Abstract

Using a quaternion method, the polarization mode-coupling coefficient can be derived from three components of the Stokes vectors at three adjacent points along a fiber. A complete polarization optical time-domain reflectometry scheme for polarization mode coupling distributed measurement in polarization-maintaining fiber ring is proposed based on the above theoretical derivations. By comparing the measurement results of two opposite incident directions and two orthogonal polarization axes of polarization-maintaining fiber rings with different lengths, the feasibility and repeatability of the measurement scheme are verified experimentally with a positioning spatial resolution of 1 meter.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2017 (2)

Z. Huang, C. Wu, and Z. Wang, “Stress direction measurement based on polarization state in optical fibers using quaternion method,” IEEE. Photonics J. 9(6), 1–11 (2017).

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

2016 (1)

2015 (5)

2012 (3)

2011 (1)

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

2010 (1)

2007 (1)

Y. H. Yang, T. Shen, and J. J. Guo, “Fiber optic gyroscope technology and application,” Infr. Laser Eng. 36(5), 626 (2007).

2003 (1)

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

1998 (2)

J. G. Elhison and A. S. Siddiqui, “A fully polarimetric optical time-domain reflectometer,” IEEE Photonics Technol. Lett. 10(2), 246–248 (1998).
[Crossref]

K. Takada and S. Mitachi, “Polarization crosstalk dependence on length in silica-based waveguides measured by using optical low coherence interference,” J. Lightwave Technol. 16(8), 1413–1422 (1998).
[Crossref]

1997 (1)

J. Zhang and V. A. Handerek, “Distributed sensing of polarization mode coupling in high birefringence optical fibers using intense arbitrarily polarized coherent light,” J. Lightwave Technol. 15(5), 794–802 (1997).
[Crossref]

1996 (1)

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

1992 (1)

K. Takiguchi and K. Hotate, “Bias of an optical passive ring-resonator gyro caused by the misalignment of the polarization axis in the polarization-maintaining fiber resonator,” J. Lightwave Technol. 10(4), 514–522 (1992).
[Crossref]

1989 (1)

1988 (1)

1986 (3)

1983 (2)

1982 (1)

K. Okamoto, Y. Sasaki, and N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. 18(11), 1890–1899 (1982).
[Crossref]

1981 (3)

1976 (1)

Bai, J.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Bebbington, D. H. O.

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

Canning, J.

Cao, C.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Chen, H.

Chen, Q.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Chen, X.

Culshaw, B.

B. Culshaw and I. P. Giles, “Fibre optic gyroscopes,” J. Phys. E Sci. Instrum. 16(1), 5–15 (1983).
[Crossref]

Dong, H.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Elhison, J. G.

J. G. Elhison and A. S. Siddiqui, “A fully polarimetric optical time-domain reflectometer,” IEEE Photonics Technol. Lett. 10(2), 246–248 (1998).
[Crossref]

Ellison, J. G.

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

Floridia, C.

Franciscangelis, C.

Fruett, F.

Giles, I. P.

Guo, J. J.

Y. H. Yang, T. Shen, and J. J. Guo, “Fiber optic gyroscope technology and application,” Infr. Laser Eng. 36(5), 626 (2007).

Handerek, V. A.

J. Zhang and V. A. Handerek, “Distributed sensing of polarization mode coupling in high birefringence optical fibers using intense arbitrarily polarized coherent light,” J. Lightwave Technol. 15(5), 794–802 (1997).
[Crossref]

He, Z.

Higashi, T.

Higashiguchi, M.

Hotate, K.

Huang, Z.

Z. Huang, C. Wu, and Z. Wang, “Stress direction measurement based on polarization state in optical fibers using quaternion method,” IEEE. Photonics J. 9(6), 1–11 (2017).

Ioannidis, Z. K.

Iwatsuki, K.

Jin, Z.

Kadiwar, R.

Kintner, E. C.

Le Boudec, G.

P. Martin, G. Le Boudec, and H. C. Lefevre, “Test apparatus of distributed polarization coupling in fiber gyro coils using white light interferometry,” in 15th Anniversary Conf. International Society for Optics and Photonics (1992), pp. 173–180.
[Crossref]

Lee, B.

B. Lee, “Review of the present status of optical fiber sensors,” Opt. Fiber Technol. 9(2), 57–79 (2003).
[Crossref]

Lefevre, H. C.

P. Martin, G. Le Boudec, and H. C. Lefevre, “Test apparatus of distributed polarization coupling in fiber gyro coils using white light interferometry,” in 15th Anniversary Conf. International Society for Optics and Photonics (1992), pp. 173–180.
[Crossref]

Li, Z.

Li, Z.-Y.

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

Li Gao, Z. Y. K. Q.

S. S. Yang, C. Q. Wu, Z. Y. K. Q. Li Gao, and C. Shang, “Measurement of bend radius based on PPC-assisted POTDR,” J. Chin. Railway Soc. 34(2), 47–51 (2012).

Liu, J.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Liu, L.

L. Liu, C. Wu, C. Shang, Z. Li, and J. Wang, “Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers,” IEEE Photonics J. 7(4), 1–14 (2015).

Liu, T.

Liu, Y.

Lu, J.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Ma, H.

Martin, P.

P. Martin, G. Le Boudec, and H. C. Lefevre, “Test apparatus of distributed polarization coupling in fiber gyro coils using white light interferometry,” in 15th Anniversary Conf. International Society for Optics and Photonics (1992), pp. 173–180.
[Crossref]

Meng, Z.

Mitachi, S.

Monerie, M.

Nakazawa, M.

Negishi, Y.

Noda, J.

Okamoto, K.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

K. Takada, J. Noda, and K. Okamoto, “Measurement of spatial distribution of mode coupling in birefringent polarization-maintaining fiber with new detection scheme,” Opt. Lett. 11(10), 680–682 (1986).
[Crossref] [PubMed]

K. Okamoto, Y. Sasaki, and N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. 18(11), 1890–1899 (1982).
[Crossref]

Pan, Y.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Peng, G. D.

Ren, J.

Rogers, A. J.

Sasaki, Y.

J. Noda, K. Okamoto, and Y. Sasaki, “Polarization-maintaining fibers and their applications,” J. Lightwave Technol. 4(8), 1071–1089 (1986).
[Crossref]

K. Okamoto, Y. Sasaki, and N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. 18(11), 1890–1899 (1982).
[Crossref]

Schmmidt, F.

Schuh, R. E.

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

Shang, C.

L. Liu, C. Wu, C. Shang, Z. Li, and J. Wang, “Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers,” IEEE Photonics J. 7(4), 1–14 (2015).

S. S. Yang, C. Q. Wu, Z. Y. K. Q. Li Gao, and C. Shang, “Measurement of bend radius based on PPC-assisted POTDR,” J. Chin. Railway Soc. 34(2), 47–51 (2012).

C. Shang, C. Wu, Z. Wang, Y. Wang, J. Wang, Z. Li, and S. Yang, “Method to measure the second-order birefringence vector distribution along optical fibers based on high-speed polarization optical time domain reflectometry,” Appl. Opt. 51(14), 2548–2553 (2012).
[Crossref] [PubMed]

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

Shen, T.

Y. H. Yang, T. Shen, and J. J. Guo, “Fiber optic gyroscope technology and application,” Infr. Laser Eng. 36(5), 626 (2007).

Shibata, N.

K. Okamoto, Y. Sasaki, and N. Shibata, “Mode coupling effects in stress-applied single polarization fibers,” IEEE J. Quantum Electron. 18(11), 1890–1899 (1982).
[Crossref]

Shorthill, R. W.

Siddiqui, A. S.

J. G. Elhison and A. S. Siddiqui, “A fully polarimetric optical time-domain reflectometer,” IEEE Photonics Technol. Lett. 10(2), 246–248 (1998).
[Crossref]

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

Simões, G. C.

Song, D.

Sun, B.

Sun, W.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Takada, K.

Takiguchi, K.

K. Takiguchi and K. Hotate, “Bias of an optical passive ring-resonator gyro caused by the misalignment of the polarization axis in the polarization-maintaining fiber resonator,” J. Lightwave Technol. 10(4), 514–522 (1992).
[Crossref]

Tokuda, M.

Tong, Y.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Tsubokawa, M.

Vali, V.

Wang, F.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Wang, J.

Wang, X.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

X. Wang, Z. He, and K. Hotate, “Reduction of polarization-fluctuation induced drift in resonator fiber optic gyro by a resonator with twin 90 ° polarization-axis rotated splices,” Opt. Express 18(2), 1677–1683 (2010).
[Crossref] [PubMed]

Wang, Y.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

C. Shang, C. Wu, Z. Wang, Y. Wang, J. Wang, Z. Li, and S. Yang, “Method to measure the second-order birefringence vector distribution along optical fibers based on high-speed polarization optical time domain reflectometry,” Appl. Opt. 51(14), 2548–2553 (2012).
[Crossref] [PubMed]

Wang, Z.

Wu, C.

Z. Huang, C. Wu, and Z. Wang, “Stress direction measurement based on polarization state in optical fibers using quaternion method,” IEEE. Photonics J. 9(6), 1–11 (2017).

L. Liu, C. Wu, C. Shang, Z. Li, and J. Wang, “Quaternion Approach to the Measurement of the Local Birefringence Distribution in Optical Fibers,” IEEE Photonics J. 7(4), 1–14 (2015).

C. Shang, C. Wu, Z. Wang, Y. Wang, J. Wang, Z. Li, and S. Yang, “Method to measure the second-order birefringence vector distribution along optical fibers based on high-speed polarization optical time domain reflectometry,” Appl. Opt. 51(14), 2548–2553 (2012).
[Crossref] [PubMed]

Wu, C. Q.

S. S. Yang, C. Q. Wu, Z. Y. K. Q. Li Gao, and C. Shang, “Measurement of bend radius based on PPC-assisted POTDR,” J. Chin. Railway Soc. 34(2), 47–51 (2012).

Wu, C.-Q.

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

Yang, J.

Yang, S.

Yang, S. S.

S. S. Yang, C. Q. Wu, Z. Y. K. Q. Li Gao, and C. Shang, “Measurement of bend radius based on PPC-assisted POTDR,” J. Chin. Railway Soc. 34(2), 47–51 (2012).

Yang, S.-S.

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

Yang, Y. H.

Y. H. Yang, T. Shen, and J. J. Guo, “Fiber optic gyroscope technology and application,” Infr. Laser Eng. 36(5), 626 (2007).

Yao, X. S.

Yu, X.

Yuan, H.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Yuan, L.

Zhang, H.

Zhang, J.

Y. Zhao, B. Sun, Y. Liu, J. Ren, J. Zhang, J. Yang, J. Canning, G. D. Peng, and L. Yuan, “Polarization mode coupling and related effects in fiber Bragg grating inscribed in polarization maintaining fiber,” Opt. Express 24(1), 611–619 (2016).
[Crossref] [PubMed]

J. Zhang and V. A. Handerek, “Distributed sensing of polarization mode coupling in high birefringence optical fibers using intense arbitrarily polarized coherent light,” J. Lightwave Technol. 15(5), 794–802 (1997).
[Crossref]

Zhang, X.

C. Cao, F. Wang, Y. Pan, X. Zhang, X. Chen, Q. Chen, and J. Lu, “Suppression of Signal Fading With Multi-Wavelength Laser in Polarization OTDR,” IEEE Photonics Technol. Lett. 29(21), 1824–1827 (2017).
[Crossref]

Zhao, Y.

Zhu, N.

Y. Tong, H. Dong, Y. Wang, W. Sun, X. Wang, J. Bai, H. Yuan, N. Zhu, and J. Liu, “Distributed incomplete polarization-OTDR based on polarization maintaining fiber for multi-event detection,” Opt. Commun. 357, 41–44 (2015).
[Crossref]

Appl. Opt. (7)

Chin. Phys. Lett. (1)

C. Shang, C.-Q. Wu, Z.-Y. Li, and S.-S. Yang, “A new distributed measurement of birefringence vectors by P-OTDR assisted by a high speed polarization analyzer,” Chin. Phys. Lett. 28(9), 094212 (2011).
[Crossref]

Electron. Lett. (1)

R. E. Schuh, J. G. Ellison, A. S. Siddiqui, and D. H. O. Bebbington, “Polarisation OTDR measurements and theoretical analysis on fibres with twist and their implications,” Electron. Lett. 32(4), 387 (1996).
[Crossref]

IEEE J. Quantum Electron. (1)

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Figures (6)

Fig. 1
Fig. 1 Three adjacent points A, B and C along a fiber.
Fig. 2
Fig. 2 The setup of complete P-OTDR. DFB: distributed feedback. PPG: programmable pattern generator. PBS: polarization beam splitter. EDFA: erbium-doped fiber amplifier. PC: polarization controller. BAR: balanced analog receiver.
Fig. 3
Fig. 3 The measured PMC coefficients along the 83 m long PM fiber ring. (a) The SOP’s of the incident pulses are aligned with the fast axis (red) and slow axis (blue) in the forward direction, respectively. (b) The incident pulses, which aligned with the slow-axis, are inputted in the forward direction (blue) and the backward direction (green), respectively.
Fig. 4
Fig. 4 The distribution of SOP’s at different positions along the 83 m long PM fiber ring on the Poincare sphere (1000 measurements). (a) Position A. (b) Position E.
Fig. 5
Fig. 5 2-D heat map of the distribution of PMC coefficients along the 83 m long PM fiber ring by measuring 4000 times repeatedly. (a) Pulses are inputted in the forward direction with SOP’s aligned with the fast-axis. (b) Pulses are inputted in the forward direction with SOP’s aligned with the slow-axis. (c) Pulses are inputted in the backward direction with SOP’s aligned with the slow-axis.
Fig. 6
Fig. 6 (a) The measured PMC coefficients along the 840 m long PM fiber ring with pulses inputted in opposite directions. (b) The variation of Rayleigh backscattered power with time at positions A, B, C and D along the 840 m long PM fiber ring.

Equations (11)

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S / z = B × S
z [ E ˙ x E ˙ y ] = [ i β x i k i k i β y ] [ E ˙ x E ˙ y ]
J / z = U J
[ i β x i k i k i β y ] = i β ¯ [ 1 1 ] + i Δ β 2 [ 1 1 ] + i k [ 1 1 ]
U = i β ¯ ( Δ β / 2 ) i ^ k j ^
J / z = ( i β ¯ ( Δ β / 2 ) i ^ k j ^ ) J J / z = J ( i β ¯ + ( Δ β / 2 ) i ^ + k j ^ ) }
S / z = 2 [ ( J / z ) J + J ( J / z ) ]
S / z = ( Δ β i ^ + 2 k j ^ ) × i S
s 0 / z = 0
S / z = ( Δ β i ^ + 2 k j ^ ) × S
B = ( Δ β i ^ + 2 k j ^ )

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