Abstract

We describe a first distributed polarization analysis (DPA) system using binary polarization rotators in an optical frequency domain reflectormeter (OFDR) capable of measuring the variations of polarization states along a single-mode fiber (SMF). We demonstrate using such a DPA system to accurately measure the distance-resolved birefringence with 12 fiber loops of different radii with different birefringence values along a length of SMF and obtain a bending-induced birefringence coefficient (BBC) of 6.601 × 10−10 m2, agreeing well with the theoretically estimated value of 5.334 × 10−10 m2. To further verify the measurement accuracy, we obtain the birefringence values of the 12 fiber loops of different radii one at a time using a non-distributed polarization analysis system with an accuracy traceable to a birefringence standard made with a quartz crystal, and obtain a BBC value of 6.490 × 10−10 m2, agreeing well with our distributed measurement with a relative error of only 1.68%. In addition, we measure the residual birefringence of the SMF with both distributed and non-distributed polarization analysis systems and obtain similar results with a relative error of only 0.59%. Our experiments not only validate the performances of our DPA system, but also the first to use DPA to experimentally obtain the accurate birefringence values along the SMF and verify the theory of bending-induced birefringence. Our work further proves that such an OFDR-based DPA system is a practical tool for optical component characterization, nondestructive optical material inspection, and distributed fiber optic transversal stress sensing.

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

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2017 (2)

D. Zhao, D. Pustakhod, K. Williams, and X. Leijtens, “High resolution optical frequency domain reflectometry for analyzing intra-chip reflections,” IEEE Photonics Technol. Lett. 29(16), 1379–1382 (2017).
[Crossref]

Z. Xu, X. S. Yao, Z. Ding, X. J. Chen, X. Zhao, H. Xiao, T. Feng, and T. Liu, “Accurate measurements of circular and residual linear birefringences of spun fibers using binary polarization rotators,” Opt. Express 25(24), 30780–30792 (2017).
[Crossref] [PubMed]

2016 (1)

2015 (2)

2014 (1)

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

2013 (2)

B. Wang, A. Leadbetter, and B. Seipel, “Measuring stress in Si ingots using linear birefringence,” Energy Procedia 38, 959–967 (2013).
[Crossref]

L. Palmieri, “Distributed polarimetric measurements for optical fiber sensing,” Opt. Fiber Technol. 19(6), 720–728 (2013).
[Crossref]

2012 (3)

2011 (1)

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
[Crossref]

2010 (5)

2009 (5)

2007 (1)

B. Y. Kim and S. C. Sang, “Backscattering measurement of bending-induced birefringence in single mode fibres,” Electron. Lett. 17(5), 193–194 (2007).
[Crossref]

2006 (4)

2005 (3)

2004 (3)

B. H. Park, M. C. Pierce, B. Cense, and J. F. de Boer, “Jones matrix analysis for a polarization-sensitive optical coherence tomography system using fiber-optic components,” Opt. Lett. 29(21), 2512–2514 (2004).
[Crossref] [PubMed]

E. Simova, I. Golub, and A. Delage, “Analysis of polarization properties of lateral antiresonant reflecting optical waveguides,” Opt. Commun. 230(1-3), 95–103 (2004).
[Crossref]

P. Williams, “PMD measurement techniques and how to avoid the pitfalls,” J. Opt. Fiber Comm. Rep. 1(1), 84–105 (2004).
[Crossref]

2003 (1)

T. Wanner, B. S. Marks, C. R. Menyuk, and J. Zweck, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence,” J. Lightwave Technol. 14, 148–157 (2003).

2002 (1)

2001 (1)

M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
[Crossref]

2000 (1)

M. Wuilpart, A. J. Rogers, P. Megret, and M. Blondel, “Fully distributed polarization properties of an optical fiber using the backscattering technique,” in Applications of Photonic Technology, Proc. SPIE 4087, 396–404 (2000).
[Crossref]

1999 (1)

1997 (1)

T. Saida and K. Hotate, “Distributed fiber-optic stress sensor by synthesis of the optical coherence function,” IEEE Photonics Technol. Lett. 9(4), 484–486 (1997).
[Crossref]

1996 (1)

1995 (1)

A. B. D. Patterson, “Characterization of active waveguide photonic devices using optical coherence domain reflectometry,” Opt. Eng. 34(8), 2289–2298 (1995).
[Crossref]

1984 (1)

J. Makovitzky, “Polarization optical analysis of blood cell membranes,” Prog. Histochem. Cytochem. 15(3), 1–100 (1984).
[Crossref] [PubMed]

1981 (1)

1980 (3)

Bao, X.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

D.-P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
[Crossref] [PubMed]

Blondel, M.

M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
[Crossref]

M. Wuilpart, A. J. Rogers, P. Megret, and M. Blondel, “Fully distributed polarization properties of an optical fiber using the backscattering technique,” in Applications of Photonic Technology, Proc. SPIE 4087, 396–404 (2000).
[Crossref]

Cense, B.

Chen, D.

Chen, H.

Chen, L.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

D.-P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
[Crossref] [PubMed]

X. Bao and L. Chen, “Recent progress in distributed fiber optic sensors,” Sensors (Basel) 12(7), 8601–8639 (2012).
[Crossref] [PubMed]

Chen, X.

Chen, X. J.

Cheon, M.-W.

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
[Crossref]

Cho, K.-J.

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
[Crossref]

de Boer, J. F.

Defosse, Y.

M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
[Crossref]

Delage, A.

E. Simova, I. Golub, and A. Delage, “Analysis of polarization properties of lateral antiresonant reflecting optical waveguides,” Opt. Commun. 230(1-3), 95–103 (2004).
[Crossref]

Ding, Z.

Dong, H.

Du, Y.

Eickhoff, W.

Emody, L.

W. Gährs, Z. Tigyi, L. Emody, and J. Makovitzky, “Polarization optical analysis of the surface structures of various fungi,” Acta Histochem. 111(4), 308–315 (2009).
[Crossref] [PubMed]

Feng, T.

Froggatt, M.

Gährs, W.

W. Gährs, Z. Tigyi, L. Emody, and J. Makovitzky, “Polarization optical analysis of the surface structures of various fungi,” Acta Histochem. 111(4), 308–315 (2009).
[Crossref] [PubMed]

Galtarossa, A.

Garus, D.

Geisler, T.

Gifford, D.

Gisin, B.

Gisin, N.

Gogolla, T.

Golub, I.

E. Simova, I. Golub, and A. Delage, “Analysis of polarization properties of lateral antiresonant reflecting optical waveguides,” Opt. Commun. 230(1-3), 95–103 (2004).
[Crossref]

Gong, Y.

Gong, Y. D.

Gonzalez-Herraez, M.

Grosso, D.

Gundel, P.

P. Gundel, M. C. Schubert, and W. Warta, “Simultaneous stress and defect luminescence study on silicon,” Phys. Status Solidi 207(2), 436–441 (2010).
[Crossref]

Han, Q.

He, Z.

Hirose, T.

Hotate, K.

Z. He and K. Hotate, “Distributed fiber-optic stress-location measurement by arbitrary shaping of optical coherence function,” J. Lightwave Technol. 20(9), 1715–1723 (2002).
[Crossref]

T. Saida and K. Hotate, “Distributed fiber-optic stress sensor by synthesis of the optical coherence function,” IEEE Photonics Technol. Lett. 9(4), 484–486 (1997).
[Crossref]

Huttner, B.

Jia, D.

X. Chen, H. Zhang, D. Jia, T. Liu, and Y. Zhang, “Implementation of distributed polarization maintaining fiber polarization coupling pressure sensing system,” Chin. J. Lasers 37(6), 1467–1472 (2010).
[Crossref]

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Jing, W.

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Kang, S.-H.

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
[Crossref]

Kim, B. Y.

B. Y. Kim and S. C. Sang, “Backscattering measurement of bending-induced birefringence in single mode fibres,” Electron. Lett. 17(5), 193–194 (2007).
[Crossref]

Kim, T.-G.

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
[Crossref]

Krebber, K.

Leadbetter, A.

B. Wang, A. Leadbetter, and B. Seipel, “Measuring stress in Si ingots using linear birefringence,” Energy Procedia 38, 959–967 (2013).
[Crossref]

Leijtens, X.

D. Zhao, D. Pustakhod, K. Williams, and X. Leijtens, “High resolution optical frequency domain reflectometry for analyzing intra-chip reflections,” IEEE Photonics Technol. Lett. 29(16), 1379–1382 (2017).
[Crossref]

Li, W.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

D.-P. Zhou, Z. Qin, W. Li, L. Chen, and X. Bao, “Distributed vibration sensing with time-resolved optical frequency-domain reflectometry,” Opt. Express 20(12), 13138–13145 (2012).
[Crossref] [PubMed]

Li, Z.

Liu, K.

Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, Q. Han, Z. Meng, and H. Chen, “Long-range vibration sensor based on correlation analysis of optical frequency-domain reflectometry signals,” Opt. Express 20(27), 28319–28329 (2012).
[Crossref] [PubMed]

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
[Crossref]

Liu, T.

Lu, P.

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

Lu, X.

Makovitzky, J.

W. Gährs, Z. Tigyi, L. Emody, and J. Makovitzky, “Polarization optical analysis of the surface structures of various fungi,” Acta Histochem. 111(4), 308–315 (2009).
[Crossref] [PubMed]

J. Makovitzky, “Polarization optical analysis of blood cell membranes,” Prog. Histochem. Cytochem. 15(3), 1–100 (1984).
[Crossref] [PubMed]

Marks, B. S.

T. Wanner, B. S. Marks, C. R. Menyuk, and J. Zweck, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence,” J. Lightwave Technol. 14, 148–157 (2003).

Martelli, P.

Martinelli, M.

Martins, H. F.

Megret, P.

M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
[Crossref]

M. Wuilpart, A. J. Rogers, P. Megret, and M. Blondel, “Fully distributed polarization properties of an optical fiber using the backscattering technique,” in Applications of Photonic Technology, Proc. SPIE 4087, 396–404 (2000).
[Crossref]

Mégret, P.

Meng, Z.

Menyuk, C. R.

T. Wanner, B. S. Marks, C. R. Menyuk, and J. Zweck, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence,” J. Lightwave Technol. 14, 148–157 (2003).

Ning, G.

Ning, G. X.

Palmieri, L.

Park, B. H.

Park, Y.-P.

T.-G. Kim, Y.-P. Park, K.-J. Cho, S.-H. Kang, and M.-W. Cheon, “Analysis of polarization properties of optical isolator for fiber laser,” Trans. Electr. Electron. Mater. 12(6), 241–244 (2011).
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Patterson, A. B. D.

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[Crossref]

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Schubert, M. C.

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B. Wang, A. Leadbetter, and B. Seipel, “Measuring stress in Si ingots using linear birefringence,” Energy Procedia 38, 959–967 (2013).
[Crossref]

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Shum, P.

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Soller, B.

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J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

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Takada, K.

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B. Wang, A. Leadbetter, and B. Seipel, “Measuring stress in Si ingots using linear birefringence,” Energy Procedia 38, 959–967 (2013).
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Williams, K.

D. Zhao, D. Pustakhod, K. Williams, and X. Leijtens, “High resolution optical frequency domain reflectometry for analyzing intra-chip reflections,” IEEE Photonics Technol. Lett. 29(16), 1379–1382 (2017).
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P. Williams, “PMD measurement techniques and how to avoid the pitfalls,” J. Opt. Fiber Comm. Rep. 1(1), 84–105 (2004).
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M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
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T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
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J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
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T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
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X. Chen, H. Zhang, D. Jia, T. Liu, and Y. Zhang, “Implementation of distributed polarization maintaining fiber polarization coupling pressure sensing system,” Chin. J. Lasers 37(6), 1467–1472 (2010).
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T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
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D. Zhao, D. Pustakhod, K. Williams, and X. Leijtens, “High resolution optical frequency domain reflectometry for analyzing intra-chip reflections,” IEEE Photonics Technol. Lett. 29(16), 1379–1382 (2017).
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Zhou, J. Q.

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T. Wanner, B. S. Marks, C. R. Menyuk, and J. Zweck, “Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying elliptical birefringence,” J. Lightwave Technol. 14, 148–157 (2003).

Acta Histochem. (1)

W. Gährs, Z. Tigyi, L. Emody, and J. Makovitzky, “Polarization optical analysis of the surface structures of various fungi,” Acta Histochem. 111(4), 308–315 (2009).
[Crossref] [PubMed]

Appl. Opt. (2)

Chin. J. Lasers (1)

X. Chen, H. Zhang, D. Jia, T. Liu, and Y. Zhang, “Implementation of distributed polarization maintaining fiber polarization coupling pressure sensing system,” Chin. J. Lasers 37(6), 1467–1472 (2010).
[Crossref]

Electron. Lett. (1)

B. Y. Kim and S. C. Sang, “Backscattering measurement of bending-induced birefringence in single mode fibres,” Electron. Lett. 17(5), 193–194 (2007).
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Energy Procedia (1)

B. Wang, A. Leadbetter, and B. Seipel, “Measuring stress in Si ingots using linear birefringence,” Energy Procedia 38, 959–967 (2013).
[Crossref]

IEEE Photonics J. (1)

J. Song, W. Li, P. Lu, Y. Xu, L. Chen, and X. Bao, “Long-range high spatial resolution distributed temperature and strain sensing based on optical frequency-domain reflectometry,” IEEE Photonics J. 6(3), 6801408 (2014).
[Crossref]

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T. Saida and K. Hotate, “Distributed fiber-optic stress sensor by synthesis of the optical coherence function,” IEEE Photonics Technol. Lett. 9(4), 484–486 (1997).
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M. Wuilpart, P. Megret, M. Blondel, A. J. Rogers, and Y. Defosse, “Measurement of the spatial distribution of birefringence in optical fibers,” IEEE Photonics Technol. Lett. 13(8), 836–838 (2001).
[Crossref]

D. Zhao, D. Pustakhod, K. Williams, and X. Leijtens, “High resolution optical frequency domain reflectometry for analyzing intra-chip reflections,” IEEE Photonics Technol. Lett. 29(16), 1379–1382 (2017).
[Crossref]

in Applications of Photonic Technology, Proc. SPIE (1)

M. Wuilpart, A. J. Rogers, P. Megret, and M. Blondel, “Fully distributed polarization properties of an optical fiber using the backscattering technique,” in Applications of Photonic Technology, Proc. SPIE 4087, 396–404 (2000).
[Crossref]

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P. Williams, “PMD measurement techniques and how to avoid the pitfalls,” J. Opt. Fiber Comm. Rep. 1(1), 84–105 (2004).
[Crossref]

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E. Simova, I. Golub, and A. Delage, “Analysis of polarization properties of lateral antiresonant reflecting optical waveguides,” Opt. Commun. 230(1-3), 95–103 (2004).
[Crossref]

Opt. Eng. (1)

A. B. D. Patterson, “Characterization of active waveguide photonic devices using optical coherence domain reflectometry,” Opt. Eng. 34(8), 2289–2298 (1995).
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H. Dong, P. Shum, M. Yan, J. Q. Zhou, G. X. Ning, Y. D. Gong, and C. Q. Wu, “Generalized Mueller matrix method for polarization mode dispersion measurement in a system with polarization-dependent loss or gain,” Opt. Express 14(12), 5067–5072 (2006).
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Z. Ding, X. S. Yao, T. Liu, Y. Du, K. Liu, Q. Han, Z. Meng, and H. Chen, “Long-range vibration sensor based on correlation analysis of optical frequency-domain reflectometry signals,” Opt. Express 20(27), 28319–28329 (2012).
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K. Yüksel, M. Wuilpart, and P. Mégret, “Analysis and suppression of nonlinear frequency modulation in an optical frequency-domain reflectometer,” Opt. Express 17(7), 5845–5851 (2009).
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X. S. Yao, X. Chen, and T. Liu, “High accuracy polarization measurements using binary polarization rotators,” Opt. Express 18(7), 6667–6685 (2010).
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Z. Xu, X. S. Yao, Z. Ding, X. J. Chen, X. Zhao, H. Xiao, T. Feng, and T. Liu, “Accurate measurements of circular and residual linear birefringences of spun fibers using binary polarization rotators,” Opt. Express 25(24), 30780–30792 (2017).
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Opt. Fiber Technol. (2)

T. Xu, W. Jing, H. Zhang, K. Liu, D. Jia, and Y. Zhang, “Influence of birefringence dispersion on a distributed stress sensor using birefringent optical fiber,” Opt. Fiber Technol. 15(1), 83–89 (2009).
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L. Palmieri, “Distributed polarimetric measurements for optical fiber sensing,” Opt. Fiber Technol. 19(6), 720–728 (2013).
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Figures (7)

Fig. 1
Fig. 1 Schematic of distributed polarization analysis (DPA) system, PA-OFDR. TL: tunable laser; C1, C2, C3, C4, C5: couplers; PSG: polarization state generator; PSA: polarization state analyzer; PMF: polarization maintaining fiber; SMF: single mode fiber; CIR1, CIR2: circulators; BPD1, BPD2: balanced photodetectors; FRM: Faraday rotation mirror; SMF-UT: SMF under test.
Fig. 2
Fig. 2 Data acquisition and processing flow chart for obtaining the state of polarization (SOP) matrix as a function of z . Note that M s ( z ) can be reduced to a 3 × 3 matrix if polarization dependent loss (PDL) in the fiber can be neglected [43]. Also note that the SOP vectors along z are derived from r i j ( f ) and therefore already contain the information of SOP variations caused by frequency variations.
Fig. 3
Fig. 3 (a) Experimental setup of bending-induced birefringence measurement. (b) Illustration of a setup of 12 fiber loops with different bending radii in SMF-UT, with each loop having a single turn. Inset showing the photo of the 12 fiber loops.
Fig. 4
Fig. 4 (a) Birefringence curves of the SMF-UT section with 12 fiber loops of different radii measured by PA-OFDR in different birefringence spatial resolutions (BSRs). (b) Zoom-in curves located around loop No. 10 in (a).
Fig. 5
Fig. 5 (a) Bending-induced birefringence as a function of fiber bending radius measured with our DPA system called PA-OFDR; The residual birefringence (RB) is apparent as the bending radius goes to infinity. (b) Birefringence curve of a SMF-UT section without any birefringence inducing loop, measured by our PA-OFDR, showing fiber’s distributed RB; The average value of the RB was also shown.
Fig. 6
Fig. 6 Measurement setup of FUT’s residual birefringence (RB) based on PSGA system.
Fig. 7
Fig. 7 (a) Measurement setup of bending-induced birefringence of SMF with only a single loop made on the fiber; Twelve loops were successively made and measured, one at a time, with radii gradually decreasing from ~3.75 cm to ~1.00 cm with a 0.25 cm interval. (b) Bending-induced birefringence as a function of the fiber bending radius measured by the PSGA system (red squares). The green error bars indicating the high precision of the PSGA measurements. For comparison, the birefringence values measured with the PA-OFDR are also plotted (blue circles) and note that the residual birefringence has been subtracted from every measured birefringence data.

Tables (1)

Tables Icon

Table 1 Repeated measurements of FUT’s RB with NDPA system

Equations (12)

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S ( z ) z = W r t ( z ) × S ( z ) ,
M Δ ( z ) = M s ( z + Δ z ) M s 1 ( z ) ,
θ ( z ) = cos 1 ( T r [ M Δ ( z ) ] 1 2 ) = 2 · 2 π Δ n ( z ) Δ z λ ,
Δ n ( z ) = θ ( z ) λ 4 π Δ z ,
Δ n = n 3 4 ( P 12 P 11 ) ( 1 + σ ) ( r R ) 2 ,
k = n 3 r 2 4 ( P 12 P 11 ) ( 1 + σ ) .
Δ n = k ( 1 R ) 2 .
Δ n = 6.601 × 10 10 ( 1 R ) 2 + 2.365 × 10 7 .
Δ n R B = τ ( ω ) c L ,
Δ n l o o p = τ l o o p ( ω ) c l l o o p .
M l o o p = M t o t a l · M r e f 1 .
Δ n P S G A = 6.490 × 10 10 ( 1 R ) 2 .

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