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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 10 — May. 20, 2013
  • pp: 11913–11920
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In fiber Bragg grating twist sensor based on analysis of polarization dependent loss

Wang Yiping, Ming Wang, and Xiaoqin Huang  »View Author Affiliations


Optics Express, Vol. 21, Issue 10, pp. 11913-11920 (2013)
http://dx.doi.org/10.1364/OE.21.011913


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Abstract

In this paper, a new technique exploiting the polarization properties of normal fiber Bragg grating (FBG) for twist sensing is firstly proposed and experimentally demonstrated. The evolution of the polarization dependent loss (PDL) response of the FBG with respect to the twist is studied. The physical model is presented and a numerical simulation based on the transfer matrix method is used to calculate the PDL spectrum of the twisted FBG. The theoretical and experimental results suggest that the PDL response of the FBG have higher twist sensitivities than that of the reflected or transmitted amplitude spectra. Based on comprehensive analysis of the resonant wavelength and the amplitude of the two main lobes of the PDL spectrum, this sensor can measure twist angle and determine twist direction simultaneously. Moreover, the performance of the sensor is not affected by strain and temperature variations.

© 2013 OSA

1. Introduction

Twist sensing is important to monitor the health condition of engineering structures such as bridges and buildings. Conventional twist sensors are normally bulk devices based on angle measurement, which have a large size and is impossible to embed them into the structures. In recent years, twist sensors based on FBG have received considerable attention due to their distinct advantages including immunity to electromagnetic interference, flexibility, and even durability against high radiation environments, et al. Especially, their lightweight, non-obstructive characteristics offer the possibility for embedding them into the structure to realize so-called “smart structures”. So far, a number of optical fiber twist sensors have been demonstrated, which include the use of combinatorial torsion beam, CO2 laser fabricated ultra-long period fiber grating [1

1. Y. J. Rao, T. Zhu, and Q. J. Mo, “Highly sensitive fiber-optic torsion sensor based on an ultra-long period fiber grating,” Opt. Commun. 266(1), 187–190 (2006). [CrossRef]

], corrugated long period fiber grating [2

2. C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol. 19(8), 1159–1168 (2001). [CrossRef]

], 81° tilted Bragg grating [3

3. X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fiber twist sensor based on a fiber Bragg grating with 81 tilted structure,” IEEE Photon. Technol. Lett. 18, 2596–2598 (2006). [CrossRef]

], some fiber ring lasers that contain FBGs [4

4. L. L. Shi, T. Zhu, Y. E. Fan, K. S. Chiang, and Y. J. Rao, “Torsion sensing with a fiber ring laser incorporating a pair of rotary long-period fiber gratings,” Opt. Commun. 284(22), 5299–5302 (2011). [CrossRef]

,5

5. J. H. Wo, M. Jiang, M. Malnou, Q. Sun, J. Zhang, P. P. Shum, and D. Liu, “Twist sensor based on axial strain insensitive distributed Bragg reflector fiber laser,” Opt. Express 20(3), 2844–2850 (2012). [CrossRef] [PubMed]

] and some special fibers [6

6. O. Frazao, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-Optic Interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009). [CrossRef]

8

8. W. G. Chen, S. Q. Lou, L. W. Wang, H. Zou, W. L. Lu, and S. S. Jian, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal Fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011). [CrossRef]

]. Many of these sensors, however, would be quite difficult to be used in practice due to the factors such as complicated structure, special fiber gratings are expensive and difficult to fabricate, et al. On the other hand, those FBG twist sensors are susceptible to the cross sensitivity of the axial strain and temperature [9

9. O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010). [CrossRef] [PubMed]

], because their sensing theories are generally based on the reflected or transmitted amplitude spectra analysis and the unvarying strain or temperature is hardly kept in an actual application. Therefore, how to realize a strain and temperature independent measurement of twist by using the ordinary uniform FBG written in standard telecom single-mode fiber is an attractive topic.

Here, we report a new twist sensor using the ordinary uniform FBG based on its PDL analysis. PDL is the difference between the minimum and the maximum transmission of an optical component versus all possible input polarization states. The PDL of FBG is generally caused by the birefringence of optical fiber, and is also induced by single-side irradiation of the fiber by an UV laser during the grating inscription process. In the field of telecommunication, the PDL of FBG in the high bit rate WDM systems should be as small as possible because the existence of the PDL can lead to pulse distortion and deteriorate the systems performance [10

10. S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express 13(25), 9954–9960 (2005). [CrossRef] [PubMed]

]. For sensing applications, however, converting the measurements into a change in the PDL spectrum offers great potential for development of new types of FBG-based optical sensors [11

11. C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(13), 966–968 (2007). [CrossRef]

,12

12. C. Caucheteur, Y. Shevchenko, L. Y. Shao, M. Wuilpart, and J. Albert, “High resolution interrogation of tilted fiber grating SPR sensors from polarization properties measurement,” Opt. Express 19(2), 1656–1664 (2011). [CrossRef] [PubMed]

]. This sensing principle has been successfully demonstrated for measuring different parameters and a lot of studies have been reported [13

13. Y. Su, Y. Zhu, B. F. Zhang, J. Li, and Y. Li, “Use of the polarization properties of magneto-optic fiber Bragg gratings for magnetic field sensing purposes,” Opt. Fiber Technol. 17(3), 196–200 (2011). [CrossRef]

,14

14. S. T. Oh, W. T. Han, U. C. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG based on the birefringence effect,” Opt. Express 12(4), 724–729 (2004). [CrossRef] [PubMed]

].

In this paper, we propose and demonstrate a FBG twist sensor based on analysis of the PDL properties of FBG. The relationship between twist and the FBG’s PDL response is analyzed and numerically simulated following the coupled mode theory and the transfer matrix method. Due to the fiber birefringence changes caused by twist, the PDL of the FBG is sensitive to the variation of twist angle. By measuring the PDL amplitude changes, the twist sensing can be achieved without strain and temperature confusion. In addition, both twist direction and angle can simultaneously be obtained simply. The experiments are then carried out and good agreements between experimental results and numerical simulation have been obtained.

2. Theoretical model

To validate the theoretical concept, we present simulation results of the PDL properties of our FBG twist sensor. This study can be performed using the Jones matrix formulation and transfer matrix method [15

15. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

]. According to this method, the grating is divided into a series of n smaller uniform subgratings and the effect of twist on each subgrating can be treated as uniform. We consider the transmitted light of the FBG because our past research shows that the PDL evolution of reflected light is usually irregular and the transmitted one is more suitable for sensing [16

16. Y. P. Wang, M. Wang, and X. Q. Huang, “High sensitivity fiber Bragg grating transversal force sensor based on centroid measurement of polarization dependent loss,” Meas. Sci. Technol. 21(6), 065304–065308 (2010). [CrossRef]

]. The optical transmission process of the twisted FBG can be described as follows: If ω is the twist rate, once the light pass through a subgrating section (of length dl = L/n), the variation of the orientation of the polarization axe is ωdl. For the section i, the rotation will reach iωdl (i = 1,2,…n). Thetotal twist angle over the whole FBG length L is thus given by θ = ωL. Figure 1
Fig. 1 Schematic diagram of our FBG twist sensor.
shows the model of the twisted FBGs. As shown in Fig. 1, the x and y subscripts correspond to the x and y polarization modes of the transmitted electric fields. The forward and backward field amplitudes of x and y polarization modes after traversing section i is defined by Ei = [Exi+ Exi- Eyi+ Eyi- ]T. And then the propagation through each uniform section can be described by a matrix Ti defined such that:
Ei+1=R(iωdl)Ti(dl)R(ωdl)Ei
(1)
where,
R(ωdl)=[cos(ωdl)sin(ωdl)sin(ωdl)cos(ωdl)]
(2)
R is the matrix used to transform the Cartesian system, as it is done in the Jones formalism.
Ti(dl)=[AxBx00Bx*Ax*0000AyBy00By*Ay*]
(3)
and
Ax(y)=cosh(γx(y)dl)jσx(y)^γx(y)sinh(γx(y)dl)
(4)
Bx(y)=jσx(y)^γx(y)sinh(γx(y)dl)
(5)
γB=κ2σ2^,σ^=δ+σ,
(6)
here δ is detuning, σ and k are respectively “dc” and “ac” coupling coefficient. Once all of the matrices for the individual sections are known, multiplying all of these matrices together could obtain a single 2x2 matrix which describes the whole grating. The output amplitude could thus be obtained by substituting the boundary conditions:

En=R(θ)(i=1nTi(dl)R(ωdl))E0
(7)

The reflected coefficients of the x and y modes rx(y) = Ex(y)i-/ Ex(y)i+ can be derived from Eq. (7). PDL is defined as the maximum change in the transmitted power when the input state of polarization is varied over all polarization states:
PDL=10log10(|tmax|2/|tmin|2)
(8)
where |tmax|2and |tmin|2 denote the maximum and minimum power transmitted through the component. In the case of FBG, the final expression of PDL for transmission is [17

17. Y. P. Wang, M. Wang, and X. Q. Huang, “Spectral characterization of polarization dependent loss of locally pressed fiber Bragg grating,” Opt. Express 19(25), 25535–25544 (2011). [CrossRef] [PubMed]

]:

PDL=10|log10(1|rx|21|ry|2)|
(9)

Generally, when a FBG is twisted, the changes in the spectra of the FBG are hard to detect, because the sensitivity of transverse effects of the FBG is considerably smaller than the longitudinal ones. Therefore, in most applications, simply detecting the changes of the amplitude spectra of the FBG is hard to realize the twist sensing. Unlike the amplitude spectra, the PDL spectrum is very distinct even if the twist is extremely low. Thus, the PDL spectrum would be very useful for sensing purpose.

3. Numerical simulation and experimental investigation

A numerical simulation based on the method described in section 2 is adopted to simulate the PDL spectrum of a twisted FBG. The simulated result is then analyzed to determine the relationship between the evolution of the PDL response and the twist angle. The major parameters for all the simulations in this section are as follows: the central wavelength of the FBG without perturbation is 1524.5nm, the FBG length L is 6mm, theinherent birefringence of the simulated FBG is 10−6. Figure 2(a)
Fig. 2 Simulated evolutions of (a). Transmitted spectra. (b) PDL response for a variety of twist angles.
shows the transmitted spectra response of the FBG verse twist angle. As seen in Fig. 2(a), the transmitted spectrum broadens slightly and its valley shows a small redshift with the increase of twist angle. In addition, the transmissivity of the FBG decreases faintly with the increase of the angle. To understand clearly the transmission property of the twisted FBG, the transmitted spectra of x and y polarized modes are also simulated, both the transmitted spectra of x and y polarized modes show similar results as Fig. 2(a). It is obvious that the precise measurement of the twist through the monitoring of spectral response is very difficult because the changes of the spectra are too weak to detect. Figure 2(b) shows the PDL response of the transmitted light. From Fig. 2(b) we can see that the PDL shows two distinct lobes and their changes with the increase of twist angle are quite obvious, which provides meaningful information for the twist measurement. Figure 3(a)
Fig. 3 FBG’s PDL response to (a) Counter-clockwise twisting; (b) Clockwise twist; (c)Temperature; (d) Strain.
illustrates thePDL evolution of the FBG for various magnitude of the twist angle more clearly for the case of a counter-clockwise twist. We can observe in Fig. 3(a) that the bigger lobe of the PDL spectrum corresponding to the longer wavelength increases constantly with respect to the increasing angle, while the smaller lobe corresponding to the shorter wavelength decreases in height slowly. It also can be seen that the relationship between the variation of the maximum PDL values and the twist angle is almost linear for both lobes. This characteristic will be very useful for twist measurement. In contrast, when the FBG is twisted clockwise, the response of the PDL spectrum exhibits exactly the opposite characteristics, as shown in Fig. 3(b). These different responses provide the potential for realizing the measurement of twist angle and direction determination of twist simultaneously. To understand how the temperature and strain will affect the PDL properties of the FBG, the PDL evolutions of FBG at different temperatures and strain values are simulated by use of the well-known sensing principle of the FBG and the theory described in section 2. As shown in Fig. 3(c), there is no change in the shape of the PDL lobes with the increase of the temperature, while the resonance wavelength shifts almost linearly with temperature. Figure 3(d) shows the PDL spectral changes with the different strain values have properties similar to the temperature effect. Only the resonance wavelength decrease or increase could be observed when a lower or higher strain is applied, the heights of the two main lobes of the PDL spectrum remain unchanged. Therefore, we can affirm that the twist is the only origin of the variation of the PDL lobes in depth. Namely, this twist sensing configuration shows strain and temperature independent characteristics.

A simple experiment was set up to confirm the correctness of the simulated model and results. The schematic of the experiment setup is illustrated in in Fig. 4
Fig. 4 Experimental set-up of the proposed FBG based twist sensor.
. The input light from a tunable laser source (1500-1580nm) was launched into the PDL multimeter (GPC PDL-101). The PDL meter can also be replaced by low cost polarization adjustor and power meter. The modulated polarized light was launched into one end of the fiber and the output was monitored from the other end by the PDL multimeter. For our used PDL multimeter, the working principle is deterministic techniques, which are obtained by measuring the transmission properties of the FBG over a set of defined input polarization states, like for example in the Mueller method. The recorded PDL measurement data was read out via an USB interface and transferred to the PC. The test FBG which has an untwisted Bragg wavelength of 1524.5 nm was written with a length of 1 cm. The testfiber with the test FBG positioned in the middle was 30mm length. One end of the fiber was fixed by a clamp, the other end was fixed on a fiber rotator with an engraved dial.In the experiment of testing the PDL characteristic of this kind of twist sensor, firstly, the FBG was twisted counter-clockwise from 0° to 180° with a step of 9°. And then the PDL spectrum for each applied twist was recorded and analyzed. As an example, Fig. 5(a)
Fig. 5 Measured PDL spectra when the FBG was twisted 90° (a) Counter-clockwise; (c) Clockwise; and the relationship between P1-P2 and applied twist angle for (b) Counter-clockwise; (d) Clockwise.
shows the experimental result of the PDL spectrum when the FBG was twisted 90 degrees. As the Fig. 5(a) clearly shows, the PDL spectrum exhibits two distinct lobes. The two highest peaks corresponding to the longer wavelength and shorter wavelength were labeled as P1 and P2 respectively. As soon as the twist angle increases, the strength of P1 will increase while P2 will decrease, as described in section 2. In order to reduce the PDL measurement errors caused by the instability of the laser source and the connector reflection et al, the difference between P1 and P2 was utilized as the sensor’s coding. In a close examination of the measurement results, the difference between P1 and P2 have good linear response to the applied twist angle, and the twist characteristic has high sensitivity and good repeatability, as shown in Fig. 5(b). The same experimental process by twisting the FBG in clockwise direction was repeated. As shown in Fig. 5(c) and Fig. 5(d), the experimental results of P1 and P2 show opposite trend of variations when the FBG is twisted clockwise, which correspond well with the theoretical predictions mentioned in section 2. Eventually, the twist angle can be obtained by measuring the change of P1-P2. By implementing the linear least-squares fit to the measurement data and calculating the slope, the twist sensitivity of the difference between P1 and P2 is 0.955dB/rad at the twist length of 1cm. The twist direction is determined by determining the polarity of P1-P2, i.e. the FBG is twisted counterclockwise when P1-P2>0, on the other contrary, the condition of P1-P2<0 shows that FBG is twisted clockwise. Finally, we repeated the experiment more than once and did not see any obvious performance degradation, this confirmed the sensor having good repetitiveness.

To confirm the expected temperature and strain insensitivity of the twist sensor, the changes of P1-P2 versus temperature and strain dependences were tested. In the experiment, the pre-twisted FBG was mounted in a laboratory oven and the temperature was varied stepwise between 20° and 80° while recording the P1-P2 value at each set point after 10 min interval. For strain characteristic test, the twisted FBG was fixed at one end and the other was mounted to a step motor. The strain applied by the step motor was increased from 0με to 500με. The pre-twisting angles were selected as 30°,60° and 90°, we firstly record the P1-P2 values with no temperature and strain applying to the FBG. And then we apply different temperatures and different strain to the twisted FBG, we find that the final measurement results were almost exactly equal to the FBG with no temperature and strain applied. As an example, the temperature and strain response of the 90 o twisted sensor is shown in Fig. 6
Fig. 6 Measured P1-P2 with different (a) Temperature; (b) Strain levels for 90o twisted FBG.
.It can be seen that the difference between P1 and P2 almost keeps stable in both cases, confirming that the twist sensor based on PDL analysis is nearly independent with the temperature and strain.

4. Conclusion

In summary a temperature and strain insensitive FBG twist sensor by utilizing analysis of PDL have been proposed and demonstrated. It was observed that the amplitude of the lobes in the PDL spectra were very sensitive to twist. The difference between the peaks of the two lobes was shown as linear function with the twist angle, which is well agreed with the theoretical prediction. The capability of the sensor for measuring amplitude and direction of the twist simultaneously was demonstrated. A twist sensitivity of 0.955dB/rad at the twist length of 1cm was obtained. The work offers new theories and methods for twist sensing by use of the normal FBG, which have wide application prospects in the area of structural health monitoring.

Acknowledgments

This work is supported by the Key Project of Natural Science Foundation of the Education Department of Jiangsu Province of China (Grant No.11KJA510003), the National Natural Science Foundation of China (Grant No.61178044, 91123015) and the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20103207120004).

References and links

1.

Y. J. Rao, T. Zhu, and Q. J. Mo, “Highly sensitive fiber-optic torsion sensor based on an ultra-long period fiber grating,” Opt. Commun. 266(1), 187–190 (2006). [CrossRef]

2.

C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol. 19(8), 1159–1168 (2001). [CrossRef]

3.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fiber twist sensor based on a fiber Bragg grating with 81 tilted structure,” IEEE Photon. Technol. Lett. 18, 2596–2598 (2006). [CrossRef]

4.

L. L. Shi, T. Zhu, Y. E. Fan, K. S. Chiang, and Y. J. Rao, “Torsion sensing with a fiber ring laser incorporating a pair of rotary long-period fiber gratings,” Opt. Commun. 284(22), 5299–5302 (2011). [CrossRef]

5.

J. H. Wo, M. Jiang, M. Malnou, Q. Sun, J. Zhang, P. P. Shum, and D. Liu, “Twist sensor based on axial strain insensitive distributed Bragg reflector fiber laser,” Opt. Express 20(3), 2844–2850 (2012). [CrossRef] [PubMed]

6.

O. Frazao, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-Optic Interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett. 21(17), 1277–1279 (2009). [CrossRef]

7.

H. M. Kim, T. H. Kim, B. K. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett. 22(20), 1539–1541 (2010). [CrossRef]

8.

W. G. Chen, S. Q. Lou, L. W. Wang, H. Zou, W. L. Lu, and S. S. Jian, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal Fiber,” IEEE Photon. Technol. Lett. 23(21), 1639–1641 (2011). [CrossRef]

9.

O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett. 35(16), 2777–2779 (2010). [CrossRef] [PubMed]

10.

S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express 13(25), 9954–9960 (2005). [CrossRef] [PubMed]

11.

C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett. 19(13), 966–968 (2007). [CrossRef]

12.

C. Caucheteur, Y. Shevchenko, L. Y. Shao, M. Wuilpart, and J. Albert, “High resolution interrogation of tilted fiber grating SPR sensors from polarization properties measurement,” Opt. Express 19(2), 1656–1664 (2011). [CrossRef] [PubMed]

13.

Y. Su, Y. Zhu, B. F. Zhang, J. Li, and Y. Li, “Use of the polarization properties of magneto-optic fiber Bragg gratings for magnetic field sensing purposes,” Opt. Fiber Technol. 17(3), 196–200 (2011). [CrossRef]

14.

S. T. Oh, W. T. Han, U. C. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG based on the birefringence effect,” Opt. Express 12(4), 724–729 (2004). [CrossRef] [PubMed]

15.

T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol. 15(8), 1277–1294 (1997). [CrossRef]

16.

Y. P. Wang, M. Wang, and X. Q. Huang, “High sensitivity fiber Bragg grating transversal force sensor based on centroid measurement of polarization dependent loss,” Meas. Sci. Technol. 21(6), 065304–065308 (2010). [CrossRef]

17.

Y. P. Wang, M. Wang, and X. Q. Huang, “Spectral characterization of polarization dependent loss of locally pressed fiber Bragg grating,” Opt. Express 19(25), 25535–25544 (2011). [CrossRef] [PubMed]

OCIS Codes
(060.2370) Fiber optics and optical communications : Fiber optics sensors
(230.1480) Optical devices : Bragg reflectors

ToC Category:
Sensors

History
Original Manuscript: March 28, 2013
Revised Manuscript: April 28, 2013
Manuscript Accepted: May 3, 2013
Published: May 8, 2013

Citation
Wang Yiping, Ming Wang, and Xiaoqin Huang, "In fiber Bragg grating twist sensor based on analysis of polarization dependent loss," Opt. Express 21, 11913-11920 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-10-11913


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References

  1. Y. J. Rao, T. Zhu, and Q. J. Mo, “Highly sensitive fiber-optic torsion sensor based on an ultra-long period fiber grating,” Opt. Commun.266(1), 187–190 (2006). [CrossRef]
  2. C. Y. Lin, L. A. Wang, and G. W. Chern, “Corrugated long-period fiber gratings as strain, torsion, and bending sensors,” J. Lightwave Technol.19(8), 1159–1168 (2001). [CrossRef]
  3. X. Chen, K. Zhou, L. Zhang, and I. Bennion, “In-fiber twist sensor based on a fiber Bragg grating with 81 tilted structure,” IEEE Photon. Technol. Lett.18, 2596–2598 (2006). [CrossRef]
  4. L. L. Shi, T. Zhu, Y. E. Fan, K. S. Chiang, and Y. J. Rao, “Torsion sensing with a fiber ring laser incorporating a pair of rotary long-period fiber gratings,” Opt. Commun.284(22), 5299–5302 (2011). [CrossRef]
  5. J. H. Wo, M. Jiang, M. Malnou, Q. Sun, J. Zhang, P. P. Shum, and D. Liu, “Twist sensor based on axial strain insensitive distributed Bragg reflector fiber laser,” Opt. Express20(3), 2844–2850 (2012). [CrossRef] [PubMed]
  6. O. Frazao, C. Jesus, J. M. Baptista, J. L. Santos, and P. Roy, “Fiber-Optic Interferometric torsion sensor based on a two-LP-mode operation in birefringent fiber,” IEEE Photon. Technol. Lett.21(17), 1277–1279 (2009). [CrossRef]
  7. H. M. Kim, T. H. Kim, B. K. Kim, and Y. J. Chung, “Temperature-insensitive torsion sensor with enhanced sensitivity by use of a highly birefringent photonic crystal fiber,” IEEE Photon. Technol. Lett.22(20), 1539–1541 (2010). [CrossRef]
  8. W. G. Chen, S. Q. Lou, L. W. Wang, H. Zou, W. L. Lu, and S. S. Jian, “Highly sensitive torsion sensor based on Sagnac interferometer using side-leakage photonic crystal Fiber,” IEEE Photon. Technol. Lett.23(21), 1639–1641 (2011). [CrossRef]
  9. O. Frazão, R. M. Silva, J. Kobelke, and K. Schuster, “Temperature- and strain-independent torsion sensor using a fiber loop mirror based on suspended twin-core fiber,” Opt. Lett.35(16), 2777–2779 (2010). [CrossRef] [PubMed]
  10. S. Bette, C. Caucheteur, M. Wuilpart, P. Mégret, R. Garcia-Olcina, S. Sales, and J. Capmany, “Spectral characterization of differential group delay in uniform fiber Bragg gratings,” Opt. Express13(25), 9954–9960 (2005). [CrossRef] [PubMed]
  11. C. Caucheteur, S. Bette, R. Garcia-Olcina, M. Wuilpart, S. Sales, J. Capmany, and P. Mégret, “Transverse strain measurements using the birefringence effect in fiber Bragg gratings,” IEEE Photon. Technol. Lett.19(13), 966–968 (2007). [CrossRef]
  12. C. Caucheteur, Y. Shevchenko, L. Y. Shao, M. Wuilpart, and J. Albert, “High resolution interrogation of tilted fiber grating SPR sensors from polarization properties measurement,” Opt. Express19(2), 1656–1664 (2011). [CrossRef] [PubMed]
  13. Y. Su, Y. Zhu, B. F. Zhang, J. Li, and Y. Li, “Use of the polarization properties of magneto-optic fiber Bragg gratings for magnetic field sensing purposes,” Opt. Fiber Technol.17(3), 196–200 (2011). [CrossRef]
  14. S. T. Oh, W. T. Han, U. C. Paek, and Y. Chung, “Discrimination of temperature and strain with a single FBG based on the birefringence effect,” Opt. Express12(4), 724–729 (2004). [CrossRef] [PubMed]
  15. T. Erdogan, “Fiber Grating Spectra,” J. Lightwave Technol.15(8), 1277–1294 (1997). [CrossRef]
  16. Y. P. Wang, M. Wang, and X. Q. Huang, “High sensitivity fiber Bragg grating transversal force sensor based on centroid measurement of polarization dependent loss,” Meas. Sci. Technol.21(6), 065304–065308 (2010). [CrossRef]
  17. Y. P. Wang, M. Wang, and X. Q. Huang, “Spectral characterization of polarization dependent loss of locally pressed fiber Bragg grating,” Opt. Express19(25), 25535–25544 (2011). [CrossRef] [PubMed]

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