Abstract

A novel optical fiber torsion sensor head is proposed. A section of polarization-maintaining fiber (PMF) is spliced between single mode fiber (SMF), and a twist taper is fabricated by a commercial electric-arc fusion splicer in the middle of the PMF. The asymmetric characteristics are obtained by the twist taper so that a fiber torsion sensor with directional discrimination is fabricated. Due to the characteristics of the asymmetric structure, the torsion sensitivity for the twist rate from 0 rad/m to −8 rad/m reaches 2.392 nm/rad·m−1, and for the twist rate from 0 rad/m to 8 rad/m reaches 1.071 nm/rad·m−1 respectively.

© 2015 Optical Society of America

1. Introduction

Fiber optics sensors have attracted much attention for engineering applications, such as traffic, energy and biological monitoring. Twist is one of the most important mechanical parameters for security monitoring of buildings [1]. By measuring the twist of the structure, the stress state and internal injury of the structure can be monitored, it is helpful for us to analyze whether the buildings are under a healthy state. In principle, twist can be detected by electrical methods, which are associated essentially with variations in strain-based electrical resistance [2]. However, for these sensors, interferences from electrical noise and temperature are inevitable. Compared to the electric sensors, fiber optics sensors have advantages such as light weight, small size, no electromagnetic interference, and more importantly most fiber optics sensors can achieve high sensitivity to meet the requirement of engineering.

In recent years, a variety of torsion sensors have been fabricated based on different principles. The most common approach to the fabrication of fiber torsion sensors is the natural characteristics of the polarization in the fiber [3–7 ]. The orthogonal polarization modes or single polarization mode can be stimulated through various kinds of fiber components, such as UV-inscription tilted fiber gratings [8], polarization-maintaining fiber Bragg gratings [9], and high-birefringence fibers [10]. X. Chen et al. fabricated a twist sensor by utilizing strong polarization dependent coupling behavior of fiber Brag gratings with excessively tilted structures up to 81°, which shown high torsion sensitivity and capability of direction recognition [11]. H. M. Kim et al. reported on enhanced torsion sensitivity by using a highly birefringent photonic crystal fiber based Sagnac interferometer [12]. X. M. Xi et al. used helical photonic crystal fiber to measure mechanical strain and twist [13]. A novel helical long period fiber grating with multi-phase-shifted was reported by R. Gao et al. to measure twist and direction [14]. Recently, we proposed an in-fiber torsion sensor based on dual polarized Mach-Zehnder interference [15]. More recently, femtosecond laser-fabricated waveguides were formed into helical paths throughout the cladding of single-mode optical fibers by Luís A. et al. to measure torsion [16].

In this paper, we fabricate a low temperature cross-sensitivity fiber optics torsion sensor by making a twist taper in PMF (PANDA type). Compared with prior structures, the stress in the taper region will be concentrated, so it will improve the sensitivity of the sensor. To be different from the normal taper in PMF [17], the twist taper breaks the symmetry of the PMF, so the sensor head has the ability of directional discrimination. Furthermore, this structure has an ultra-low temperature sensitivity. Thereupon, a high sensitivity torsion sensor with directional discrimination and low temperature cross-sensitivity is proposed and experimentally confirmed.

2. Principle and experiment

The schematic diagram of our sensor head is shown in Fig. 1(a) . The PMF we used in our experiment is PM15-1(06003)-4A. The diameter of the core is 7.2 ± 1 μm, and the diameter of the stress region is 33 ± 1 μm, as its cross-section is shown in Fig. 1(b). We splice the two ends of the PMF with SMF. The length of the PMF is ~1.6 cm, and the core diameter of SMF is 8.5 μm. Due to the mismatch of the mode fields, a loss exists when we spliced the PMF with SMF. The input light will be split into two optical path beams. A portion of the light propagates in core, while the other propagates in cladding. At the other fusion-splicing point, a part of the cladding mode will be coupled back to the core, so a Mach-Zehnder interferometer has been formed due to the phase difference between the core mode and the cladding mode. The phase difference between the core mode and cladding mode can be expressed as:

ϕ=2π(neffconeffcl)Lλ
ϕ=(2m+1)π,m=0,1,2...
λmf/s=2(neffco,f/sneffcl,f/s)L2m+1
where neffco,f/s and neffcl,f/s are the effective refractive index of the core and cladding for the fast/slow axis.

 figure: Fig. 1

Fig. 1 Schematic diagram of the twist sensor: (a) sensor head, (b) cross-section of the PMF, (c) twist taper, (d) microscopic image, (e) coordinate, (f) coupling between core mode and cladding mode.

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In order to obtain a higher sensitivity for torsion and directional discrimination, we fabricate a twist taper with a commercial electric-arc fusion splicer in the middle of the PMF. For the normal taper, a force along the fiber axis is exerted before discharging. In our experiment, besides the axis force, a twist stress will also be applied by introducing a pre-torsion before discharging. The clockwise torsion is defined as the positive torsion. As shown in Fig. 1(c), the stress region is helical-shaped around the core after discharging. The microscopic image of the twist taper is shown in Fig. 1(d). The minimum diameter of the taper is ~42 μm, the length is ~200 μm, and the pre-torsion rate of the twist taper after discharging is ~15.1 rad/mm. In the twist taper region, a portion of the core mode and cladding mode will be coupled to each other, and a portion of the modes will keep propagating as before.

Here we take the two modes into account, which are coupled at the two fusion-splicing points. For the wavelength demodulation method, we mainly consider about the phase change. For the birefringence of the PMF, the effective refractive indexes of the core mode and cladding mode will be different between the fast and slow axes. As shown in Fig. 1(e), the length of m is the difference of effective refractive indexes between the core mode and cladding mode, and the x and y axes are the fast and slow axes of the PMF. In order to analyze the effect of torsion on the PMF, we assume the length of m as an elliptical distribution according to the axial angle.

x2a2+y2b2=1
x=acosθ,y=bsinθ
a=neffco,fneffcl,f,b=neffco,sneffcl,s

The phase difference between the core mode and cladding mode can be expressed approximately:

ϕ=2πλl/2l/2a2cos2θ+b2sin2θdz
θ={d2(α+γβ)+(z+d2)β,     l2z<d2(α+γβ)z,                            d2z<d2d2(α+γβ)+(zd2)β,          d2<zl2
where α and β are the pre-torsion rate of the twist taper and torsion rate of the sensor head. While the stress in the taper region is concentrated, so the torsion rate of the taper region is larger than the sensor head. The value of α+γβ represents the torsion rate of the taper region, γ is the amplification factor which is caused by the taper. The values of l and d mean to the length of the sensor head and twist taper respectively, while dl, we simplify a and b as constants along z axis. The phase difference of the cladding mode and core mode changes with the shifting of the twist rate.

As shown in Fig. 1(f), mode coupling exists both in the two fusion-splicing points and the taper region, the interferences occur between four modes in the same polarization direction, as noted in Fig. 1(f). Mode 1 is the core mode; mode 2 is the cladding mode; mode 3 and mode 4 are the modes, which are coupled at the taper region and one fusion-splicing point. The interferences between different modes show different responses to torsion. We have analyzed the interference between mode 1 and mode 2 in the Eqs. (4)-(8) . Mode 3 and mode 4 are symmetrical modes, and the phase changes of the two modes are synchronous with the twist rate [16]. We can predict that some resonance dips are insensitive with torsion. In addition, for the interferences of the mode 1 and 3 (4) or the mode 2 and 3 (4), the length of the interference arm is shorter than the interference arm of mode 1 and 2, and the coupling occurs in the taper region. It makes the torsion sensitivity lower and directional discrimination weaker. So an appropriate resonance dip should be chosen for the torsion sensing.

The proposed experiment setup is shown in Fig. 2 . A broadband source (BBS) with wavelength range from 1250 nm to 1650 nm and an optical spectrum analyzer (OSA, Yokogawa AQ6370C,) with resolution of 0.02 nm are used to perform our experiment. One side of the fiber is fixed with the fiber hold, and the other side is fixed with the rotator. The length between the fiber hold and the rotator S is 34 cm, the length of the sensor head l is 1.6 cm. Twist will be applied when we rotate the rotator.

 figure: Fig. 2

Fig. 2 Schematic diagram of the experiment setup.

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Figure 3(a) has shown the transmission spectra of the structure without taper and with normal taper, Fig. 3(b) has shown the transmission spectra of the structure with twist taper. Firstly, we trace the torsion responses of the structure with twist taper. We rotate the rotator in increments of 10°. When the twist is applied to the sensor head, the refractive index modulation will be caused by twist, which will lead to resonance dip wavelength shift. Figures 4(a) and 4(b) have shown the transmission spectra for the resonance dip wavelengths at 1358.89 nm and 1429.51 nm with the torsion angle changing from −150° to 150°. As we expected aforementioned, the resonance dip at 1358.89 nm is insensitive with torsion. While the resonance dip at 1429.51 nm has lost the directional discrimination, it is worth noting that the resonance dip has a blue shift when negative torsion or small positive torsion is applied. While the applied positive torsion is larger than 90°, it shifts to the opposite direction. The reason is that for the interference between mode 1 and 3 (4) or the mode 2 and 3 (4), the torsion affects both the effective refractive indexes of the modes and the length of interference arm. Negative torsion and small positive torsion mainly affect the effective refractive indexes of the modes, but larger positive torsion will change the coupling efficiency of the twist taper region, which will change the length of interference arm. As a result, an opposite shift occurs.

 figure: Fig. 3

Fig. 3 Transmission spectra of the structure: (a) without taper and with a normal taper, (b) with twist taper.

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 figure: Fig. 4

Fig. 4 Torsion responses of the resonance dip wavelengths: (a) at 1358.89 nm, (b) at 1429.51 nm.

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At the last part, we trace the resonance dip wavelength at 1496.24 nm. As shown in Figs. 5(a) and 5(b) , it is obvious that a high sensitivity and the directional discrimination are obtained. The resonance dip is formed by the interference between mode 1 and mode 2. An appropriate resonance dip is found to perform our sensing experiment. When the sensor head is twisted from 0° to 150°, the resonance wavelength has a blue shift. On the contrary, when the sensor head is twisted from 0° to −150°, the resonance wavelength has a red shift. The sensitivities of positive and negative torsion reach 1.071 nm/rad·m−1 and 2.395 nm/rad·m−1 respectively. As a contrast, we have measured the torsion responses of the structure without adding twist taper. Figures 5(c) and 5(d) have shown its transmission spectra with the torsion angle from −150° to 150°,we can see the dip shifts to the same direction when twist is applied in different directions. The sensitivities of positive and negative torsion are 0.263 nm/rad·m−1 and 0.293 nm/rad·m−1, respectively. Finally, in order to analyze the difference between the twist taper and the normal taper, we have measured the shift of the resonance dip wavelength at 1496.24 nm for the structure with a normal taper. Figure 6(a) has shown the torsion responses of the three structures by line fitting. It is obvious that a higher sensitivity for torsion and directional discrimination have been obtained by fabricating the twist taper. The blue dotted line in Fig. 6(a) is the torsion responses of the structure with twist taper which is calculated by Eqs. (7)~(8) with a=0.025, b=0.011, and γ=9. The theoretical values are in good agreement with the experiment.

 figure: Fig. 5

Fig. 5 Resonance dip wavelength shift of the structure: (a) with twist taper at −8~0 rad/m, (b) with twist taper at 0~8 rad/m, (c) without taper at −8~0 rad/m, (d) without taper at 0~8 rad/m.

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 figure: Fig. 6

Fig. 6 Wavelength shift: (a) torsion, (b) temperature.

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As we see in Fig. 6(b), the interferometer has a very low temperature response. The resonance dip wavelength only changes 1.12 nm for the temperature range from 30°C to 70°C. Compared to the high sensitivity about torsion, our twist sensor can be considered as temperature-insensitive for small temperature range.

3. Conclusion

In conclusion, for the first time to our knowledge, a torsion sensor with directional discrimination based on a twist taper in polarization-maintaining fiber has been experimentally demonstrated. The torsion sensitivity for the twist rate from 0 rad/m to 8 rad/m reaches 1.071 nm/rad·m−1, and for the twist rate from 0 rad/m to −8 rad/m reaches 2.392 nm/rad·m−1, respectively. We analyze the directional responses of the asymmetric structure. Compared with other published structures, the proposed structure possesses several advantages such as simple structure, compactness, easily fabricated, and due to the novel twist taper, higher sensitivity and directional discrimination for torsion have been achieved. Additionally, as we enhance the sensitivity for torsion, the sensitivity for temperature changes lower relatively. The advantages enable the sensor to be used in various applications that require the information for both the torsion amplitude and orientation simultaneously.

Acknowledgments

This work was jointly supported by the National Natural Science Foundation under Grant Nos. 11274181, 10974100, 10674075, the Doctoral Scientific Fund Project of the Ministry of Education under Grant No.20120031110033 and by the Tianjin Key Program of Application Foundations and Future Technology Research Project under Grant No.15JCZDJC39800, the Opening Project of Key laboratory of Optical Information Science and Technology, Ministry of Education under Grant No. 2014KFKT001.

References and links

1. B. Song, Y. Miao, W. Lin, H. Zhang, J. Wu, and B. Liu, “Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers,” Opt. Express 21(22), 26806–26811 (2013). [CrossRef]   [PubMed]  

2. D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995). [CrossRef]  

3. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014). [CrossRef]   [PubMed]  

4. J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012). [CrossRef]  

5. W. Yiping, M. Wang, and X. Huang, “In fiber Bragg grating twist sensor based on analysis of polarization dependent loss,” Opt. Express 21(10), 11913–11920 (2013). [CrossRef]   [PubMed]  

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

7. H. Y. Fu, S. K. Khijwania, H. Y. Tam, P. K. A. Wai, and C. Lu, “Polarization-maintaining photonic-crystal-fiber-based all-optical polarimetric torsion sensor,” Appl. Opt. 49(31), 5954–5958 (2010). [CrossRef]  

8. Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011). [CrossRef]  

9. F. Yang, Z. Fang, Z. Pan, Q. Ye, H. Cai, and R. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012). [CrossRef]   [PubMed]  

10. D. Lesnik and D. Donlagic, “In-line, fiber-optic polarimetric twist/torsion sensor,” Opt. Lett. 38(9), 1494–1496 (2013). [CrossRef]   [PubMed]  

11. X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005). [CrossRef]  

12. 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 Photonics Technol. Lett. 22(20), 1539–1541 (2010). [CrossRef]  

13. X. Xi, G. K. L. Wong, T. Weiss, and P. St. J. Russell, “Measuring mechanical strain and twist using helical photonic crystal fiber,” Opt. Lett. 38(24), 5401–5404 (2013). [CrossRef]   [PubMed]  

14. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014). [CrossRef]   [PubMed]  

15. L. Chen, W. G. Zhang, L. Wang, H. Zhang, J. Sieg, Q. Zhou, L. Y. Zhang, B. Wang, and T. Y. Yan, “In-fiber torsion sensor based on dual polarized Mach-Zehnder interference,” Opt. Express 22(26), 31654–31664 (2014). [CrossRef]   [PubMed]  

16. L. A. Fernandes, J. R. Grenier, J. S. Aitchison, and P. R. Herman, “Fiber optic stress-independent helical torsion sensor,” Opt. Lett. 40(4), 657–660 (2015). [CrossRef]   [PubMed]  

17. Y. Jung, G. Brambilla, and D. J. Richardson, “Polarization-maintaining optical microfiber,” Opt. Lett. 35(12), 2034–2036 (2010). [CrossRef]   [PubMed]  

References

  • View by:

  1. B. Song, Y. Miao, W. Lin, H. Zhang, J. Wu, and B. Liu, “Multi-mode interferometer-based twist sensor with low temperature sensitivity employing square coreless fibers,” Opt. Express 21(22), 26806–26811 (2013).
    [Crossref] [PubMed]
  2. D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
    [Crossref]
  3. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014).
    [Crossref] [PubMed]
  4. J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
    [Crossref]
  5. W. Yiping, M. Wang, and X. Huang, “In fiber Bragg grating twist sensor based on analysis of polarization dependent loss,” Opt. Express 21(10), 11913–11920 (2013).
    [Crossref] [PubMed]
  6. J. Y. Cho, J. H. Lim, and K. H. Lee, “Optical fiber twist sensor with two orthogonally oriented mechanically induced long-period grating sections,” IEEE Photonics Technol. Lett. 17(2), 453–455 (2005).
    [Crossref]
  7. H. Y. Fu, S. K. Khijwania, H. Y. Tam, P. K. A. Wai, and C. Lu, “Polarization-maintaining photonic-crystal-fiber-based all-optical polarimetric torsion sensor,” Appl. Opt. 49(31), 5954–5958 (2010).
    [Crossref]
  8. Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
    [Crossref]
  9. F. Yang, Z. Fang, Z. Pan, Q. Ye, H. Cai, and R. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012).
    [Crossref] [PubMed]
  10. D. Lesnik and D. Donlagic, “In-line, fiber-optic polarimetric twist/torsion sensor,” Opt. Lett. 38(9), 1494–1496 (2013).
    [Crossref] [PubMed]
  11. X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
    [Crossref]
  12. 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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
    [Crossref]
  13. X. Xi, G. K. L. Wong, T. Weiss, and P. St. J. Russell, “Measuring mechanical strain and twist using helical photonic crystal fiber,” Opt. Lett. 38(24), 5401–5404 (2013).
    [Crossref] [PubMed]
  14. R. Gao, Y. Jiang, and L. Jiang, “Multi-phase-shifted helical long period fiber grating based temperature-insensitive optical twist sensor,” Opt. Express 22(13), 15697–15709 (2014).
    [Crossref] [PubMed]
  15. L. Chen, W. G. Zhang, L. Wang, H. Zhang, J. Sieg, Q. Zhou, L. Y. Zhang, B. Wang, and T. Y. Yan, “In-fiber torsion sensor based on dual polarized Mach-Zehnder interference,” Opt. Express 22(26), 31654–31664 (2014).
    [Crossref] [PubMed]
  16. L. A. Fernandes, J. R. Grenier, J. S. Aitchison, and P. R. Herman, “Fiber optic stress-independent helical torsion sensor,” Opt. Lett. 40(4), 657–660 (2015).
    [Crossref] [PubMed]
  17. Y. Jung, G. Brambilla, and D. J. Richardson, “Polarization-maintaining optical microfiber,” Opt. Lett. 35(12), 2034–2036 (2010).
    [Crossref] [PubMed]

2015 (1)

2014 (3)

2013 (4)

2012 (2)

F. Yang, Z. Fang, Z. Pan, Q. Ye, H. Cai, and R. Qu, “Orthogonal polarization mode coupling for pure twisted polarization maintaining fiber Bragg gratings,” Opt. Express 20(27), 28839–28845 (2012).
[Crossref] [PubMed]

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

2011 (1)

2010 (3)

2005 (2)

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

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

1995 (1)

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Aitchison, J. S.

Bennion, I.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

Brambilla, G.

Cai, H.

Chen, L.

Chen, X.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

Chen, X. F.

Cho, J. Y.

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

Chung, Y. J.

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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Donlagic, D.

Fang, Z.

Fernandes, L. A.

Fu, H. Y.

Gao, R.

Geng, P. C.

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Grenier, J. R.

Herman, P. R.

Huang, X.

Jiang, L.

Jiang, Y.

Jung, Y.

Khatib, O.

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Khijwania, S. K.

Kim, B. K.

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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, H. M.

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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Kim, T. H.

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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

Lee, K. H.

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

Lesnik, D.

Li, X. L.

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Lim, J. H.

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

Lin, W.

Liu, B.

Lu, C.

Miao, Y.

Mou, C. B.

Pan, Z.

Qu, R.

Richardson, D. J.

Ruan, J.

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Russell, P. St. J.

Sieg, J.

Song, B.

Tam, H. Y.

Vischer, D.

D. Vischer and O. Khatib, “Design and development of high-performance torque controlled joints,” IEEE Trans. Robot. Autom. 11(4), 537–544 (1995).
[Crossref]

Wai, P. K. A.

Wang, B.

Wang, L.

Wang, M.

Weiss, T.

Wong, G. K. L.

Wu, J.

Xi, X.

Xue, X. L.

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Yan, T. Y.

Yan, Z. J.

Yang, F.

Ye, Q.

Yin, L. M.

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Yiping, W.

Zhang, H.

Zhang, L.

Z. J. Yan, C. B. Mou, K. M. Zhou, X. F. Chen, and L. Zhang, “UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings,” J. Lightwave Technol. 29(18), 2715–2724 (2011).
[Crossref]

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

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Zhang, W. G.

L. Chen, W. G. Zhang, L. Wang, H. Zhang, J. Sieg, Q. Zhou, L. Y. Zhang, B. Wang, and T. Y. Yan, “In-fiber torsion sensor based on dual polarized Mach-Zehnder interference,” Opt. Express 22(26), 31654–31664 (2014).
[Crossref] [PubMed]

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Zhou, K.

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

Zhou, K. M.

Zhou, Q.

Appl. Opt. (1)

IEEE Photonics Technol. Lett. (3)

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

X. Chen, K. Zhou, L. Zhang, and I. Bennion, “Optical chemsensor based on etched tilted Bragg grating structures in multimode fiber,” IEEE Photonics Technol. Lett. 17(4), 864–866 (2005).
[Crossref]

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 Photonics Technol. Lett. 22(20), 1539–1541 (2010).
[Crossref]

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[Crossref]

J. Lightwave Technol. (1)

J. Opt. (1)

J. Ruan, W. G. Zhang, H. Zhang, L. M. Yin, X. L. Li, P. C. Geng, and X. L. Xue, “Temperature and twist characteristics of cascaded long-period fiber gratings written in polarization-maintaining fibers,” J. Opt. 14(10), 105403 (2012).
[Crossref]

Opt. Express (6)

Opt. Lett. (4)

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the twist sensor: (a) sensor head, (b) cross-section of the PMF, (c) twist taper, (d) microscopic image, (e) coordinate, (f) coupling between core mode and cladding mode.
Fig. 2
Fig. 2 Schematic diagram of the experiment setup.
Fig. 3
Fig. 3 Transmission spectra of the structure: (a) without taper and with a normal taper, (b) with twist taper.
Fig. 4
Fig. 4 Torsion responses of the resonance dip wavelengths: (a) at 1358.89 nm, (b) at 1429.51 nm.
Fig. 5
Fig. 5 Resonance dip wavelength shift of the structure: (a) with twist taper at −8~0 rad/m, (b) with twist taper at 0~8 rad/m, (c) without taper at −8~0 rad/m, (d) without taper at 0~8 rad/m.
Fig. 6
Fig. 6 Wavelength shift: (a) torsion, (b) temperature.

Equations (8)

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ϕ = 2 π ( n e f f c o n e f f c l ) L λ
ϕ = ( 2 m + 1 ) π , m = 0 , 1 , 2...
λ m f / s = 2 ( n e f f c o , f / s n e f f c l , f / s ) L 2 m + 1
x 2 a 2 + y 2 b 2 = 1
x = a cos θ , y = b sin θ
a = n e f f c o , f n e f f c l , f , b = n e f f c o , s n e f f c l , s
ϕ = 2 π λ l / 2 l / 2 a 2 cos 2 θ + b 2 sin 2 θ d z
θ = { d 2 ( α + γ β ) + ( z + d 2 ) β ,       l 2 z < d 2 ( α + γ β ) z ,                              d 2 z < d 2 d 2 ( α + γ β ) + ( z d 2 ) β ,            d 2 < z l 2

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