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Fiber-grating sensor using dynamic PZT modulation
1 October 2002
Optics Communications 211 (2002) 129–133 www.elsevier.com/locate/optcom
Fiber-grating sensor using dynamic PZT modulation Qianghua Li *, Chunfei Li, Junqing Li, Bingsheng Liu Department of Physics, Harbin Institute of Technology, Harbin 150001, China Received 31 January 2002; received in revised form 1 June 2002; accepted 7 August 2002
Abstract In this paper we propose a new sensor based on a periodically modulated fiber grating. The fiber grating is fixed on a PZT plate, which is modulated by an alternating voltage. In order to measure strains, we only use an oscilloscope and a single-mode-laser source to measure the change of the reflected-light pulse period. Comparing with the original method of strain measurement that using an optical spectrum analyzer and a broadband light source to measure the wavelength shift of reflected power peak, this method is much simpler and has lower cost. Our research results show that two methods are equivalent, and theoretical analysis well consists with experimental results. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.81.Pa; 77.84.Dy; 07.10.Pz Keywords: Fiber grating sensor; PZT modulator; Strain measurement
1. Introduction Recently, the investigation of sensor technology using fiber gratings has made great progress [1–3]. The fiber-grating sensor has such good characteristics as high sensitivity, low electromagnetism interference, and high repetition. When a fiber grating is stretched, the grating constant is then changed, which leads to a shift of reflected light power peak. Many fiber-grating sensors are based
*
Corresponding author. Qianghua Li is a Ph.D. candidate in Department of Physics, Harbin Institute of Technology and he is also working in Department of Physics, Harbin Normal University, Harbin 150080, China. E-mail address: [email protected] (Q. Li).
on this principle. For example, a fiber grating fixed on a polymer slice with high expansion coefficient, the length of fiber grating can be changed with changing of polymer length [4]. In another experiment [5], the fiber grating is fixed on an elastic cantilever, which changes the length of grating, hence the wavelength location of reflected power peak. Set et al. [6] has showed the 40 nm shift of reflected power peak. However, in all above works, the expensive optical spectrum analyzer (OSA) and broadband source (BBS) have to be used. In this paper, we propose a new kind of the fiber-grating sensor. The fiber grating is fixed on a PZT plate applied a periodical electric voltage. It induces a periodic change in the grating length, and then makes a periodical shift of reflected power peak in time domain. If a narrow light
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 8 5 6 - 4
130
Q. Li et al. / Optics Communications 211 (2002) 129–133
source such as DFB laser is used, the central wavelength of grating periodically scans over the laser wavelength; a serial of pulses can be generated. At the same time, applying an outer strain onto the fiber grating, the interval time of pulses will be changed. We can measure the intervaltime change by using a common oscilloscope only. This dynamic fiber-grating sensor can also be used to measure the displacement and the temperature etc.
2.2. Relationship between the time interval of reflected power peaks and the strain
2.1. Relationship between the wavelength shift of reflected power peak and the measured strain
In our method, we fix a fiber grating on two ends of a PZT plate, which has two electrodes in its two side. The light from a DFB laser is launched into the grating. When a periodical voltage applies on the PZT plate, the grating is stretched periodically. At same time, we apply a measured outer strain force on the one end of the PZT plate. The scheme is shown in Fig. 1. The laser emits the narrow-band beam, the input light intensity can be written as: " !# 2 ð k kB Þ ; ð4Þ I ðkÞ ¼ I0 exp 4 ln 2 Dr2B
When the light from BBS is launched into a fiber grating, the spectrum of reflected light can be shown on an OSA. If an outer strain applies onto the fiber grating, one could see the wavelength shift of reflected power peak. Neglecting the influence of temperature, the wavelength shift can be described as [7]
where I0 is the center intensity with the wavelength kB ; DrB is the full-width half maximum (FWHM) of the intensity profile. The reflection rate of the fiber grating can be described as a Gaussian function [8]: " !# ð k kF Þ 2 RðkÞ ¼ R0 exp 4 ln 2 ; ð5Þ Dr2F
2. Theory
k0F kF ¼ ð1 Pe ÞekF þ kkF f ;
ð1Þ
k0F
are wavelengths of reflected light where kF and from fiber grating. kF is the original wavelength and k0F is the shifted wavelength. Pe is the elasticoptical coefficient, for the silica fiber, Pe ¼ 0:22. e is the fiber strain coefficient, k is the force coefficient, and f is the outer strain. We can see that the wavelength shift is related to the outer strain and elastic-optical effect. When a periodic voltage is applied onto the PZT plate, it causes the periodic stretch of the fiber grating and change in the strain coefficient of fiber grating. The relation between the fiber strain coefficient and the periodic voltage is: 2p e ¼ d33 V0 sin t ; ð2Þ T where d33 is an coefficient of the piezoelectricity, T is the modulation period. The wavelength after shift is 2p k0F ¼ ð1 Pe Þd33 kF V0 sin t þ kkF f þ kF : ð3Þ T
where R0 is the reflection rate of fiber grating at the center wavelength kF ; DrF is the full-width half maximum of the reflected intensity profile. When an outer strain is applied onto the fiber grating, the corresponding reflection rate becomes 2 0
2 13 0 k k F C7 6 B ð6Þ R0 ðkÞ ¼ R0 exp 4 @4 ln 2 A5 ; Dr2F where k0F is the reflected center wavelength of grating after the fiber grating is stretched. In our experiment, the total reflected power PR received by photodetector is the integral of I ðkÞR0 ðkÞ in wavelength domain
Fig. 1. Scheme of FBG modulated by using a PZT plate with a periodic voltage and an outer strain.
Q. Li et al. / Optics Communications 211 (2002) 129–133
PR ¼
Z
131
1
1
I ðkÞR0 ðkÞ dk 2
6 ¼ P0 exp 4 4 ln 2
kB k0F
2 3
Dr2B þ Dr2F
7 5;
where P0 is defined as pffiffiffi p DrB DrF P0 ¼ I0 R0 pffiffiffiffiffiffiffiffi : 2 ln 2 ðDr2B þ Dr2F Þ1=2
ð7Þ
ð8Þ
Substituting the formula (3) into (7), we obtain " PR ¼ P0 exp 2 # kB k0 sin 2p t kk f k F F T 4 ln 2 ; Dr2B þ Dr2F
Fig. 2. Simulated curves of reflective power versus time under different outer strain: (a) when the outer strain is zero and corresponding interval time is zero; (b), (c), and (d) when the outer strains are 0.15, 0.25, 0.75 N and corresponding the interval time are 5, 6, 11 ms, respectively.
ð9Þ where k0 ¼ ð1 Pe Þd33 kF V0 . Therefore, we get the PR –t curves with different outer strains as shown in Fig. 2. Setting oPR =ot ¼ 0 and defining the time interval of neighbored peaks is s, we get (10)
s i
s k0 h 0 p ; ð10Þ f ¼ p cos cos T kkF T where s0 is the initial time interval of reflected power peaks when f is zero. It is obvious that we can get the value of the strain by measuring the time intervals.
3. Experimental results and discussion 3.1. Strain sensor measurements using oscilloscope The experimental setup is given in Fig. 3. The beam from a DFB laser enters into a fiber grating through a circulator. The reflected light beam modulated by both the dynamic PZT plate and the outer strain passes through the circulator, and it is received by a photodetector (PD). The converted electrical signal is sent into an oscilloscope for displaying. The PZT plate controlled by alternative voltage changes the central wavelength of reflected light from grating periodically. Therefore, the relative
Fig. 3. Experiment setup for measurement of the strain using a periodic modulated PZT.
position between the laser wavelength and central wavelength of reflected peak is also changed periodically. When the reflected central wavelength of grating scans over the incident laser wavelength, the reflected power will reach the maximum. If the reflected central wavelength of grating is far from the central wavelength of incident laser, the light will transmit directly through the grating without any reflection. On the other hand, the fiber grating is pulled by the static outer strain, which is measured by an ergometer. In our experiment, the central wavelength of DFB laser kB is 1554.8 nm. The FWHM of the laser DrB is 0.2 nm. The wavelength of reflected peak kF without strain is 1553.2 nm. The reflection rate of grating R0 is 90%. The FWHM of the
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Q. Li et al. / Optics Communications 211 (2002) 129–133
Fig. 4. Oscilloscope photos of the pulse interval time under different outer strain. The curves (a), (b), (c) and (d) correspond to the interval time s ¼ 0, 5.0, 6.3, 11.7 ms, respectively.
grating DrF is 0.8 nm. The coefficient of piezoelectricity d33 ¼ 3:00 1010 C N1 . The amplitude and period of modulation voltage V0 and T are 150 V and 22.0 ms, respectively. We can easily get K ¼ 1:5636 101 and K0 ¼ 1:7134 109 m. In our experiment, the modulated frequency is 50 Hz, which is much lower than the resonance frequency of PZT, 2000 Hz, so that the hysteresis of this device can be neglected. The four experimental curves shown in Fig. 4 are directly taken from the oscilloscope under different outer strains. Fig. 4(a) shows a set of periodic single pulses without outer strain, with initial time interval of the peak s0 ¼ 0 ms and s ¼ 0 ms. When the outer strain is gradually applied, every pulse in Fig. 4(a) will separate into two pulses, in Figs. 4(b)–(d) we can see such results when the interval time s are 5.0, 6.3, 11.7 ms, respectively. According to the formula (10), the outer strains can be calculated as 0.154, 0.249, 0.774 N, respectively. On the other hand, the outer strains directly measured by an ergometer are 0.158, 0.255, 0.780 N, respectively. It is clear that the calculated results agree with that of measurement by the ergometer.
Fig. 5. Outer strain as a function of the time. (M) denotes the data measured by pulse interval from oscilloscope; ( ) denotes the data tested by an ergometer; (–) denotes the curve calculated by the computer from Formula (10).
In the Fig. 5, we plot the relationship between outer strains f and interval time s which shows the good coherence of calculated results with the results measured by the ergometer in a wide range. 3.2. Strain sensor measurements using OSA To compression, we also carried out an experiment using a OSA and a BBS, instead of above
Q. Li et al. / Optics Communications 211 (2002) 129–133
Fig. 6. The relationship between the outer strain and wavelength shift. The solid points show the calculated results from OSA data and the circles points show the results from the ergometer.
experiment using a laser, a PD and an oscilloscope. We got a set of curves for wavelength shift of reflected power peaks versus strains calculated from Eq. (1). To proof these results we have measured by an ergometer. It is obvious that the two results are very close in the strain region of 0–0:6 N as shown in Fig. 6. However, when the strain is stronger than 0.6 N, the curve becomes lower than theoretical curve. The experiment by Guo et al. [9] has proved that the shifting of central wavelength of fiber grating has a linear correlation with changing of the outer strain. Therefore, the difference in Fig. 6 may arise from the non-linear response of PZT plate. 4. Conclusion In this paper, we proposed a new technique of fiber-grating sensor, in which the grating on a PZT
133
plate is periodically modulated. We derived the theoretical formula of outer strain as the function of time interval of the reflected power peak. In measurement of strains, we got the same results by using two different measuring methods: one is using a dynamic fiber grating and an oscilloscope; another is using a regular fiber grating and an OSA. The two methods are proven to be equivalent in low strain range. The experiment result agrees with the theory. Because the wavelength widths of incident laser and the reflected light of fiber grating cannot be ignored, the measurement precision may be influenced by these affects. To compress the wavelength widths of laser and the reflected light of fiber grating will improve the measurement precision. Our dynamic fiber-grating sensor has the advantages such as low cost and simple structure. It can be widely used in other applications, such as the measurements for length, temperature, pressure, and so on.
References [1] T.T. Berkoff, A.D. Hersey, IEEE Photon. Technol. Lett. 8 (12) (1996) 1677. [2] M.G. Xu, L. Reekie, Y.T. Chow, J.P. Dakin, Electron. Lett. 29 (4) (1993) 398. [3] S. Gupta, T. Mizunami, T. Yamao, T. Shimomura, Appl. Opt. 35 (25) (1996) 2502. [4] J.L. Cruz, L. Dong, L. Reekie, Electron. Lett. 32 (4) (1996) 386. [5] Y. Yu, B. Guan, et al., Acta Opt. Sinica 20 (3) (2000). [6] S.Y. Set, B. Dabarsyah, C.S. Goh, K. Katoh, Y. Yakushima, K. Kikuchi, A widely tunable fiber Bragg grating with a wavelength tunability over 40 nm. OFC2001, MC4-1. [7] G.A. Ball, W.W. Morey, Opt. Lett. 17 (6) (1992) 420. [8] A.B. Lobo, L.A. Ferreira, J.L. Santos, et al., Appl. Opt. 36 (4) (1997) 934. [9] W. Guo, K. Liu, et al., J. Optoelectron. Laser 11 (1) (2000).
Optics Communications 211 (2002) 129–133 www.elsevier.com/locate/optcom
Fiber-grating sensor using dynamic PZT modulation Qianghua Li *, Chunfei Li, Junqing Li, Bingsheng Liu Department of Physics, Harbin Institute of Technology, Harbin 150001, China Received 31 January 2002; received in revised form 1 June 2002; accepted 7 August 2002
Abstract In this paper we propose a new sensor based on a periodically modulated fiber grating. The fiber grating is fixed on a PZT plate, which is modulated by an alternating voltage. In order to measure strains, we only use an oscilloscope and a single-mode-laser source to measure the change of the reflected-light pulse period. Comparing with the original method of strain measurement that using an optical spectrum analyzer and a broadband light source to measure the wavelength shift of reflected power peak, this method is much simpler and has lower cost. Our research results show that two methods are equivalent, and theoretical analysis well consists with experimental results. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 42.81.Pa; 77.84.Dy; 07.10.Pz Keywords: Fiber grating sensor; PZT modulator; Strain measurement
1. Introduction Recently, the investigation of sensor technology using fiber gratings has made great progress [1–3]. The fiber-grating sensor has such good characteristics as high sensitivity, low electromagnetism interference, and high repetition. When a fiber grating is stretched, the grating constant is then changed, which leads to a shift of reflected light power peak. Many fiber-grating sensors are based
*
Corresponding author. Qianghua Li is a Ph.D. candidate in Department of Physics, Harbin Institute of Technology and he is also working in Department of Physics, Harbin Normal University, Harbin 150080, China. E-mail address: [email protected] (Q. Li).
on this principle. For example, a fiber grating fixed on a polymer slice with high expansion coefficient, the length of fiber grating can be changed with changing of polymer length [4]. In another experiment [5], the fiber grating is fixed on an elastic cantilever, which changes the length of grating, hence the wavelength location of reflected power peak. Set et al. [6] has showed the 40 nm shift of reflected power peak. However, in all above works, the expensive optical spectrum analyzer (OSA) and broadband source (BBS) have to be used. In this paper, we propose a new kind of the fiber-grating sensor. The fiber grating is fixed on a PZT plate applied a periodical electric voltage. It induces a periodic change in the grating length, and then makes a periodical shift of reflected power peak in time domain. If a narrow light
0030-4018/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 3 0 - 4 0 1 8 ( 0 2 ) 0 1 8 5 6 - 4
130
Q. Li et al. / Optics Communications 211 (2002) 129–133
source such as DFB laser is used, the central wavelength of grating periodically scans over the laser wavelength; a serial of pulses can be generated. At the same time, applying an outer strain onto the fiber grating, the interval time of pulses will be changed. We can measure the intervaltime change by using a common oscilloscope only. This dynamic fiber-grating sensor can also be used to measure the displacement and the temperature etc.
2.2. Relationship between the time interval of reflected power peaks and the strain
2.1. Relationship between the wavelength shift of reflected power peak and the measured strain
In our method, we fix a fiber grating on two ends of a PZT plate, which has two electrodes in its two side. The light from a DFB laser is launched into the grating. When a periodical voltage applies on the PZT plate, the grating is stretched periodically. At same time, we apply a measured outer strain force on the one end of the PZT plate. The scheme is shown in Fig. 1. The laser emits the narrow-band beam, the input light intensity can be written as: " !# 2 ð k kB Þ ; ð4Þ I ðkÞ ¼ I0 exp 4 ln 2 Dr2B
When the light from BBS is launched into a fiber grating, the spectrum of reflected light can be shown on an OSA. If an outer strain applies onto the fiber grating, one could see the wavelength shift of reflected power peak. Neglecting the influence of temperature, the wavelength shift can be described as [7]
where I0 is the center intensity with the wavelength kB ; DrB is the full-width half maximum (FWHM) of the intensity profile. The reflection rate of the fiber grating can be described as a Gaussian function [8]: " !# ð k kF Þ 2 RðkÞ ¼ R0 exp 4 ln 2 ; ð5Þ Dr2F
2. Theory
k0F kF ¼ ð1 Pe ÞekF þ kkF f ;
ð1Þ
k0F
are wavelengths of reflected light where kF and from fiber grating. kF is the original wavelength and k0F is the shifted wavelength. Pe is the elasticoptical coefficient, for the silica fiber, Pe ¼ 0:22. e is the fiber strain coefficient, k is the force coefficient, and f is the outer strain. We can see that the wavelength shift is related to the outer strain and elastic-optical effect. When a periodic voltage is applied onto the PZT plate, it causes the periodic stretch of the fiber grating and change in the strain coefficient of fiber grating. The relation between the fiber strain coefficient and the periodic voltage is: 2p e ¼ d33 V0 sin t ; ð2Þ T where d33 is an coefficient of the piezoelectricity, T is the modulation period. The wavelength after shift is 2p k0F ¼ ð1 Pe Þd33 kF V0 sin t þ kkF f þ kF : ð3Þ T
where R0 is the reflection rate of fiber grating at the center wavelength kF ; DrF is the full-width half maximum of the reflected intensity profile. When an outer strain is applied onto the fiber grating, the corresponding reflection rate becomes 2 0
2 13 0 k k F C7 6 B ð6Þ R0 ðkÞ ¼ R0 exp 4 @4 ln 2 A5 ; Dr2F where k0F is the reflected center wavelength of grating after the fiber grating is stretched. In our experiment, the total reflected power PR received by photodetector is the integral of I ðkÞR0 ðkÞ in wavelength domain
Fig. 1. Scheme of FBG modulated by using a PZT plate with a periodic voltage and an outer strain.
Q. Li et al. / Optics Communications 211 (2002) 129–133
PR ¼
Z
131
1
1
I ðkÞR0 ðkÞ dk 2
6 ¼ P0 exp 4 4 ln 2
kB k0F
2 3
Dr2B þ Dr2F
7 5;
where P0 is defined as pffiffiffi p DrB DrF P0 ¼ I0 R0 pffiffiffiffiffiffiffiffi : 2 ln 2 ðDr2B þ Dr2F Þ1=2
ð7Þ
ð8Þ
Substituting the formula (3) into (7), we obtain " PR ¼ P0 exp 2 # kB k0 sin 2p t kk f k F F T 4 ln 2 ; Dr2B þ Dr2F
Fig. 2. Simulated curves of reflective power versus time under different outer strain: (a) when the outer strain is zero and corresponding interval time is zero; (b), (c), and (d) when the outer strains are 0.15, 0.25, 0.75 N and corresponding the interval time are 5, 6, 11 ms, respectively.
ð9Þ where k0 ¼ ð1 Pe Þd33 kF V0 . Therefore, we get the PR –t curves with different outer strains as shown in Fig. 2. Setting oPR =ot ¼ 0 and defining the time interval of neighbored peaks is s, we get (10)
s i
s k0 h 0 p ; ð10Þ f ¼ p cos cos T kkF T where s0 is the initial time interval of reflected power peaks when f is zero. It is obvious that we can get the value of the strain by measuring the time intervals.
3. Experimental results and discussion 3.1. Strain sensor measurements using oscilloscope The experimental setup is given in Fig. 3. The beam from a DFB laser enters into a fiber grating through a circulator. The reflected light beam modulated by both the dynamic PZT plate and the outer strain passes through the circulator, and it is received by a photodetector (PD). The converted electrical signal is sent into an oscilloscope for displaying. The PZT plate controlled by alternative voltage changes the central wavelength of reflected light from grating periodically. Therefore, the relative
Fig. 3. Experiment setup for measurement of the strain using a periodic modulated PZT.
position between the laser wavelength and central wavelength of reflected peak is also changed periodically. When the reflected central wavelength of grating scans over the incident laser wavelength, the reflected power will reach the maximum. If the reflected central wavelength of grating is far from the central wavelength of incident laser, the light will transmit directly through the grating without any reflection. On the other hand, the fiber grating is pulled by the static outer strain, which is measured by an ergometer. In our experiment, the central wavelength of DFB laser kB is 1554.8 nm. The FWHM of the laser DrB is 0.2 nm. The wavelength of reflected peak kF without strain is 1553.2 nm. The reflection rate of grating R0 is 90%. The FWHM of the
132
Q. Li et al. / Optics Communications 211 (2002) 129–133
Fig. 4. Oscilloscope photos of the pulse interval time under different outer strain. The curves (a), (b), (c) and (d) correspond to the interval time s ¼ 0, 5.0, 6.3, 11.7 ms, respectively.
grating DrF is 0.8 nm. The coefficient of piezoelectricity d33 ¼ 3:00 1010 C N1 . The amplitude and period of modulation voltage V0 and T are 150 V and 22.0 ms, respectively. We can easily get K ¼ 1:5636 101 and K0 ¼ 1:7134 109 m. In our experiment, the modulated frequency is 50 Hz, which is much lower than the resonance frequency of PZT, 2000 Hz, so that the hysteresis of this device can be neglected. The four experimental curves shown in Fig. 4 are directly taken from the oscilloscope under different outer strains. Fig. 4(a) shows a set of periodic single pulses without outer strain, with initial time interval of the peak s0 ¼ 0 ms and s ¼ 0 ms. When the outer strain is gradually applied, every pulse in Fig. 4(a) will separate into two pulses, in Figs. 4(b)–(d) we can see such results when the interval time s are 5.0, 6.3, 11.7 ms, respectively. According to the formula (10), the outer strains can be calculated as 0.154, 0.249, 0.774 N, respectively. On the other hand, the outer strains directly measured by an ergometer are 0.158, 0.255, 0.780 N, respectively. It is clear that the calculated results agree with that of measurement by the ergometer.
Fig. 5. Outer strain as a function of the time. (M) denotes the data measured by pulse interval from oscilloscope; ( ) denotes the data tested by an ergometer; (–) denotes the curve calculated by the computer from Formula (10).
In the Fig. 5, we plot the relationship between outer strains f and interval time s which shows the good coherence of calculated results with the results measured by the ergometer in a wide range. 3.2. Strain sensor measurements using OSA To compression, we also carried out an experiment using a OSA and a BBS, instead of above
Q. Li et al. / Optics Communications 211 (2002) 129–133
Fig. 6. The relationship between the outer strain and wavelength shift. The solid points show the calculated results from OSA data and the circles points show the results from the ergometer.
experiment using a laser, a PD and an oscilloscope. We got a set of curves for wavelength shift of reflected power peaks versus strains calculated from Eq. (1). To proof these results we have measured by an ergometer. It is obvious that the two results are very close in the strain region of 0–0:6 N as shown in Fig. 6. However, when the strain is stronger than 0.6 N, the curve becomes lower than theoretical curve. The experiment by Guo et al. [9] has proved that the shifting of central wavelength of fiber grating has a linear correlation with changing of the outer strain. Therefore, the difference in Fig. 6 may arise from the non-linear response of PZT plate. 4. Conclusion In this paper, we proposed a new technique of fiber-grating sensor, in which the grating on a PZT
133
plate is periodically modulated. We derived the theoretical formula of outer strain as the function of time interval of the reflected power peak. In measurement of strains, we got the same results by using two different measuring methods: one is using a dynamic fiber grating and an oscilloscope; another is using a regular fiber grating and an OSA. The two methods are proven to be equivalent in low strain range. The experiment result agrees with the theory. Because the wavelength widths of incident laser and the reflected light of fiber grating cannot be ignored, the measurement precision may be influenced by these affects. To compress the wavelength widths of laser and the reflected light of fiber grating will improve the measurement precision. Our dynamic fiber-grating sensor has the advantages such as low cost and simple structure. It can be widely used in other applications, such as the measurements for length, temperature, pressure, and so on.
References [1] T.T. Berkoff, A.D. Hersey, IEEE Photon. Technol. Lett. 8 (12) (1996) 1677. [2] M.G. Xu, L. Reekie, Y.T. Chow, J.P. Dakin, Electron. Lett. 29 (4) (1993) 398. [3] S. Gupta, T. Mizunami, T. Yamao, T. Shimomura, Appl. Opt. 35 (25) (1996) 2502. [4] J.L. Cruz, L. Dong, L. Reekie, Electron. Lett. 32 (4) (1996) 386. [5] Y. Yu, B. Guan, et al., Acta Opt. Sinica 20 (3) (2000). [6] S.Y. Set, B. Dabarsyah, C.S. Goh, K. Katoh, Y. Yakushima, K. Kikuchi, A widely tunable fiber Bragg grating with a wavelength tunability over 40 nm. OFC2001, MC4-1. [7] G.A. Ball, W.W. Morey, Opt. Lett. 17 (6) (1992) 420. [8] A.B. Lobo, L.A. Ferreira, J.L. Santos, et al., Appl. Opt. 36 (4) (1997) 934. [9] W. Guo, K. Liu, et al., J. Optoelectron. Laser 11 (1) (2000).