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Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 22 — Nov. 4, 2013
  • pp: 26806–26811
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Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers

Binbin Song, Yinping Miao, Wei Lin, Hao Zhang, Jixuan Wu, and Bo Liu  »View Author Affiliations


Optics Express, Vol. 21, Issue 22, pp. 26806-26811 (2013)
http://dx.doi.org/10.1364/OE.21.026806


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Abstract

An all-fiber twist sensor based on multimode interferometer (MMI) has been proposed and fabricated by splicing both ends of a section of square no-core fiber (NCF) with a single mode fiber. We have investigated the transmission spectral characteristics of the square fiber under different applied twisting angles. Within a torsion angle range of -360°~360°, the wavelength and transmission sensitivities are 1.28615nm/(rad × m−1) and 0.11863%/ (rad × m−1), respectively. Moreover due to the trivial thermal expansion coefficient of pure silica fiber, the proposed twist sensor has a low temperature sensitivity, which is desirable to solve the temperature cross sensitivity.

© 2013 Optical Society of America

1. Introduction

Currently, security monitoring in civil engineering applications, such as bridges, buildings, many other civil structures, has been an important and indispensable subject. Generally, the studies on structural health status are almost focused on several physical parameters including bend, axial stress, transverse load, temperature, twist and so on. Twist is one of the most important mechanical parameters for security monitoring of buildings. And accordingly, various twist sensors have been developed before. Traditional twist sensors such as optical encoders and magnetic sensors [1

1. V. Lemarquand, “Synthesis study of magnetic torque sensors,” IEEE Trans. Magn. 35(6), 4503–4510 (1999). [CrossRef]

] always have a large size, which is hardly compatible with building structures. Recently, fiber-based torsion sensors have been widely applied in the civil engineering owing to their excellent advantages such as strong flexible, compact structure, ease of integration, and strong resistance to environmental interferences.

A variety of optical torsion sensors have been reported utilizing different fiber devices, which could be classified into the ones elastic beams or without elastic beams. On the one hand, when a twist is applied to the fiber which is firmly bonded to the surface of elastic beam, the center of rotation shaft is not along the fiber axis, but along the elastic beam axis [2

2. W. G. Zhang, G. Y. Kai, X. Y. Dong, S. Z. Yuan, and Q. D. Zhao, “Temperature-independent FBG-type torsion sensor based on combinatorial torsion beam,” IEEE Photon. Technol. Lett. 14(8), 1154–1156 (2002). [CrossRef]

], and in this case the relationship between resonance wavelength shift Δλ and strain ɛ along the fiber axis could be used for sensing purposes. However, the indirect measurement method would produce a larger error and impose some limit on the angle measurement range. On the other hand, the torsion shaft of twist sensor without elastic beams is along the fiber axis. Conventional fiber-optic torsion sensors based on LPFGs fabricated by UV radiation or corrugated structures [3

3. D. A. Gonzalez, C. Jauregui, A. Quintela, F. J. Madruga, P. Marquez, and J. M. Lopez-Higuera, “Torsion-induced effects on UV long-period fiber gratings,” In Second European Workshop on Optical Fibre Sensors. International Society for Optics and Photonics. (192–195) (2004). [CrossRef]

,4

4. 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]

], CO2 radiation and electric arc [5

5. Y. P. Wang, J. P. Chen, and Y. J. Rao, “Torsion characteristics of long period fiber gratings induced by high-frequency laser pulses,” J. Opt. Soc. Am. B 22(6), 1167–1172 (2005). [CrossRef]

], and mechanical [6

6. J. Y. Cho, J. H. Lim, and K. S. Lee, “Optical fiber twist sensor with two orthogonally oriented mechanically induced long-period grating sections,” IEEE Photon. Technol. Lett. 17(2), 453–455 (2005). [CrossRef]

8

8. O. V. Ivanov, “Propagation and coupling of hybrid modes in twisted fibers,” J. Opt. Soc. Am. A 22(4), 716–723 (2005). [CrossRef] [PubMed]

] were reported, the unsymmetrical distribution of refractive index change induced by the photoabsorption or thermal damage in the cladding or core region of the optical fiber results in many unique torsion characteristics [9

9. Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003). [CrossRef]

]. However, LPFGs present cross sensitivities between different physical parameters such as temperature, strain, pressure, refractive index, load, and so on [10

10. V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21(9), 692–694 (1996). [CrossRef] [PubMed]

]. Utilizing the birefringence property of titled fiber Bragg grating (TFBG) and retroreflection capability of FBG, the twist sensors based on tilted fiber gratings [11

11. 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]

] and distributed Bragg reflector (DBR) fiber laser [12

12. J. 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]

] were reported. Recently, many studies on pohotonic-crystal-fiber-(PCF-) based torsion sensors were also reported. Since fiber twist causes certain circular birefringence, various high-birefringent pohotonic crystal fibers (HB-PCFs) were used in Sagnac loop structure to construct twist sensors [13

13. 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]

,14

14. O. Frazão, S. O. Silva, J. M. Baptista, J. L. Santos, G. Statkiewicz-Barabach, W. Urbanczyk, and J. Wojcik, “Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber,” Appl. Opt. 47(27), 4841–4848 (2008). [CrossRef] [PubMed]

]. Low-birefringent pohotonic crystal fibers (LB-PCFs) have been also utilized in the Sagnac loop structure [15

15. J. M. Estudillo-Ayala, J. Ruiz-Pinales, R. Rojas-Laguna, J. A. Andrade-Lucio, O. G. Ibarra-Manzano, E. Alvarado-Mendez, M. Torres-Cis-neros, B. Ibarra-Escamilla, and E. A. Kuzin, “Analysis of a Sagnac interferometer with low-birefringence twisted fiber,” Opt. Lasers Eng. 39(5-6), 635–643 (2003). [CrossRef]

,16

16. P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011). [CrossRef]

]. In addition, twist sensors based on the interference between two linear polarization (LP) modes in HB-PCFs have been achieved [17

17. 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]

]. However, as well known, the fabrication of PCFs is costly, which limits their applications to a large extend. Therefore, there is always the demand for the developing fiber-optic twist sensors with simple configuration, performance reliability, and low cost.

In this paper, we have proposed a compact MMI-based all-fiber twist sensor. A section of square NCF is employed instead of the conventional MMF, which is simply spliced between two SMFs. As twist effect is applied the MMI, the transmission spectral with multimode interferential fringes have been investigated. Within a torsion angle range of −360~360°, the wavelength shift and transmission loss both exhibit the sinuous relationship with the change of twist rate for the spectral notches. Furthermore, the NCF interferometer has ultra-low temperature sensitivity. And high twist angle sensitivity without temperature cross-sensitivity has been achieved.

2. Principle and experiment

Fig. 1 Schematic experiment setup of the twist sensor (a) experimental setup; (b) Enlarged view of dotted circle.
The schematic diagram of our proposed fiber twist test system is shown in the Fig. 1 (b), when the light is coupled from the lead-in SMF into the square NCF, multitude of low or high-order eigenmodes, i.e. Emnxor Emnymodes, are excited and the interference between different modes occurs while the light propagates along the square NCF [23

23. Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photon. Technol. Lett. 23(11), 679–681 (2011). [CrossRef]

]. The electric field distribution at any point in the NCF can be written as [22

22. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

]:

Ψ(x,y,z)=m=0Mn=0N[amnψmnx(x,y)exp(jβmnxz)+bmnψmny(x,y)exp(jβmnyz)]
(1)

where the timedependent factor is omitted, and amn, ψmnx, and βmnx are the excitation coefficient, field profile and the propagation constant of the Emnx mode in the square NCF, respectively; and bmn, ψmny, and βmny have the same connotations for the Emny mode. As analyzed in reference [22

22. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

], the field excitation coefficients amn and bmn can be estimated using the overlap integral:
αmn=00Ψ(x,y,0)ψmn(x,y)dxdy00ψmn2(x,y)dxdy;(α=a,ψ=ψxorα=b,ψ=ψy)
(2)
The propagation constant βmn can be expressed as [22

22. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

]:
βmnk0n0(m+1)2λπ4n0Wxme2(n+1)2λπ4n0Wyne2
(3)
where, n0 (1.444) is the refractive index of the square NCF. Wxme and Wyne are the effective widths of mn-order Emnxand Emnymodes along x- and y- directions, which are associated with the Goos-Hahnchen shifts at the ridge boundaries. For the square NCF, they can be approximated as the sum of waveguide width W0 and lateral penetration depths [22

22. L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

]:
Weff(σ)W0+(λπ)(1n0)2σ1n021
(4)
where, W0=90μm, for Emnx mode Wxme=Weff(1),Wyme=Weff(0) and for Emny mode Wxme=Weff(0), Wyme=Weff(1). The transmission loss in percentage can be expressed approximately [24

24. Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett. 31(3), 317–319 (2006). [CrossRef] [PubMed]

]:
ηout=|00Ψ(x,y,L0)Ψout(x,y)dxdy|20|Ψ(x,y,L0)|2dxdy0|Ψ(x,y)|2dxdy
(5)
where Ψout(x,y)is the eigenmode field profile of the out single-mode fiber, and L0 is the length of the MMI.

Based on the interference theory, intermodal interference condition for spectral notches can be expressed as(βmnβuv)l=(2p+1)π, and for our proposed device, l=L0. Therefore, using Eq. (3), the expression of notch wavelengths can be obtained:

λ=4(2p+1)n0(u+1)2Wxue2+(v+1)2Wyve2(m+1)2Wxme2(n+1)2Wyne21L0,(pisinteger) 
(6)

The experiment setup of the proposed twist sensor is shown in Fig. 1 which consists of a supercontinuum broadband source (SBS) and an optical spectrum analyzer (OSA, Yokogawa AQ6370C, operation wavelength ranges from 600nm to 1700nm) with a resolution of 0.5nm. The MMI as sensing element spliced between the SBS and OSA is shown in dotted circle region. The enlarged view of MMI is shown in the Fig. 1(b) The two ends of the square NCF are spliced between two SMFs (SMF-28e, Corning, Inc), the NCF with a cross section size of 90μm × 90μm and length L0 = 1.9cm is a pure silica square rod with air as its cladding. The distance L between the fiber holder and rotator is 37cm. When incident light propagates through the square NCF, a large number of high-order modes would be excited, and multimodeinterference simultaneously occurs.

3. Experimental results and discussion

As twist is applied, multi torsional stress zones were formed along the fiber axis, and thus twist effect would cause the periodic refractive index modulation, which ultimately affects the wavelength shifts and interference strength. Also due to twist effect that has an influence on the polarization state of incident light, the degeneracy state of Emnx or Emny modes with the same orders also changed, which eventually lead to the split of resonant dips.
Fig. 2 Transmission spectral characteristics of the MMI under different torsion angles ranging from −360°-360°, inset is the enlarged view of the dip in red dotted frame.
Figure 2 shows the transmission spectrum with different torsion angles ranging from −360°-360°. As shown in Fig. 2, because of the obvious multimode interference effect, complicated interference spectrum appears with a contrast ratio over 20dB. With the increment of torsion angles, resonance wavelength shifts, transmission intensity and spectral split change simultaneously. The transmission dip in the red dotted frame is shown in the inset of Fig. 2. With the increment of torsion angles, a new dip emerges in the shorter wavelength region which is induced by the breaks of degeneracy state of Emnx or Emny modes with the same orders.

Fig. 3 Transmission response of the dip to the torsion angle: (a) wavelength response; (b) transmission response.
Figure 3 shows the wavelength shift and transmission loss change of the dip, respectively. The torsion angle is different for different points along the distance between fiber holder and rotator, and thus it is necessary to use γ = θ/L to quantify the twist rate. As shown in Fig. 3(a), the red line is the nonlinear fitting of a sine function with R2 = 0.99658 for the torsion angle ranging from −360° to 360°, and the wavelength of dip A shifts by 17nm from 1335.7nm to 1352.7nm. The same responses can be seen in Fig. 3(b), in which the red line is also the nonlinear fitting of a sine function with R2 = 0.98412, and the transmission loss variation is 16.9dB, equal to 0.996% in percentage. By linear fitting the particular region, the wavelength shifts and transmission losses reach the maximum sensitivities of 1.28615nm/(rad × m−1) and 0.11863%/ (rad × m−1), respectively, which is in good agreement with our theoretical analysis.

Fig. 4 Transmission spectral characteristics of the MMI for different temperatures, inset is the enlarged view of the dip in red dotted frame.
Figure 4 shows the transmission spectral characteristics of the MMI for different temperatures, and the inset corresponds to the same dip for twist effect analysis. Due to the low thermal-expansion coefficient of the pure silica fiber, the NCF interferometer has a very low temperature sensitivity, as shown in the Fig. 5, within a temperature range from room temperature to 95°C, the measured wavelength shift and intensity variation are only 0.8nm and less than 0.2dB, respectively. The environmental temperature has been kept stable to minimize the influence of temperature fluctuation and achieve highly accurate twist angle measurement. Therefore, for a small temperature range, the twist sensor can be considered as temperature-insensitive.
Fig. 5 Transmission-dependent transmission response of the dip, above is the wavelength response; below is transmission response.

4. Conclusion

A twist sensor based on multimode interferometer employing the square NCF with ultra- low temperature sensitivity has been proposed and experimentally demonstrated in this paper. Experimental results indicate the wavelength and transmission loss reach the maximum twist sensitivities of 1.28615nm/(rad × m−1) and 0.11863%/ (rad × m−1), respectively, which is in good agreement with our theoretical analysis. Since the MMI is fabricated using pure silica square NCF, the temperature cross-sensitivity issue has been resolved. The proposed twist sensor with several advantages such as compact structure, low cost and immunity to temperature cross-sensitivity is highly desirable for civil engineering applications.

Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 11204212, 11274182, and 11004110, Science & Technology Support Project of Tianjin under Grant No. 11ZCKFGX01800, Key Natural Science Foundation Project of Tianjin under Grant No. 13JCZDJC26100, China Postdoctoral Science Foundation Funded Project under Grant No. 2012M520024, the National Key Basic Research and Development Program of China under Grant No. 2010CB327605, and the Fundamental Research funds for the Central Universities.

References and links

1.

V. Lemarquand, “Synthesis study of magnetic torque sensors,” IEEE Trans. Magn. 35(6), 4503–4510 (1999). [CrossRef]

2.

W. G. Zhang, G. Y. Kai, X. Y. Dong, S. Z. Yuan, and Q. D. Zhao, “Temperature-independent FBG-type torsion sensor based on combinatorial torsion beam,” IEEE Photon. Technol. Lett. 14(8), 1154–1156 (2002). [CrossRef]

3.

D. A. Gonzalez, C. Jauregui, A. Quintela, F. J. Madruga, P. Marquez, and J. M. Lopez-Higuera, “Torsion-induced effects on UV long-period fiber gratings,” In Second European Workshop on Optical Fibre Sensors. International Society for Optics and Photonics. (192–195) (2004). [CrossRef]

4.

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]

5.

Y. P. Wang, J. P. Chen, and Y. J. Rao, “Torsion characteristics of long period fiber gratings induced by high-frequency laser pulses,” J. Opt. Soc. Am. B 22(6), 1167–1172 (2005). [CrossRef]

6.

J. Y. Cho, J. H. Lim, and K. S. Lee, “Optical fiber twist sensor with two orthogonally oriented mechanically induced long-period grating sections,” IEEE Photon. Technol. Lett. 17(2), 453–455 (2005). [CrossRef]

7.

O. V. Ivanov, “Fabrication of long-period fiber gratings by twisting a standard single-mode fiber,” Opt. Lett. 30(24), 3290–3292 (2005). [CrossRef] [PubMed]

8.

O. V. Ivanov, “Propagation and coupling of hybrid modes in twisted fibers,” J. Opt. Soc. Am. A 22(4), 716–723 (2005). [CrossRef] [PubMed]

9.

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21(5), 1320–1327 (2003). [CrossRef]

10.

V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett. 21(9), 692–694 (1996). [CrossRef] [PubMed]

11.

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]

12.

J. 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]

13.

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]

14.

O. Frazão, S. O. Silva, J. M. Baptista, J. L. Santos, G. Statkiewicz-Barabach, W. Urbanczyk, and J. Wojcik, “Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber,” Appl. Opt. 47(27), 4841–4848 (2008). [CrossRef] [PubMed]

15.

J. M. Estudillo-Ayala, J. Ruiz-Pinales, R. Rojas-Laguna, J. A. Andrade-Lucio, O. G. Ibarra-Manzano, E. Alvarado-Mendez, M. Torres-Cis-neros, B. Ibarra-Escamilla, and E. A. Kuzin, “Analysis of a Sagnac interferometer with low-birefringence twisted fiber,” Opt. Lasers Eng. 39(5-6), 635–643 (2003). [CrossRef]

16.

P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett. 23(13), 920–922 (2011). [CrossRef]

17.

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]

18.

O. Frazão, J. Viegas, P. Caldas, J. L. Santos, F. M. Araújo, L. A. Ferreira, and F. Farahi, “All-fiber Mach-Zehnder curvature sensor based on multimode interference combined with a long-period grating,” Opt. Lett. 32(21), 3074–3076 (2007). [CrossRef] [PubMed]

19.

Y. Gong, T. Zhao, Y. J. Rao, Y. Wu, and Y. Guo, “A ray-transfer-matrix model for hybrid fiber Fabry-Perot sensor based on graded-index multimode fiber,” Opt. Express 18(15), 15844–15852 (2010). [CrossRef] [PubMed]

20.

Y. Jung, G. Brambilla, K. Oh, and D. J. Richardson, “Highly birefringent silica microfiber,” Opt. Lett. 35(3), 378–380 (2010). [CrossRef] [PubMed]

21.

J. Li, L. P. Sun, S. Gao, Z. Quan, Y. L. Chang, Y. Ran, L. Jin, and B. O. Guan, “Ultrasensitive refractive-index sensors based on rectangular silica microfibers,” Opt. Lett. 36(18), 3593–3595 (2011). [CrossRef] [PubMed]

22.

L. B. Soldano and E. C. M. Pennings, “Optical multi-mode interference devices based on self-imaging: principles and applications,” J. Lightwave Technol. 13(4), 615–627 (1995). [CrossRef]

23.

Y. Gong, T. Zhao, Y. J. Rao, and Y. Wu, “All-fiber curvature sensor based on multimode interference,” IEEE Photon. Technol. Lett. 23(11), 679–681 (2011). [CrossRef]

24.

Q. Wang and G. Farrell, “All-fiber multimode-interference-based refractometer sensor: proposal and design,” Opt. Lett. 31(3), 317–319 (2006). [CrossRef] [PubMed]

OCIS Codes
(060.2270) Fiber optics and optical communications : Fiber characterization
(060.2370) Fiber optics and optical communications : Fiber optics sensors

ToC Category:
Sensors

History
Original Manuscript: July 17, 2013
Revised Manuscript: October 2, 2013
Manuscript Accepted: October 6, 2013
Published: October 30, 2013

Citation
Binbin Song, Yinping Miao, Wei Lin, Hao Zhang, Jixuan Wu, and Bo Liu, "Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers," Opt. Express 21, 26806-26811 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-22-26806


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References

  1. V. Lemarquand, “Synthesis study of magnetic torque sensors,” IEEE Trans. Magn.35(6), 4503–4510 (1999). [CrossRef]
  2. W. G. Zhang, G. Y. Kai, X. Y. Dong, S. Z. Yuan, and Q. D. Zhao, “Temperature-independent FBG-type torsion sensor based on combinatorial torsion beam,” IEEE Photon. Technol. Lett.14(8), 1154–1156 (2002). [CrossRef]
  3. D. A. Gonzalez, C. Jauregui, A. Quintela, F. J. Madruga, P. Marquez, and J. M. Lopez-Higuera, “Torsion-induced effects on UV long-period fiber gratings,” In Second European Workshop on Optical Fibre Sensors. International Society for Optics and Photonics. (192–195) (2004). [CrossRef]
  4. 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]
  5. Y. P. Wang, J. P. Chen, and Y. J. Rao, “Torsion characteristics of long period fiber gratings induced by high-frequency laser pulses,” J. Opt. Soc. Am. B22(6), 1167–1172 (2005). [CrossRef]
  6. J. Y. Cho, J. H. Lim, and K. S. Lee, “Optical fiber twist sensor with two orthogonally oriented mechanically induced long-period grating sections,” IEEE Photon. Technol. Lett.17(2), 453–455 (2005). [CrossRef]
  7. O. V. Ivanov, “Fabrication of long-period fiber gratings by twisting a standard single-mode fiber,” Opt. Lett.30(24), 3290–3292 (2005). [CrossRef] [PubMed]
  8. O. V. Ivanov, “Propagation and coupling of hybrid modes in twisted fibers,” J. Opt. Soc. Am. A22(4), 716–723 (2005). [CrossRef] [PubMed]
  9. Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol.21(5), 1320–1327 (2003). [CrossRef]
  10. V. Bhatia and A. M. Vengsarkar, “Optical fiber long-period grating sensors,” Opt. Lett.21(9), 692–694 (1996). [CrossRef] [PubMed]
  11. 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]
  12. J. 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]
  13. 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]
  14. O. Frazão, S. O. Silva, J. M. Baptista, J. L. Santos, G. Statkiewicz-Barabach, W. Urbanczyk, and J. Wojcik, “Simultaneous measurement of multiparameters using a Sagnac interferometer with polarization maintaining side-hole fiber,” Appl. Opt.47(27), 4841–4848 (2008). [CrossRef] [PubMed]
  15. J. M. Estudillo-Ayala, J. Ruiz-Pinales, R. Rojas-Laguna, J. A. Andrade-Lucio, O. G. Ibarra-Manzano, E. Alvarado-Mendez, M. Torres-Cis-neros, B. Ibarra-Escamilla, and E. A. Kuzin, “Analysis of a Sagnac interferometer with low-birefringence twisted fiber,” Opt. Lasers Eng.39(5-6), 635–643 (2003). [CrossRef]
  16. P. Zu, C. C. Chan, Y. X. Jin, T. X. Gong, Y. F. Zhang, L. H. Chen, and X. Y. Dong, “A temperature-insensitive twist sensor by using low-birefringence photonic-crystal-fiber-based Sagnac interferometer,” IEEE Photon. Technol. Lett.23(13), 920–922 (2011). [CrossRef]
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