- Email: [email protected]
Fiber optic pressure sensor based on a single-mode fiber F–P cavity
Measurement 43 (2010) 370–374
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Fiber optic pressure sensor based on a single-mode fiber F–P cavity Haiyan Chen School of Physics Science and Technology, Yangtze University, Jingzhou 434023, PR China
a r t i c l e
i n f o
Article history: Received 29 April 2009 Received in revised form 4 September 2009 Accepted 2 December 2009 Available online 6 December 2009 Keywords: Optical fiber sensor Pressure sensor Birefringence sensor Optical heterodyne
a b s t r a c t In this paper, we propose and experimentally demonstrate a pressure sensor based on birefringent single-mode fiber F–P cavity using optical heterodyne. The proof of concept device consists of a light source, a polarizer controller, a modulator, a RF generator, a single-mode fiber Fabry–Perot cavity, a strain inspector, an erbium doped fiber amplifier, a filter, a polarizer, an optical spectrum analyzer, and a digital communication analyzer. The dynamic range of the proposed sensor is explored. The results demonstrate the new concept of fiber pressure sensors and the technical feasibility for pressure measurements. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Fiber optic sensors are well known. They have the basic property that the sensing element is a single piece of single-mode fiber and that all the perturbations which affect the length of the fiber are common to both eigenpolarizations [1,2]. Moreover, fiber optic sensors have some advantages such as high sensitivity, fast response, low cost, light weight, as well as immunity to electromagnetic interference. These application features benefit a wide range of industries, including the aerospace, military, petrochemical, transportation, building and structural monitoring, chemical, and biomedical sectors. The most popular fiber pressure sensor structure used is Fabry–Perot cavity, including fiber Fabry–Perot interference (FFPI) [3], fiber Bragg gratings (FBG) [4]. In 2004, Chuji Wang et al. presented a conceptually new approach: a fiber loop ringdown (FLRD) to develop a fiber pressure sensor [5]. This new fiber ringdown technique utilized a singlemode fiber resonator (SMFR) as the ringdown cavity. A signal light is coupled into the SMFR, when the light source is rapidly shut off, the output intensity of SMFR follows an exponential decay because of losses in the SMFR. The lower the losses of the light in the fiber, the longer the decay time E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2009.12.002
constant (ringdown time) [6]. However, this method did not distinguish both eigenpolarizations in a single-mode fiber, since different polarizations have different effective refractive index and decay time constant, moreover, there exists measure error because the ringdown time is determined by the light intensity to decrease to 1/e of the initial light intensity, not the gap of peak to peak. To our best knowledge, there were three publications referring to ringdown beat frequency [7–9]. In 2004, Lerber et al. reported their conceptual studies of minute birefringence using ringdown beat frequency [8]. In 2006, Lerber et al. reported their conceptual studies of Rate All-Optical Clock Recovery based on ringdown beat frequency [9]. So far, no one has reported an attempt to introduce the ringdown beat concept for fiber pressure sensors. In this paper we report our exploratory researches on the ringdown beat concept to pressure measurements. 2. Theoretical mode 2.1. Beat generation The principle diagram of a single-mode fiber F–P (SMF F–P) cavity with birefringence is shown as Fig. 1. It consists of an input polarizer, SMF F–P cavity, and an output polarizer. Assuming the effective axis of birefringence of SMF
H. Chen / Measurement 43 (2010) 370–374
R¼
Fig. 1. Schematic diagram of a single-mode fiber F–P cavity.
F–P cavity are x- and y-axis, the direction of output polarizer is xy, the azimuthal angles of input polarizer and output polarizer with respect to the effective axis of birefringence of the cavity are a and b, respectively. For a short SMF F–P cavity, we assume that the electric field amplitude and intensity after input polarizer are E0 and I0, I0 / E20 , and this input light stimulates two polarization modes in a SMF F–P cavity, the phase shift of polarized modes (x- and y-direction) propagating in the cavity after a single roundtrip is
/x ¼
4nx pL k
ð1aÞ
/y ¼
4ny pL k
ð1bÞ
where Ux (nx) and Uy (ny) are the phase (effective index) and of x- and y-direction, k is the resonance wavelength of SMF F–P cavity, L is the length of F–P cavity. The phase difference of the two polarized modes after single roundtrip is
D/ ¼ j/x /y j ¼
4p L jnx ny j k
ð2Þ
This difference is determined by the birefringence degree. Using continuously injecting monochromatic light of E0 into the cavity, the complex cavity field amplitude after p accumulated roundtrip will be
Epx
1 r pþ1 exp ½j/x ðp þ 1Þ ¼ E0 cos a 1 r expði/x Þ 1 r exp½j/y ðp þ 1Þ E0 sin a 1 r expði/y Þ
ð6Þ
c Dn kn
ð7Þ
where n = (nx + ny)/2 is the average refractive indices of the two polarizations.
pþ1
Epy ¼
E20
where E* is the conjugate of E. R is generated by the combination of two polarized modes in SMF F–P cavity. The signal R has a beat nature, because the electric fields both eigen-polarized modes originate from the same light source and thus the frequency is equal for both modes. The propagating time difference of two modes in the cavity after a single roundtrip is DT = 2DnL/c, where Dn = |nxny|, c is the velocity of light in the vacuum. For silica glass fiber, material refractive index is n = 1.47. For Dn = 2 106, L = 2 mm, the free spectrum range (FSR) of SMF F–P cavity is c/ (2nL) = 50 GHz, DT = 2.7 1017 s. When r = 0.995, a = 30°, b = 45°, L = 2 mm, k = 1550.337 nm, p = 0, . . ., 1500, and q = 0, . . ., 1000, Dn = |nxny|=5.38 106, 10.76 106, 16.15 106, the output characteristics of output polarizer is shown in Fig. 2. There are three phases: build-up, stability, and ring-down phase. Build-up phase shows the injection of light, stability expresses that the cavity reaches a maximum after about 1500 roundtrips, ring-down phase denotes that the injection of light is ceased. We also find that mode beats are generated. It demonstrates that the beat is generated at both the rising and the falling slopes of the pulse, and disappears when the field inside the cavity approaches steady-state. The beat frequency increases with the increase of the degree of phase mismatch of two eigen-polarization modes, but the intensity of beat signal decreases with the increase of Dn. this is because that variety of Dn shift the wavelength of input signal away the transmission wavelength of SMF F–P cavity, the transmission wavelength of SMF F–P cavity is determined by 2nx,yL/m, where m is a integer, nx,y is the effective refractive index of transmission modes. The homodyne beat frequency is [9]
fB ¼ ð3aÞ
Exx Eyy þ Exx Eyy
371
ð3bÞ
pffiffiffiffiffiffiffi where j ¼ 1, r is the fractional amplitude attenuation factor by the cavity mirrors and by absorption and scattering in the cavity medium. When the injecting phase of light is stopped, the remaining light in the cavity is still to circulate within the resonator for q additional roundtrips, the total electric field after the SMF F–P cavity can be written as:
Epqx ¼ rq expðjq/x ÞEpx
ð4aÞ
Epqy ¼ rq expðjq/y ÞEpy
ð4bÞ
The output electric field after the output polarizer is
Exx ¼ Epqx cos b þ Epqy sin b
ð5aÞ
Eyy ¼ Epqy cos b Epqx sin b
ð5bÞ
The beat signal can be expressed as
Fig. 2. output characteristics of output polarizer ((a) Dn = 5.38 106, (b) Dn = 10.76 106, (c) Dn = 16.15 106).
372
H. Chen / Measurement 43 (2010) 370–374
Fig. 3. Experimental setup (MOD: modulator).
2.2. Pressure sensor principle using ringdown beat
f0 ¼
Eq. (7) shows that the beat frequency is proportional to the degree of phase mismatch of two eigen-polarization modes (Dn). Optical fibers in practice always exhibit some birefringence generated in fabrication [10], so we can divide the beat frequency into two terms
fB ¼ f0 þ fext
ð8Þ
where f0 is the eigen-beat frequency caused by eigen-birefringence of SMF F–P cavity, fext is the beat frequency induced by strain birefringence by applied external force. And
cDn0 k0 n
fext ¼
cDnest k0 n
ð9Þ
ð10Þ
where c is the speed of light and k0 the laser wavelength in vacuum, Dn0 indicates the degree of eigen-birefringence of single-mode fiber, and Dnext denotes the degree of strain birefringence caused by the applied external pressure, and n is the average index refraction of the two eigenpolarization modes (Dn0, Dnext n). When an external force applied to a section of the fiber, the induced birefringence is given by [1]:
Fig. 4. Transmission spectrum of SMF F–P cavity.
H. Chen / Measurement 43 (2010) 370–374
373
In Eq. (14), when F is 0, the intercept of the curve corresponds to the eigen-beat frequency f0, that characterizes SMF F–P cavity eigen birefringence. For the low birefringence of standard single-mode fibers (Dn/ n 2 106| f0 0.4 GHz, fB (0.4 + 0.101F) GHz). 3. Experiment
Fig. 5. 50 MHz modulated signal.
bext ¼
8jAj F kr
ð11Þ
where F is the applied force per unit length, A is the stressoptic coefficient (A = 3.7 1012 m2/N for silica), r (2r = 125 lm) is the fiber radius, and k is the wavelength of the light. The stress induced normalized birefringence is given by
B¼
Dn 8jAj ¼ F n 2pnr
ð12Þ
By substituting Eq. (11) in (9), we obtain
fext ¼
fB ¼
c 8jAj F k0 2pnr
c Dn0 8jAj þ F k0 2pnr n
ð13Þ
ð14Þ
Experimental setup (see Fig. 3) is composed of a light source (PRO 8000 Profile WDM source, tunable range 1549.266–1550.966 nm), a polarizer controller, a modulator (JDS Uniphase OC-192), a RF generator (hp 8341B synthesized sweeper, range: 10 MHz to 20 GHz), a singlemode fiber Fabry–Perot cavity, a strain inspector (INFCS400B strain meter, Newport), an erbium doped fiber amplifier (EDFA, Highwave Optical Technologies), a bandpass tunable filter (Newport), a polarizer, an optical spectrum analyzer (Agilent 86142B optical spectrum analyzer), and a digital communication analyzer (hp 83480A digital communication analyzer). Single-mode fiber Fabry–Perot cavity is constructed by attaching standard FC/PC connector to a conventional single-mode fiber (Corning SMF-28). The EDFA is used to compensate the line loss. Properly adjusting the wavelength of input laser to the transmission wavelength of SMF F–P cavity, adjusting the polarizer controller to excite two eigen-polarization modes in SMF F–P cavity, then rotating the output polarizer to combine the two polarization modes, one can then observe the beat which is generated by birefringence of SMF F–P cavity. The transmission spectrum of the SMF F–P cavity is plotted in Fig. 4, it shows that the FSR and length of SMF F–P cavity are 50 GHz and 2 mm, respectively. The transmission wavelength of the SMF F–P cavity is 1550.337 nm. The CW laser from Tunable DFB laser @ 1550.337 nm goes through JDS Uniphase OC-192 modulator derived by a 50 MHz RF signal generated by synthesized sweeper, the modulated waveform is monitored by digital commu-
Fig. 6. Ringdown beat RF spectrum.
374
H. Chen / Measurement 43 (2010) 370–374
133.476 N, The measured beat period (frequency) decreases (increases) from 2 ns (0.5 GHz) at 0 lbs to 0.25 ns (4 GHz). A polynomial fitting of the measured beat period versus applied force shows good linearity, as is readily interpreted by use of Eq. (14), the fitting polynomial is fB = 0.52336 + 0.1119F, this results is consistent with that theory predicts (Eq. (14)). We have made another issue to address the relation of beat period versus the modulated rate of signal. It is found that the beat period is independent of the modulated rate of signal, but the beat number observed decreases with the increase of modulated rate of signal. This result indicates that it could be better using a signal with lower modulated rate. 4. Conclusions We propose and demonstrate a birefringence singlemode fiber F–P cavity based pressure sensor, theoretical analysis and experimental results. It is shown that experimental results are consistent with theory predicts, the pressure is measured in time domain, it could be better using lower modulated rate signal than higher one. A pressure range of 0–133.476 N is given. The advantage of the proposed approach is temperature insensitivity, high stability, low cost and easy fabrication.
Fig. 7. Falling-slope beat signals illumination.
4.5
Measure dots Polynomial fitting curve f B=0.52336+0.1119F R=0.97411
4.0
Beat frequency (GHz)
3.5 3.0
Acknowledgments
2.5
This work was supported partly by the Hubei Provincial Natural Science Fund of China (No. 2008CDB317), The Key item foundation of Hubei Provincial Department of Education (No. D20091203), and the Funds for Creative Research Groups of Yangtze University, China. The author is grateful to Prof. Franko Kuppers and Dr. Qing Wang (Optical Sciences Center, University of Arizona) for useful discussions.
2.0 1.5 1.0 0.5 0.0 -20
0
20
40
60
80
100
120
140
Applied force ( N ) Fig. 8. Beat frequency versus applied force.
nication analyzer (DCA), the synthesized sweeper sends a triggering signal to DCA at the falling slope of the pulse, DCA starts the data acquisition when it receives the triggering signal from the synthesized sweeper. By adjusting the bias voltage of the modulator, one can obtain a perfect 50 MHz modulated signal. When bias voltage is DC-5.18 V, the modulated waveform is plotted in Fig. 5. Letting the modulated signal goes through the SMF F–P cavity, using an EDFA to compensate the line loss, rotating the output polarizer, we observe the combination of the two cavity modes in SMF F–P cavity. When the output polarizer is at a specific azimuthal angle, the beat appears which is caused by a phase mismatch of the polarization modes in the SMF F–P cavity and the magnitude of the birefringence is proportional to the beat frequency. Ringdown beat diagram is plotted in Figs. 6 and 7. The beat period is 2 ns, i.e. the frequency is 0.5 GHz, the applied force is 0 lbs. Fig. 8 shows a typical testing beat frequency versus applied forces. The applied forces are in the range 0–
References [1] Y. Namihira, M. Kudo, Y. Mushiaka, Effect of mechanical stress on the transmission characteristics of optical fibers, Trans. IECE Jpn. 60-C (1977) 107–115. [2] Frangois Maystre, Rene Dandliker, Polarimetric fiber optical sensor with high sensitivity using a Fabry–Perot structure, Appl. Opt. 28 (1989) 1995–2000. [3] Cheng Chih Lai, Wei-Yu Lee, Way-Seen Wang, Gamma radiation effect on the fiber Fabry–Perot interference sensor, IEEE Photonics Technol. 15 (2003) 1132–1134. [4] Bao-Jin Peng, Yong Zhao, Jian Yang, Mingguo Zhao, Pressure sensor based on a free elastic cylinder and birefringence effect on an FBG with temperature-compensation, Measurement 38 (2005) 176–180. [5] Chuji Wang, Susan T. Scherrer, Fiber ringdown pressure sensors, Opt. Lett. 29 (2004) 352–354. [6] Chuji Wang, Susan T. Scherrer, Fiber loop ringdown for physical sensor development pressure sensor, Appl. Opt. 43 (2004) 6458– 6464. [7] T.V. Lerber, M.W. Sigrist, Cavity-ring-down principle for fiber-optic resonators, experimental realization of bending loss and evanescentfield sensing, Appl. Opt. 41 (2002) 3567–3575. [8] T.V. Lerber, H. Ludvigsen, Resonator based measurement technique for quantification of minute birefringence, Opt. Exp. 12 (2004) 1363– 1371. [9] T.V. Lerber, J. Tuominen, H. Ludvigsen, S. Honkanen, F. Kueppers, Multichannel and rate all-optical clock recovery, IEEE Photonics Technol. Lett. 18 (2006) 1395–1397. [10] R. Ulrich, A. Simon, Polarization optics of twisted single-mode fibers, Appl. Opt. 18 (1979) 2241–2251.
Contents lists available at ScienceDirect
Measurement journal homepage: www.elsevier.com/locate/measurement
Fiber optic pressure sensor based on a single-mode fiber F–P cavity Haiyan Chen School of Physics Science and Technology, Yangtze University, Jingzhou 434023, PR China
a r t i c l e
i n f o
Article history: Received 29 April 2009 Received in revised form 4 September 2009 Accepted 2 December 2009 Available online 6 December 2009 Keywords: Optical fiber sensor Pressure sensor Birefringence sensor Optical heterodyne
a b s t r a c t In this paper, we propose and experimentally demonstrate a pressure sensor based on birefringent single-mode fiber F–P cavity using optical heterodyne. The proof of concept device consists of a light source, a polarizer controller, a modulator, a RF generator, a single-mode fiber Fabry–Perot cavity, a strain inspector, an erbium doped fiber amplifier, a filter, a polarizer, an optical spectrum analyzer, and a digital communication analyzer. The dynamic range of the proposed sensor is explored. The results demonstrate the new concept of fiber pressure sensors and the technical feasibility for pressure measurements. Ó 2009 Elsevier Ltd. All rights reserved.
1. Introduction Fiber optic sensors are well known. They have the basic property that the sensing element is a single piece of single-mode fiber and that all the perturbations which affect the length of the fiber are common to both eigenpolarizations [1,2]. Moreover, fiber optic sensors have some advantages such as high sensitivity, fast response, low cost, light weight, as well as immunity to electromagnetic interference. These application features benefit a wide range of industries, including the aerospace, military, petrochemical, transportation, building and structural monitoring, chemical, and biomedical sectors. The most popular fiber pressure sensor structure used is Fabry–Perot cavity, including fiber Fabry–Perot interference (FFPI) [3], fiber Bragg gratings (FBG) [4]. In 2004, Chuji Wang et al. presented a conceptually new approach: a fiber loop ringdown (FLRD) to develop a fiber pressure sensor [5]. This new fiber ringdown technique utilized a singlemode fiber resonator (SMFR) as the ringdown cavity. A signal light is coupled into the SMFR, when the light source is rapidly shut off, the output intensity of SMFR follows an exponential decay because of losses in the SMFR. The lower the losses of the light in the fiber, the longer the decay time E-mail address: [email protected] 0263-2241/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2009.12.002
constant (ringdown time) [6]. However, this method did not distinguish both eigenpolarizations in a single-mode fiber, since different polarizations have different effective refractive index and decay time constant, moreover, there exists measure error because the ringdown time is determined by the light intensity to decrease to 1/e of the initial light intensity, not the gap of peak to peak. To our best knowledge, there were three publications referring to ringdown beat frequency [7–9]. In 2004, Lerber et al. reported their conceptual studies of minute birefringence using ringdown beat frequency [8]. In 2006, Lerber et al. reported their conceptual studies of Rate All-Optical Clock Recovery based on ringdown beat frequency [9]. So far, no one has reported an attempt to introduce the ringdown beat concept for fiber pressure sensors. In this paper we report our exploratory researches on the ringdown beat concept to pressure measurements. 2. Theoretical mode 2.1. Beat generation The principle diagram of a single-mode fiber F–P (SMF F–P) cavity with birefringence is shown as Fig. 1. It consists of an input polarizer, SMF F–P cavity, and an output polarizer. Assuming the effective axis of birefringence of SMF
H. Chen / Measurement 43 (2010) 370–374
R¼
Fig. 1. Schematic diagram of a single-mode fiber F–P cavity.
F–P cavity are x- and y-axis, the direction of output polarizer is xy, the azimuthal angles of input polarizer and output polarizer with respect to the effective axis of birefringence of the cavity are a and b, respectively. For a short SMF F–P cavity, we assume that the electric field amplitude and intensity after input polarizer are E0 and I0, I0 / E20 , and this input light stimulates two polarization modes in a SMF F–P cavity, the phase shift of polarized modes (x- and y-direction) propagating in the cavity after a single roundtrip is
/x ¼
4nx pL k
ð1aÞ
/y ¼
4ny pL k
ð1bÞ
where Ux (nx) and Uy (ny) are the phase (effective index) and of x- and y-direction, k is the resonance wavelength of SMF F–P cavity, L is the length of F–P cavity. The phase difference of the two polarized modes after single roundtrip is
D/ ¼ j/x /y j ¼
4p L jnx ny j k
ð2Þ
This difference is determined by the birefringence degree. Using continuously injecting monochromatic light of E0 into the cavity, the complex cavity field amplitude after p accumulated roundtrip will be
Epx
1 r pþ1 exp ½j/x ðp þ 1Þ ¼ E0 cos a 1 r expði/x Þ 1 r exp½j/y ðp þ 1Þ E0 sin a 1 r expði/y Þ
ð6Þ
c Dn kn
ð7Þ
where n = (nx + ny)/2 is the average refractive indices of the two polarizations.
pþ1
Epy ¼
E20
where E* is the conjugate of E. R is generated by the combination of two polarized modes in SMF F–P cavity. The signal R has a beat nature, because the electric fields both eigen-polarized modes originate from the same light source and thus the frequency is equal for both modes. The propagating time difference of two modes in the cavity after a single roundtrip is DT = 2DnL/c, where Dn = |nxny|, c is the velocity of light in the vacuum. For silica glass fiber, material refractive index is n = 1.47. For Dn = 2 106, L = 2 mm, the free spectrum range (FSR) of SMF F–P cavity is c/ (2nL) = 50 GHz, DT = 2.7 1017 s. When r = 0.995, a = 30°, b = 45°, L = 2 mm, k = 1550.337 nm, p = 0, . . ., 1500, and q = 0, . . ., 1000, Dn = |nxny|=5.38 106, 10.76 106, 16.15 106, the output characteristics of output polarizer is shown in Fig. 2. There are three phases: build-up, stability, and ring-down phase. Build-up phase shows the injection of light, stability expresses that the cavity reaches a maximum after about 1500 roundtrips, ring-down phase denotes that the injection of light is ceased. We also find that mode beats are generated. It demonstrates that the beat is generated at both the rising and the falling slopes of the pulse, and disappears when the field inside the cavity approaches steady-state. The beat frequency increases with the increase of the degree of phase mismatch of two eigen-polarization modes, but the intensity of beat signal decreases with the increase of Dn. this is because that variety of Dn shift the wavelength of input signal away the transmission wavelength of SMF F–P cavity, the transmission wavelength of SMF F–P cavity is determined by 2nx,yL/m, where m is a integer, nx,y is the effective refractive index of transmission modes. The homodyne beat frequency is [9]
fB ¼ ð3aÞ
Exx Eyy þ Exx Eyy
371
ð3bÞ
pffiffiffiffiffiffiffi where j ¼ 1, r is the fractional amplitude attenuation factor by the cavity mirrors and by absorption and scattering in the cavity medium. When the injecting phase of light is stopped, the remaining light in the cavity is still to circulate within the resonator for q additional roundtrips, the total electric field after the SMF F–P cavity can be written as:
Epqx ¼ rq expðjq/x ÞEpx
ð4aÞ
Epqy ¼ rq expðjq/y ÞEpy
ð4bÞ
The output electric field after the output polarizer is
Exx ¼ Epqx cos b þ Epqy sin b
ð5aÞ
Eyy ¼ Epqy cos b Epqx sin b
ð5bÞ
The beat signal can be expressed as
Fig. 2. output characteristics of output polarizer ((a) Dn = 5.38 106, (b) Dn = 10.76 106, (c) Dn = 16.15 106).
372
H. Chen / Measurement 43 (2010) 370–374
Fig. 3. Experimental setup (MOD: modulator).
2.2. Pressure sensor principle using ringdown beat
f0 ¼
Eq. (7) shows that the beat frequency is proportional to the degree of phase mismatch of two eigen-polarization modes (Dn). Optical fibers in practice always exhibit some birefringence generated in fabrication [10], so we can divide the beat frequency into two terms
fB ¼ f0 þ fext
ð8Þ
where f0 is the eigen-beat frequency caused by eigen-birefringence of SMF F–P cavity, fext is the beat frequency induced by strain birefringence by applied external force. And
cDn0 k0 n
fext ¼
cDnest k0 n
ð9Þ
ð10Þ
where c is the speed of light and k0 the laser wavelength in vacuum, Dn0 indicates the degree of eigen-birefringence of single-mode fiber, and Dnext denotes the degree of strain birefringence caused by the applied external pressure, and n is the average index refraction of the two eigenpolarization modes (Dn0, Dnext n). When an external force applied to a section of the fiber, the induced birefringence is given by [1]:
Fig. 4. Transmission spectrum of SMF F–P cavity.
H. Chen / Measurement 43 (2010) 370–374
373
In Eq. (14), when F is 0, the intercept of the curve corresponds to the eigen-beat frequency f0, that characterizes SMF F–P cavity eigen birefringence. For the low birefringence of standard single-mode fibers (Dn/ n 2 106| f0 0.4 GHz, fB (0.4 + 0.101F) GHz). 3. Experiment
Fig. 5. 50 MHz modulated signal.
bext ¼
8jAj F kr
ð11Þ
where F is the applied force per unit length, A is the stressoptic coefficient (A = 3.7 1012 m2/N for silica), r (2r = 125 lm) is the fiber radius, and k is the wavelength of the light. The stress induced normalized birefringence is given by
B¼
Dn 8jAj ¼ F n 2pnr
ð12Þ
By substituting Eq. (11) in (9), we obtain
fext ¼
fB ¼
c 8jAj F k0 2pnr
c Dn0 8jAj þ F k0 2pnr n
ð13Þ
ð14Þ
Experimental setup (see Fig. 3) is composed of a light source (PRO 8000 Profile WDM source, tunable range 1549.266–1550.966 nm), a polarizer controller, a modulator (JDS Uniphase OC-192), a RF generator (hp 8341B synthesized sweeper, range: 10 MHz to 20 GHz), a singlemode fiber Fabry–Perot cavity, a strain inspector (INFCS400B strain meter, Newport), an erbium doped fiber amplifier (EDFA, Highwave Optical Technologies), a bandpass tunable filter (Newport), a polarizer, an optical spectrum analyzer (Agilent 86142B optical spectrum analyzer), and a digital communication analyzer (hp 83480A digital communication analyzer). Single-mode fiber Fabry–Perot cavity is constructed by attaching standard FC/PC connector to a conventional single-mode fiber (Corning SMF-28). The EDFA is used to compensate the line loss. Properly adjusting the wavelength of input laser to the transmission wavelength of SMF F–P cavity, adjusting the polarizer controller to excite two eigen-polarization modes in SMF F–P cavity, then rotating the output polarizer to combine the two polarization modes, one can then observe the beat which is generated by birefringence of SMF F–P cavity. The transmission spectrum of the SMF F–P cavity is plotted in Fig. 4, it shows that the FSR and length of SMF F–P cavity are 50 GHz and 2 mm, respectively. The transmission wavelength of the SMF F–P cavity is 1550.337 nm. The CW laser from Tunable DFB laser @ 1550.337 nm goes through JDS Uniphase OC-192 modulator derived by a 50 MHz RF signal generated by synthesized sweeper, the modulated waveform is monitored by digital commu-
Fig. 6. Ringdown beat RF spectrum.
374
H. Chen / Measurement 43 (2010) 370–374
133.476 N, The measured beat period (frequency) decreases (increases) from 2 ns (0.5 GHz) at 0 lbs to 0.25 ns (4 GHz). A polynomial fitting of the measured beat period versus applied force shows good linearity, as is readily interpreted by use of Eq. (14), the fitting polynomial is fB = 0.52336 + 0.1119F, this results is consistent with that theory predicts (Eq. (14)). We have made another issue to address the relation of beat period versus the modulated rate of signal. It is found that the beat period is independent of the modulated rate of signal, but the beat number observed decreases with the increase of modulated rate of signal. This result indicates that it could be better using a signal with lower modulated rate. 4. Conclusions We propose and demonstrate a birefringence singlemode fiber F–P cavity based pressure sensor, theoretical analysis and experimental results. It is shown that experimental results are consistent with theory predicts, the pressure is measured in time domain, it could be better using lower modulated rate signal than higher one. A pressure range of 0–133.476 N is given. The advantage of the proposed approach is temperature insensitivity, high stability, low cost and easy fabrication.
Fig. 7. Falling-slope beat signals illumination.
4.5
Measure dots Polynomial fitting curve f B=0.52336+0.1119F R=0.97411
4.0
Beat frequency (GHz)
3.5 3.0
Acknowledgments
2.5
This work was supported partly by the Hubei Provincial Natural Science Fund of China (No. 2008CDB317), The Key item foundation of Hubei Provincial Department of Education (No. D20091203), and the Funds for Creative Research Groups of Yangtze University, China. The author is grateful to Prof. Franko Kuppers and Dr. Qing Wang (Optical Sciences Center, University of Arizona) for useful discussions.
2.0 1.5 1.0 0.5 0.0 -20
0
20
40
60
80
100
120
140
Applied force ( N ) Fig. 8. Beat frequency versus applied force.
nication analyzer (DCA), the synthesized sweeper sends a triggering signal to DCA at the falling slope of the pulse, DCA starts the data acquisition when it receives the triggering signal from the synthesized sweeper. By adjusting the bias voltage of the modulator, one can obtain a perfect 50 MHz modulated signal. When bias voltage is DC-5.18 V, the modulated waveform is plotted in Fig. 5. Letting the modulated signal goes through the SMF F–P cavity, using an EDFA to compensate the line loss, rotating the output polarizer, we observe the combination of the two cavity modes in SMF F–P cavity. When the output polarizer is at a specific azimuthal angle, the beat appears which is caused by a phase mismatch of the polarization modes in the SMF F–P cavity and the magnitude of the birefringence is proportional to the beat frequency. Ringdown beat diagram is plotted in Figs. 6 and 7. The beat period is 2 ns, i.e. the frequency is 0.5 GHz, the applied force is 0 lbs. Fig. 8 shows a typical testing beat frequency versus applied forces. The applied forces are in the range 0–
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