB DkSB Þ;
ð9Þ
DP ¼ 930DkSB 880DkFB :
ð10Þ
Fig. 4. The experimental set-up for demonstrating the gas pressure sensitivities of the FBG.
1557.0
∆λSB/∆P=0.020 (nm/MPa)
∆λFB/∆P=0.020 (nm/MPa) 0.9
λSB-λ FB (nm)
Bragg wavelength (nm)
1557.5
1556.5
0.8
0.7
0.6
0
2
4
6
8
10
1556.0 0
2
4
6
8
10
Fig. 5. The gas pressure dependence of the two Bragg wavelengths at room temperature. (d) Slow-axis mode, (N) fast-axis mode, lines are the linear fittings. Inset: Bragg wavelength difference kSB kFB dependence on the applied gas pressure.
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We tried measuring temperatures and gas pressure changes simultaneously using the Hi-Bi fiber Bragg grating. Fig. 6 shows the typical measurement results when the gas pressure applied on the fiber grating was changed at the two different temperatures ()50 and 80 °C). Table 1 summarized the calculated temperatures and gas pressure results using Eqs. 9 and 10. From the table it is shown that the deviations between the results and the set values were less than 1 °C and 0.5 MPa respectively.
Comparing with the similar sensors based on the Hi-Bi fibers, such as reported in [16], the proposed sensor element has very small diameter due to the Hi-Bi fiber Bragg gratings only need simply protect with a glass or steel capillary. Secondly, it is very easy to compose a point-distribution sensor network by writing several gratings with different Bragg wavelengths in one Hi-Bi fiber and adopting the wavelength division multiplexing technology.
Bragg wavelength (nm)
4. Conclusions
1558.4
1557.2
1558.2
1557.0
1558.0
1556.8
1557.8
1556.6
T=80o C
1557.6
1556.4
1557.4
1556.2 0
2
4
6
8
10
T= -50o C
0
2
4
6
8 10
Fig. 6. The gas pressure dependence of the two Bragg wavelengths at two different temperature of )50 and 80 °C. (d) Slow-axis mode, (N) fast-axis mode.
In summary, we have written a fiber Bragg grating in a novel Hi-Bi fiber by phase-mask method, and demonstrated its temperature and gas pressure characteristics, which agreed well with our analyses. The grating has two Bragg wavelengths and the difference between them is 0.77 nm at room temperature. The two Bragg wavelengths of the grating have different temperature sensitivities and almost the same hydrostatical pressure sensitivity. Those indicated that the grating can be used to measure the temperature and hydrostatical pressure simultaneously. The measurement results of the temperature and pressure were deviated less than 1 °C and 0.5 MPa from the set values. The sensor based on this grating will have relatively
Table 1 Measurement results with different gas pressure and temperature applied on the fiber gratings The set gas pressure
The set temperature
+80 °C +60 °C +40 °C 0 °C )20 °C )40 °C )50 °C
1.0 Mpa
3.0 MPa
5.0 MPa
6.0 MPa
7.0 MPa
8.0 MPa
9.0 MPa
1.3 Mpa 80.2 °C 1.2 MPa 60.3 °C 0.8 MPa 39.5 °C 0.9 MPa 0.5 °C 1.1 MPa )20.5 °C 1.4 MPa )40.5 °C 1.4 MPa )50.1 °C
3.4 MPa 80.1 °C 2.5 MPa 59.5 °C 2.7 MPa 39.8 °C 3.3 MPa 0.2 °C 2.9 MPa )19.5 °C 3.4 MPa )39.5 °C 3.2 MPa )49.8 °C
5.2 MPa 79.8 °C 5.5 MPa 60.8 °C 5.3 MPa 40.5 °C 4.7 MPa 0.3 °C 4.8 MPa )19.7 °C 5.3 MPa )39.8 °C 5.3 MPa )49.8 °C
6.3 MPa 80.0 °C 6.3 MPa 60.6 °C 5.8 MPa 40.1 °C 5.7 MPa )0.3 °C 6.2 MPa )20.5 °C 5.9 MPa )39.8 °C 6.4 MPa )49.7 °C
7.4 MPa 79.9 °C 7.5 MPa 61.0 °C 6.8 MPa 39.8 °C 7.2 MPa 0.1 °C 7.4 MPa )20.6 °C 7.1 MPa )40.3 °C 7.2 MPa )50.0 °C
8.4 MPa 80.2 °C 8.3 MPa 60.5 °C 7.5 MPa 40.2 °C 7.8 MPa )0.5 °C 8.1 MPa )19.8 °C 7.9 MPa )40.1 °C 8.2 MPa )50.0 °C
9.5 MPa 79.8 °C 9.5 MPa 60.8 °C 8.5 MPa 39.3 °C 8.8 MPa )0.3 °C 8.9 MPa )19.5 °C 9.4 MPa ) 39.7 °C 9.3 MPa )49.8 °C
G. Chen et al. / Optics Communications 228 (2003) 99–105
wide range of measuring temperature due to the large Bragg wavelengths separation.
Acknowledgements This work is supported by the National Nature Science Foundation of China (Grant Nos.: 10074011, 60207008) and Ministry of Science and Technology of China (project 2001CCA04600).
References [1] A.D. Kersey, M.A. Davis, H.J. Patrick, M.L. Leblane, K.P. Koo, C.G. Askings, M.P. Putnam, E.J. Friebele, J. Lightwave Technol. 15 (1997) 1442. [2] M.G. Xu, L. Reekie, Y.T. Chow, J.P. Dakin, Electron. Lett. 29 (1993) 398. [3] S. Keger, S. Calvert, E. Udd, in: Tech. Dig. OFS 2002, 2002, Paper ThA5. [4] M.G. Xu, J.-L. Archambault, L. Reekie, J.P. Dakin, Electron. Lett. 30 (1994) 1085.
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[5] H.J. Patrick, G.M. Williams, A.D. Kersey, J.R. Pedrazzani, A.M. Vengsarkar, IEEE Photon. Tech. Lett. 8 (1996) 1223. [6] Yunqi Liu, Zhuanyun Guo, Ying Zhang, Kin Seng Chiang, Xiaoyi Dong, Electron. Lett. 36 (6) (2000) 564. [7] P. Niay, P. Bernage, T. Taunay, M. Douay, E. Delevaque, S. Boj, B. Poumellec, IEEE Photon. Tech. Lett. 7 (1995) 391. [8] D. Pureur, M. Douay, P. Bernage, P. Niay, J.F. Bayon, J. Lightwave Technol. 13 (1995) 350. [9] O. Deparis, R. Kiyan, S.A. Vasiliev, O.I. Medvedkov, E.M. Dianov, O. Pottiez, P. Megret, M. Blondel, IEEE Photon. Tech. Lett. 13 (2001) 284. [10] S. Lee, R. Khosravani, J. Peng, V. Grubsky, D.S. Starodubov, A.E. Willner, J. Feinberg, IEEE Photon. Tech. Lett. 11 (1999) 1277. [11] L.A. Ferreira, F.M. Araujo, J.L. Santos, F. Farahi, Opt. Eng. 39 (8) (2000) 2226. [12] M. Sudo, M. Nakai, K. Himeno, S. Suzaki, A. Wada, R. Yamauchi, in: Proc. 12th Int. Conf. on Optical Fiber Sensors, IEEE/LEOS and OSA, 1997, p. 170. [13] J. Noda, K. Okamoto, Y. Sasaki, J. Lightwave Technol. 4 (1986) 1071. [14] K.S. Chiang, Opt. Eng. 36 (1997) 999. [15] K.S. Chiang, D. Wong, Electron. Lett. 26 (1990) 1952. [16] W.J. Bock, W. Urba nczyk, Appl. Opt. 37 (1998) 3897.
Simultaneous pressure and temperature measurement using Hi-Bi fiber Bragg gratings Guanghui Chen a,c, Liying Liu a, Hongzhi Jia b, Jimin Yu c, Lei Xu a, Wencheng Wang a,* a
State Key Lab for Advanced Photonic Materials and Devices, Department of Optical Science and Engineering, Fudan University, 220 Handan Road, Shanghai 200433, China b College of Optics and Electronics Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China c No. 23 Research Institute of China Electronics Technology Group Corporation, Shanghai 200437, China Received 22 June 2003; received in revised form 25 September 2003; accepted 26 September 2003
Abstract The fiber Bragg grating has been written in a novel high birefringence (Hi-Bi) fiber by phase-mask method. The temperature and gas pressure characteristics of the fiber Bragg grating were analyzed and demonstrated quantitatively. Two Bragg wavelengths corresponding to the fast-axis mode and slow-axis mode shift linearly with temperature change and gas pressure change. Experimental results showed that this Hi-Bi fiber Bragg grating could be used to measure temperature and gas pressure simultaneously with a deviation of less than 1 °C and 0.5 MPa from the set values respectively. Ó 2003 Elsevier B.V. All rights reserved. PACS: 42.81.Pa Keywords: Hi-Bi fiber; Fiber Bragg grating; Bragg wavelength; Sensors; Pressure measurement; Temperature measurement
1. Introduction Fiber Bragg grating (FBG) sensors have generated great interests in recent years because of their many industrial applications [1]. They are particularly suitable for monitoring the high gas pressure or fluid pressure in hostile environments
*
Corresponding author. Tel.: +86-21-65642961; fax: +86-2165641344. E-mail address: [email protected] (W. Wang).
due to being passive and intrinsically safe [2,3]. As a kind of wavelength-encoding optical fiber sensor, FBG sensors have many significant advantages, such as simplicity in fabrication, independent of overall system light level. But, in general, the Bragg wavelength shift in a FBG comes from two different effects, i.e., temperature and strain induced by pressure. It is hard to distinguish these two effects of the parameters when only the wavelength shift is measured. Many works to discriminate the strain and temperature effects have been carried out, such as superimposed
0030-4018/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.optcom.2003.09.079
100
G. Chen et al. / Optics Communications 228 (2003) 99–105
gratings [4], hybrid FBG/long-period gratings [5], and different polymer-coated fiber Bragg gratings [6]. Bragg gratings written in Hi-Bi optical fibers can play an important part in this area. Bragg gratings written in Hi-Bi optical fibers have been demonstrated [7] and used to compose some kinds of optical fiber devices, such as optical fiber lasers [8,9], compensators of polarization mode dispersion [10] and sensors [11,12]. In this letter, we introduce a Bragg grating written in a novel Hi-Bi optical fiber and demonstrate a grating sensor being capable of simultaneous measurement of gas pressure and temperature using this Hi-Bi optical fiber Bragg gratings.
2. Principle of Hi-Bi fiber Bragg grating sensor When a grating is formed in a Hi-Bi fiber, because of the slight difference of effective refractive indices for the two orthogonal polarization modes, there will be two reflective peaks at slight different wavelengths, while the shapes of two reflective spectra are similar. Their Bragg wavelengths can be written as kFB ¼ 2nF K;
ð1Þ
kSB ¼ 2nS K;
ð2Þ
It has a GeO2 -doped silica core and a circular silica cladding. This fiber has much higher birefringence (7.2 104 ) comparing with other kinds of fibers such as PANDA fiber (4.5 104 ) and bow-tie fiber (5.5 104 ) [11–13], because its two stress-inducing elements are closer to the core (see Fig. 1). In this case, the BG and the BSo can be neglected. Therefore, when there is no extra radial force applied on the fiber, the total birefringence at the core center is expressed by BS ¼ a T G E C ðTS T Þ=½2 ð1 tÞ;
ð4Þ
where aT is the difference of thermal coefficient between cladding and stress-inducing elements, G is a coefficient related to the shapes and positions of the two stress-inducing elements, E is the YoungÕs modulus, C is the photo-elastic constant, t is the PoissonÕs ratio, TS is the softening temperature of the fiber core, and T is the surrounding temperature of the fiber. From (1), (2) and (4), it can be inferred that two Bragg wavelengths of the Hi-Bi fiber grating would have different temperature sensitivities. According to [14], when the ambient temperature is changed by an amount DT , the birefringence is changed by
where kFB and nF ; kSB and nS are the Bragg wavelengths and the effective refractive indices corresponding to the fast-axis mode and slow-axis mode, K is the period of grating. The modal birefringence B ¼ nS nF of Hi-Bi fibers, produced by internal origins, is described as [13] B ¼ BG þ BSo þ BS ;
ð3Þ
where BG is the geometrical component induced by the shape difference of the core, BSo is the component induced by the thermal expansion difference of the asymmetrical core, and BS is the component induced by the stress-inducing elements. The Hi-Bi optical fiber we used is a new kind of Hi-Bi fiber called ‘‘quasi-rectangle’’ (China patent no. ZL95243466) because of the shapes of two stress-inducing elements of B2 O3 -doped silica glass. This fiber was fabricated by MCVD method.
Fig. 1. The cross-section of the ‘‘quasi-rectangle’’ Hi-Bi fiber. Two dark spots are stress-inducing elements.
G. Chen et al. / Optics Communications 228 (2003) 99–105
DBT ¼ ðDT =ðT TS ÞÞ B:
ð5Þ
In the temperature range we used for the experiments (from )50 to 80 °C), DBT is estimated to be )0.14B. The birefringence of the Hi-Bi fiber will also be changed by the hydrostatical pressure applied on it. However, for the fiber we used, the pressureinduced birefringence would be far less than that induced by the stress during the fabrication if the pressure is not too high. This conclusion can be verified by the result of previous analysis [14,15], for a bare fiber, the pressure-induced birefringence DBp can be expressed by DBp ¼ ½E2 ð1 þ t1 Þð1 2t1 Þ E1 ð1 þ t2 Þð1 2t2 Þ þ E2 ðt2 t1 Þð1 2t1 ÞP B =½E1 E2 ðTS T Þ aT ;
ð6Þ
where t1 and t2 , E1 and E2 are the PoissonÕs ratios, YoungÕs moduli of the cladding and the stress-inducing elements, P is the hydrostatical pressure applied on the fiber. For our fiber, the typical data are t1 ¼ 0:17, t2 ¼ 0:22, E1 ¼ 72:5 103 MPa, E2 ¼ 50.75 103 MPa, TS T ¼ 900 K and aT ¼ 15:6 107 K1 . When the pressure applied on the fiber is 10 MPa as in our experiments, the pressure-induced birefringence DBp was estimated to be about 1:7 102 B, less than that induced by temperature. This means the two Bragg wavelengths of Hi-Bi fiber grating would have slightly different sensitivities to the hydrostatical pressure at a fixed temperature. Based on the above analyses, we proposed a sensor using Hi-Bi fiber Bragg gratings, which can measure temperature and hydrostatical pressure simultaneously. According to the wavelength sensing principle of fiber Bragg gratings and ignoring the cross-sensitivities between two parameters, the shifts of two Bragg wavelengths, DkFB and DkSB , subjected to the applied pressure and temperature are given by DkFB ¼ KFT DT þ KFP DP ;
ð7Þ
DkSB ¼ KST DT þ KSP DP ;
ð8Þ
where KFT and KST are the temperature sensitivities of the two Bragg wavelengths corresponding to the fast-axis mode and slow-axis mode, KFP and KSP are the hydrostatical pressure sensitivities. It can
101
be seen from the above two equations that the applied hydrostatical pressure and temperature were uniquely determined if the shifts of two Bragg wavelengths in Hi-Bi fiber were measured.
3. Experiments and results Fiber Bragg gratings had been written in a new kind of Hi-Bi fiber that was fabricated by MCVD method. This novel fiber has a GeO2 -doped silica core and a circular silica cladding. Its birefringence results from two borosilicate elements (referred as stress-inducing element) beside the fiber core (see Fig. 1). The two elements have a different coefficient of thermal expansion from their surroundings, so that when they cool down to room temperature after manufacturing process ends, anisotropic stress is set up across the core of the fiber. The fiber we used has a birefringence as large as 7:2 104 . Before written Bragg gratings, the fiber was loaded with H2 under about 100 bars at room temperature for 30 days in order to increase its photosensitivity. The H2 loaded Hi-Bi fiber was exposed to the KrF excimer laser beam (248 nm, 200 mJ/cm2 ) through a nulled-zero-order phase mask (Km ¼ 1075:4 nm). Fig. 2 shows the reflection spectrum of the FBG, which was recorded with an optical spectra analyzer (ADVANTEST Q8384). It can be seen from Fig. 2 that the FBG has two similar reflection peaks corresponding to the fast-axis mode and slow-axis mode respectively. Their wavelengths were measured to be 1556.82 and 1557.59 nm at 20 °C. The difference of the wavelengths is 0.77 nm. The temperature characteristics of the FBG were studied experimentally. The light from a broad-band source was launched into the FBG through a coupler with a normal single-mode fiber. An optical spectrum analyzer (ADVANTEST Q8384) was used to measure the reflection spectra. The FBG was first placed in a temperature-circulate box and cooled to )50 °C. Then the grating temperature was increased successively to different temperature and left it at the temperature for about 10 min for the measurements. The optical spectra analyzer recorded two Bragg wavelengths at
102
G. Chen et al. / Optics Communications 228 (2003) 99–105
Fig. 2. The reflection spectrum of a FBG written in the ‘‘quasi-rectangle’’ Hi-Bi fiber. The left peak, kFB ¼ 1556:82 nm, is corresponding to the fast-axis mode, the right one, kSB ¼ 1557:59 nm, is corresponding to the slow-axis mode.
different temperature. When the temperature rose from )50 to 80 °C, both Bragg wavelengths redshifted linearly, but the difference of the two Bragg wavelengths decreased (see Fig. 3). The temperature sensitivities of these two Bragg wavelengths,
corresponding to the fast-axis mode and slow-axis mode, were measured to be KFT ¼ 0:0093 nm/°C and KST ¼ 0:0088 nm/°C, respectively. The experimental set-up for the hydrostatical pressure measurement with the FBG was shown in
Fig. 3. The temperature dependence of the two Bragg wavelengths under a normal atmosphere. (d) Slow-axis mode, (N) fast-axis mode, lines are the linear fittings. Inset: Bragg wavelength difference kSB kFB dependence on the surrounding temperature.
G. Chen et al. / Optics Communications 228 (2003) 99–105
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the errors of the barometer. The pressure sensitivities of both Bragg wavelengths were almost the same, KPF ¼ KSF ¼ 0:020 nm/MPa. From the above equations and data, it is found that for the FBG written in the Hi-Bi fiber, the applied gas or fluid pressure (in MPa) and temperature (in °C) could be obtained from the following equations:
Fig. 4. The FBG was loosely sheathed in a glass capillary in order to avoid bending under the gas flow. Then the FBG with the glass capillary was put in a gasproof steel pipe, which was filled with high-pressure nitrogen. The pressure of the gas surrounding the FBG was changed through a pressure reducer. The reflection spectra were recorded for the pressure change from 0 to 10 MPa, see Fig. 5 for the measurement results. The two curves showed good linearity and the linear fit error was less than 0.3%, which mainly came from
DT ¼ 2000ðDkFB DkSB Þ;
ð9Þ
DP ¼ 930DkSB 880DkFB :
ð10Þ
Fig. 4. The experimental set-up for demonstrating the gas pressure sensitivities of the FBG.
1557.0
∆λSB/∆P=0.020 (nm/MPa)
∆λFB/∆P=0.020 (nm/MPa) 0.9
λSB-λ FB (nm)
Bragg wavelength (nm)
1557.5
1556.5
0.8
0.7
0.6
0
2
4
6
8
10
1556.0 0
2
4
6
8
10
Fig. 5. The gas pressure dependence of the two Bragg wavelengths at room temperature. (d) Slow-axis mode, (N) fast-axis mode, lines are the linear fittings. Inset: Bragg wavelength difference kSB kFB dependence on the applied gas pressure.
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G. Chen et al. / Optics Communications 228 (2003) 99–105
We tried measuring temperatures and gas pressure changes simultaneously using the Hi-Bi fiber Bragg grating. Fig. 6 shows the typical measurement results when the gas pressure applied on the fiber grating was changed at the two different temperatures ()50 and 80 °C). Table 1 summarized the calculated temperatures and gas pressure results using Eqs. 9 and 10. From the table it is shown that the deviations between the results and the set values were less than 1 °C and 0.5 MPa respectively.
Comparing with the similar sensors based on the Hi-Bi fibers, such as reported in [16], the proposed sensor element has very small diameter due to the Hi-Bi fiber Bragg gratings only need simply protect with a glass or steel capillary. Secondly, it is very easy to compose a point-distribution sensor network by writing several gratings with different Bragg wavelengths in one Hi-Bi fiber and adopting the wavelength division multiplexing technology.
Bragg wavelength (nm)
4. Conclusions
1558.4
1557.2
1558.2
1557.0
1558.0
1556.8
1557.8
1556.6
T=80o C
1557.6
1556.4
1557.4
1556.2 0
2
4
6
8
10
T= -50o C
0
2
4
6
8 10
Fig. 6. The gas pressure dependence of the two Bragg wavelengths at two different temperature of )50 and 80 °C. (d) Slow-axis mode, (N) fast-axis mode.
In summary, we have written a fiber Bragg grating in a novel Hi-Bi fiber by phase-mask method, and demonstrated its temperature and gas pressure characteristics, which agreed well with our analyses. The grating has two Bragg wavelengths and the difference between them is 0.77 nm at room temperature. The two Bragg wavelengths of the grating have different temperature sensitivities and almost the same hydrostatical pressure sensitivity. Those indicated that the grating can be used to measure the temperature and hydrostatical pressure simultaneously. The measurement results of the temperature and pressure were deviated less than 1 °C and 0.5 MPa from the set values. The sensor based on this grating will have relatively
Table 1 Measurement results with different gas pressure and temperature applied on the fiber gratings The set gas pressure
The set temperature
+80 °C +60 °C +40 °C 0 °C )20 °C )40 °C )50 °C
1.0 Mpa
3.0 MPa
5.0 MPa
6.0 MPa
7.0 MPa
8.0 MPa
9.0 MPa
1.3 Mpa 80.2 °C 1.2 MPa 60.3 °C 0.8 MPa 39.5 °C 0.9 MPa 0.5 °C 1.1 MPa )20.5 °C 1.4 MPa )40.5 °C 1.4 MPa )50.1 °C
3.4 MPa 80.1 °C 2.5 MPa 59.5 °C 2.7 MPa 39.8 °C 3.3 MPa 0.2 °C 2.9 MPa )19.5 °C 3.4 MPa )39.5 °C 3.2 MPa )49.8 °C
5.2 MPa 79.8 °C 5.5 MPa 60.8 °C 5.3 MPa 40.5 °C 4.7 MPa 0.3 °C 4.8 MPa )19.7 °C 5.3 MPa )39.8 °C 5.3 MPa )49.8 °C
6.3 MPa 80.0 °C 6.3 MPa 60.6 °C 5.8 MPa 40.1 °C 5.7 MPa )0.3 °C 6.2 MPa )20.5 °C 5.9 MPa )39.8 °C 6.4 MPa )49.7 °C
7.4 MPa 79.9 °C 7.5 MPa 61.0 °C 6.8 MPa 39.8 °C 7.2 MPa 0.1 °C 7.4 MPa )20.6 °C 7.1 MPa )40.3 °C 7.2 MPa )50.0 °C
8.4 MPa 80.2 °C 8.3 MPa 60.5 °C 7.5 MPa 40.2 °C 7.8 MPa )0.5 °C 8.1 MPa )19.8 °C 7.9 MPa )40.1 °C 8.2 MPa )50.0 °C
9.5 MPa 79.8 °C 9.5 MPa 60.8 °C 8.5 MPa 39.3 °C 8.8 MPa )0.3 °C 8.9 MPa )19.5 °C 9.4 MPa ) 39.7 °C 9.3 MPa )49.8 °C
G. Chen et al. / Optics Communications 228 (2003) 99–105
wide range of measuring temperature due to the large Bragg wavelengths separation.
Acknowledgements This work is supported by the National Nature Science Foundation of China (Grant Nos.: 10074011, 60207008) and Ministry of Science and Technology of China (project 2001CCA04600).
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