Abstract

We present a new theoretical method, based on a layer-peeling algorithm, for extracting the spatial distribution of the birefringence parameters of an optical emulator. The method enables one to extract the spatial dependence of both the refractive index difference and the orientation angle of the birefringence axes. The layer-peeling algorithm is designed to minimize the accumulated error, and it enables one to accurately reconstruct the birefringence parameters even when a strong noise is added to the input data.

© 2006 Optical Society of America

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  1. P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence," J. Lightwave Technol. 14, 148-157 (1996).
    [CrossRef]
  2. D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
    [CrossRef]
  3. G. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
    [CrossRef]
  4. P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. Von der Weid, F. Prieto, and C. Zimmer, "Second-order polarization mode dispersion: impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
    [CrossRef]
  5. G. Foschini, R. Jopson, L. Nelson, and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion," J. Lightwave Technol. 17, 1560-1565 (1999).
    [CrossRef]
  6. C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
    [CrossRef]
  7. A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
    [CrossRef]
  8. I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
    [CrossRef]
  9. R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
    [CrossRef]
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  12. F. Corsi, A. Galtarossa, and L. Palmieri, "Beat length characterization based on backscattering analysis in randomly perturbed single-mode fibers," J. Lightwave Technol. 17, 1172-1178 (1999).
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  13. A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, "Measurements of beat length and perturbation length in long single-mode fibers," Opt. Lett. 25, 364-386 (2000).
    [CrossRef]
  14. A. Galtarossa, L. Palmieri, A. Pizzinat, M. Sachiano, and T. Tambosso, "Measurements of local beat length and differential group delay in installed single-mode fibers," J. Lightwave Technol. 18, 1389-1394 (2000).
  15. B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
    [CrossRef]
  16. M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
    [CrossRef]
  17. M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).
  18. M. Yoshida, T. Miyamoto, N. Zou, K. Nakamura, and H. Ito, "Novel PMD measurement method based on OFDR using a frequency-shifted feedback fiber laser," Opt. Express 9, 207-211 (2001).
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    [CrossRef]
  20. A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
    [CrossRef]
  21. D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).
  22. O. H. Waagaard and J. Skaar, "Synthesis of birefringent reflective grating," J. Opt. Soc. Am. A 21, 1207-1220 (2004).
    [CrossRef]
  23. D. Sandel, V. Mirvoda, S. Bhandare, F. Wust, and R. No, "Some enabling techniques for polarization mode dispersion compensation," J. Lightwave Technol. 21, 1198-1210 (2003).
    [CrossRef]
  24. J. E. Román, M. Y. Frankel, and R. D. Esman, "Spectral characterization of fiber gratings with high resolution," Opt. Lett. 23, 939-941 (1998).
    [CrossRef]
  25. S. Keren and M. Horowitz, "Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses," Opt. Lett. 26, 328-330 (2001).
    [CrossRef]
  26. W. V. Sorin and D. M. Baney, "Measurement of Rayleigh backscattering at 1.55μm with 32μm spatial resolution," in Instruments and Photonics Laboratory, Tech. Rpt. HPL-91-180 (Hewlett-Packard Laboratories, 1991).
  27. R. Passy, N. Gisin, and J. P. Von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995).
    [CrossRef]
  28. K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
    [CrossRef]
  29. E. Hecht, "Polarization," in Optics (Addison Wesley Longman, 1998), pp. 319-376.
  30. C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]

2004 (2)

O. H. Waagaard and J. Skaar, "Synthesis of birefringent reflective grating," J. Opt. Soc. Am. A 21, 1207-1220 (2004).
[CrossRef]

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

2003 (2)

D. Sandel, V. Mirvoda, S. Bhandare, F. Wust, and R. No, "Some enabling techniques for polarization mode dispersion compensation," J. Lightwave Technol. 21, 1198-1210 (2003).
[CrossRef]

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

2002 (1)

M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).

2001 (5)

M. Yoshida, T. Miyamoto, N. Zou, K. Nakamura, and H. Ito, "Novel PMD measurement method based on OFDR using a frequency-shifted feedback fiber laser," Opt. Express 9, 207-211 (2001).
[CrossRef] [PubMed]

M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

S. Keren and M. Horowitz, "Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses," Opt. Lett. 26, 328-330 (2001).
[CrossRef]

2000 (3)

A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
[CrossRef]

A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, "Measurements of beat length and perturbation length in long single-mode fibers," Opt. Lett. 25, 364-386 (2000).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, M. Sachiano, and T. Tambosso, "Measurements of local beat length and differential group delay in installed single-mode fibers," J. Lightwave Technol. 18, 1389-1394 (2000).

1999 (3)

1998 (4)

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. Von der Weid, F. Prieto, and C. Zimmer, "Second-order polarization mode dispersion: impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
[CrossRef]

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).

J. E. Román, M. Y. Frankel, and R. D. Esman, "Spectral characterization of fiber gratings with high resolution," Opt. Lett. 23, 939-941 (1998).
[CrossRef]

1997 (2)

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
[CrossRef]

1996 (1)

P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence," J. Lightwave Technol. 14, 148-157 (1996).
[CrossRef]

1995 (2)

R. Passy, N. Gisin, and J. P. Von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995).
[CrossRef]

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

1992 (1)

1991 (1)

G. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

1985 (1)

A. M. Bruckstein, B. C. Levy, and T. Kailath, "Differential methods in inverse scattering," SIAM J. Appl. Math. 45, 312-335 (1985).
[CrossRef]

1981 (1)

Baney, D. M.

W. V. Sorin and D. M. Baney, "Measurement of Rayleigh backscattering at 1.55μm with 32μm spatial resolution," in Instruments and Photonics Laboratory, Tech. Rpt. HPL-91-180 (Hewlett-Packard Laboratories, 1991).

Bhandare, S.

Borchert, B.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).

Brinkmeyer, E.

Bruckstein, A. M.

A. M. Bruckstein, B. C. Levy, and T. Kailath, "Differential methods in inverse scattering," SIAM J. Appl. Math. 45, 312-335 (1985).
[CrossRef]

Bülow, H.

H. Bülow, "PMD mitigation techniques and their effectiveness in installed fiber," in Optical Fiber Communications Conference (OFC), Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 110-112.

Ciprut, P.

Corsi, F.

Dal Forno, A. O.

A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
[CrossRef]

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

Demokan, M. S.

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

Ebrahimi, P.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

Esman, R. D.

Fischer, G.

Foschini, G.

G. Foschini, R. Jopson, L. Nelson, and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion," J. Lightwave Technol. 17, 1560-1565 (1999).
[CrossRef]

G. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

Frankel, M. Y.

Galtarossa, A.

Gisin, B.

Gisin, N.

M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).

M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
[CrossRef]

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. Von der Weid, F. Prieto, and C. Zimmer, "Second-order polarization mode dispersion: impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
[CrossRef]

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

R. Passy, N. Gisin, and J. P. Von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995).
[CrossRef]

Glingener, C.

Gottwald, E.

Haase, W.

Hecht, E.

E. Hecht, "Polarization," in Optics (Addison Wesley Longman, 1998), pp. 319-376.

Heise, G.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).

Hinz, S.

Horiguchi, T.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

Horowitz, M.

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

S. Keren and M. Horowitz, "Interrogation of fiber gratings by use of low-coherence spectral interferometry of noiselike pulses," Opt. Lett. 26, 328-330 (2001).
[CrossRef]

Huttner, B.

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

Ibragimov, E.

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

Ito, H.

Jin, W.

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

Jopson, R.

Kailath, T.

A. M. Bruckstein, B. C. Levy, and T. Kailath, "Differential methods in inverse scattering," SIAM J. Appl. Math. 45, 312-335 (1985).
[CrossRef]

Keren, S.

Khosravani, R.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

Kogelnik, H.

Koyamada, Y.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

Legre, M.

M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).

M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
[CrossRef]

Levy, B. C.

A. M. Bruckstein, B. C. Levy, and T. Kailath, "Differential methods in inverse scattering," SIAM J. Appl. Math. 45, 312-335 (1985).
[CrossRef]

Lima, I. T.

Lima, T.

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

Lu, C.

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

Marcuse, D.

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
[CrossRef]

Menyuk, C. R.

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence," J. Lightwave Technol. 14, 148-157 (1996).
[CrossRef]

Mirvoda, V.

Miyamoto, T.

Nakamura, K.

Nelson, L.

No, R.

Noe, R.

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).

Noé, R.

Palmieri, L.

Paradisi, A.

A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
[CrossRef]

Passy, R.

A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
[CrossRef]

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. Von der Weid, F. Prieto, and C. Zimmer, "Second-order polarization mode dispersion: impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
[CrossRef]

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

R. Passy, N. Gisin, and J. P. Von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995).
[CrossRef]

Pereira da Silva, J. A.

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

Pizzinat, A.

Poole, C. D.

G. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

Prieto, F.

Prola, C. H.

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

Reecht, J.

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

Román, J. E.

Rosenthal, A.

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Sandel, D.

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[CrossRef]

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Shimizu, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

Skaar, J.

Sorin, W. V.

W. V. Sorin and D. M. Baney, "Measurement of Rayleigh backscattering at 1.55μm with 32μm spatial resolution," in Instruments and Photonics Laboratory, Tech. Rpt. HPL-91-180 (Hewlett-Packard Laboratories, 1991).

Tambosso, T.

A. Galtarossa, L. Palmieri, M. Schiano, and T. Tambosso, "Measurements of beat length and perturbation length in long single-mode fibers," Opt. Lett. 25, 364-386 (2000).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, M. Sachiano, and T. Tambosso, "Measurements of local beat length and differential group delay in installed single-mode fibers," J. Lightwave Technol. 18, 1389-1394 (2000).

Tang, Q.

Tsuji, K.

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

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von der Weid, J. P.

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[CrossRef]

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[CrossRef]

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

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[CrossRef]

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D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
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P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence," J. Lightwave Technol. 14, 148-157 (1996).
[CrossRef]

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M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).

M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
[CrossRef]

Weyrauch, T.

Willner, A. E.

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
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Wust, F.

Yang, X.

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

Yoshida, M.

Yoshida-Dierolf, M.

Zhao, C. L.

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

Zhao, Y.

Zimmer, C.

Zou, N.

Appl. Opt. (1)

IEEE J. Quantum Electron. (1)

A. Rosenthal and M. Horowitz, "Inverse scattering algorithm for reconstructing strongly reflecting fiber Bragg gratings," IEEE J. Quantum Electron. 39, 1018-1026 (2003).
[CrossRef]

IEEE Photon. Technol. Lett. (9)

B. Huttner, J. Reecht, N. Gisin, R. Passy, and J. P. von der Weid, "Local birefringence measurements in single-mode fibers with coherent optical Frequency-domain reflectometry," IEEE Photon. Technol. Lett. 10, 1458-1460 (1998).
[CrossRef]

M. Wegmuller, M. Legre, and N. Gisin, "Analysis of the polarization evolution in a ribbon cable using high-resolution coherent OFDR," IEEE Photon. Technol. Lett. 13, 145-147 (2001).
[CrossRef]

M. Wegmuller, M. Legre, and N. Gisin, "Distributed beatlength measurement in single-mode fibers with optical frequency-domain reflectometry," IEEE Photon. Technol. Lett. 20, 828-835 (2002).

C. H. Prola, J. A. Pereira da Silva, A. O. Dal Forno, R. Passy, J. P. von der Weid, and N. Gisin, "PMD emulators and signal distortion in 2.48-Gb/s IM-DD lightwave systems," IEEE Photon. Technol. Lett. 9, 842-844 (1997).
[CrossRef]

A. O. Dal Forno, A. Paradisi, R. Passy, and J. P. von der Weid, "Experimental and theoretical modeling of polarization-mode dispersion in single-mode fibers," IEEE Photon. Technol. Lett. 12, 296-298 (2000).
[CrossRef]

R. Khosravani, T. Lima, P. Ebrahimi, E. Ibragimov, A. E. Willner, and C. R. Menyuk, "Time and frequency domain characteristics of polarization-mode dispersion emulators," IEEE Photon. Technol. Lett. 13, 127-129 (2001).
[CrossRef]

R. Passy, N. Gisin, and J. P. Von der Weid, "High-sensitivity-coherent optical frequency-domain reflectometry for characterization of fiber-optic network components," IEEE Photon. Technol. Lett. 7, 667-669 (1995).
[CrossRef]

K. Tsuji, K. Shimizu, T. Horiguchi, and Y. Koyamada, "Coherent optical frequency domain reflectometry for a long single-mode optical fiber using a coherent lightwave source and an external phase modulator," IEEE Photon. Technol. Lett. 7, 804-806 (1995).
[CrossRef]

C. L. Zhao, X. Yang, C. Lu, W. Jin, and M. S. Demokan, "Temperature-insensitive interferometer using a highly birefringent photonic crystal fiber loop mirror," IEEE Photon. Technol. Lett. 16, 2535-2537 (2004).
[CrossRef]

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D. Sandel, V. Mirvoda, S. Bhandare, F. Wust, and R. No, "Some enabling techniques for polarization mode dispersion compensation," J. Lightwave Technol. 21, 1198-1210 (2003).
[CrossRef]

A. Galtarossa, L. Palmieri, A. Pizzinat, M. Sachiano, and T. Tambosso, "Measurements of local beat length and differential group delay in installed single-mode fibers," J. Lightwave Technol. 18, 1389-1394 (2000).

R. Noé, D. Sandel, M. Yoshida-Dierolf, S. Hinz, V. Mirvoda, A. Schöpflin, C. Glingener, E. Gottwald, C. Scheerer, G. Fischer, T. Weyrauch, and W. Haase, "Polarization mode dispersion compensation at 10, 20, and 40Gb/s with various optical equalizers," J. Lightwave Technol. 17, 1602-1615 (1999).
[CrossRef]

I. T. Lima, R. Khosravani, P. Ebrahimi, E. Ibragimov, C. R. Menyuk, and A. E. Willner, "Comparison of polarization mode dispersion emulators," J. Lightwave Technol. 19, 1872-1881 (2001).
[CrossRef]

P. K. A. Wai and C. R. Menyuk, "Polarization mode dispersion, decorrelation and diffusion in optical fibers with randomly varying birefringence," J. Lightwave Technol. 14, 148-157 (1996).
[CrossRef]

D. Marcuse, C. R. Menyuk, and P. K. A. Wai, "Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence," J. Lightwave Technol. 15, 1735-1746 (1997).
[CrossRef]

G. Foschini and C. D. Poole, "Statistical theory of polarization dispersion in single mode fibers," J. Lightwave Technol. 9, 1439-1456 (1991).
[CrossRef]

P. Ciprut, B. Gisin, N. Gisin, R. Passy, J. Von der Weid, F. Prieto, and C. Zimmer, "Second-order polarization mode dispersion: impact on analog and digital transmissions," J. Lightwave Technol. 16, 757-771 (1998).
[CrossRef]

G. Foschini, R. Jopson, L. Nelson, and H. Kogelnik, "The statistics of PMD-induced chromatic fiber dispersion," J. Lightwave Technol. 17, 1560-1565 (1999).
[CrossRef]

D. Sandel, R. Noe, G. Heise, and B. Borchert, "Optical network analysis and longitudinal structure characterization of fiber Bragg grating," J. Lightwave Technol. 116, 2435-2442 (1998).

F. Corsi, A. Galtarossa, and L. Palmieri, "Beat length characterization based on backscattering analysis in randomly perturbed single-mode fibers," J. Lightwave Technol. 17, 1172-1178 (1999).
[CrossRef]

J. Opt. Soc. Am. A (1)

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H. Bülow, "PMD mitigation techniques and their effectiveness in installed fiber," in Optical Fiber Communications Conference (OFC), Vol. 37 of OSA Trends in Optics and Photonics Series (Optical Society of America, 2000), pp. 110-112.

E. Hecht, "Polarization," in Optics (Addison Wesley Longman, 1998), pp. 319-376.

W. V. Sorin and D. M. Baney, "Measurement of Rayleigh backscattering at 1.55μm with 32μm spatial resolution," in Instruments and Photonics Laboratory, Tech. Rpt. HPL-91-180 (Hewlett-Packard Laboratories, 1991).

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Figures (7)

Fig. 1
Fig. 1

Schematic description of the system analyzed in this paper. The system is a PMD emulator built from several PM fibers connected together using rotatable connectors. We assume that the backreflected signal is mainly formed by the connectors between the PM fibers.

Fig. 2
Fig. 2

Schematic description of the proposed experimental setup. The device under test (DUT) is built from several PM fibers as described in Fig. 1. A broadband source is sent into the DUT and into a reference arm. An input polarizer is used for setting the input SOP. The backreflected signal from the DUT and a reference signal are interfered after passing two equal variable polarizers. Reflections from different connectors cause a modulation of the interference spectrum at a different periodicity. By repeating the measurement using a circular polarizer and a linear polarizer rotated at 0 ° and 45 ° with respect to the x axis, one can extract the frequency dependence of the backreflected SOP obtained from each of the connectors.

Fig. 3
Fig. 3

Backreflected SOP formed by a reflection from the (a) first connector, (b) second connector, and (c) 15th connector of an emulator as a function of time after a wave passes through a polarizer aligned along the x (solid curve) and the y (dashed curve) axes. Each fiber section in the emulator had a RID of Δ n = 5 × 10 4 . The first, second, and the 15th connectors are located 5.1, 11.9, and 104.2 m from the input end of the emulator, respectively. The SOP was sampled with a bandwidth of 3 nm and a resolution of 0.01 nm .

Fig. 4
Fig. 4

Comparison between the RID, Δ n , reconstructed using a layer-peeling algorithm (dashed black line) and the original RID (solid gray line) for a PMD emulator with a total length of 104.2 m built from 15 PM fibers with the same RID and with different lengths, as used in Ref. [9]. The reflection spectrum was sampled with a bandwidth of 3 nm and a resolution of 0.01 nm . Noise with a STD of 13 dB with respect to the peak of the backreflected signal amplitude was added to the input data. The error in the extracted Δ n is less than 0.5%.

Fig. 5
Fig. 5

Absolute value of the orientation angle, θ , reconstructed using a layer-peeling algorithm (dashed black curve) compared with the original θ (solid gray curve) for a PMD emulator analyzed in Fig. 4. The reflection spectrum was sampled with a bandwidth of 3 nm and a resolution of 0.01 nm . Noise with a STD of 13 dB with respect to the peak of the backreflected signal amplitude was added to the input data. The error in the extracted angle θ is less than 1%.

Fig. 6
Fig. 6

Comparison between the RID, Δ n , reconstructed using a layer-peeling algorithm (dashed black curve) and the original RID (solid gray curve) for a PMD emulator with a total length of 104.2 m built from 15 PM fibers rotated at different angles. The reflection spectrum was sampled with a bandwidth of 3 nm and a resolution of 0.01 nm. Noise with a STD of 13 dB with respect to the peak of the backreflected signal amplitude was added to the input data. The error in the extracted Δ n is less than 0.5%.

Fig. 7
Fig. 7

Absolute value of the orientation angle, θ , reconstructed using a layer-peeling algorithm (dashed black curve) compared with the original θ (solid gray curve) for a PMD emulator analyzed in Fig. 6. The reflection spectrum was sampled with a bandwidth of 3 nm and a resolution of 0.01 nm . Noise with a STD of 13 dB with respect to the peak of the backreflected signal amplitude was added to the input data. The error in the extracted angle θ is less than 1%.

Equations (52)

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A ( z , ω ) A = ( A x ( z , ω ) A y ( z , ω ) ) ,
z ( A x ( z , ω ) A y ( z , ω ) ) = i ω Δ n 2 c [ cos ( 2 θ ) sin ( 2 θ ) sin ( 2 θ ) cos ( 2 θ ) ] ( A x ( z , ω ) A y ( z , ω ) ) ,
A o ( ω ) = R 1 ( θ ) D ( ω Δ τ ) R ( θ ) A i MA i ( ω ) ,
R ( θ ) = [ cos θ sin θ sin θ cos θ ] ,
D ( ω Δ τ ) = [ exp ( i ω Δ τ 2 ) 0 0 exp ( i ω Δ τ 2 ) ] ,
M = R 1 ( θ ) D ( ω Δ τ ) R ( θ ) ,
A r ( ω ) = M t M A i ( ω ) .
A r ( ω ) = R 1 ( θ ) D 2 ( ω Δ τ ) R ( θ ) A i ( ω ) .
S ( z , ω ) z = W × S ( z , ω ) ,
W ( z , ω ) = ω Δ n ( z ) c ( cos [ 2 θ ( z ) ] , sin [ 2 θ ( z ) ] , 0 ) t .
S ̂ r ( ω ) = R θ 1 R ϕ 2 R θ M r S ̂ i ( ω ) ,
R θ ( 2 θ ) = [ cos ( 2 θ ) sin ( 2 θ ) 0 sin ( 2 θ ) cos ( 2 θ ) 0 0 0 1 ] ,
R ϕ ( ϕ ) = [ 1 0 0 0 cos ( ϕ ) sin ( ϕ ) 0 sin ( ϕ ) cos ( ϕ ) ] ,
M r = [ 1 0 0 0 1 0 0 0 1 ] ,
ϕ ( ω ) = W ( ω ) L = ω Δ n c L .
W ̂ = W W = ( cos ( 2 θ ) , sin ( 2 θ ) , 0 ) t ,
S ̂ i ( ω ) W ̂ = S ̂ o ( ω ) W ̂ ,
S ̂ i ( ω ) W ̂ = S ̂ r ( ω ) W ̂ ,
[ S ̂ r ( ω j ) S ̂ i ( ω j ) ] W ̂ = 0 , j = 1 n .
d S ̂ ( ω j ) = S ̂ r ( ω j ) S ̂ i ( ω j ) S ̂ r ( ω j ) S ̂ i ( ω j ) , j = 1 n ,
d S j , 1 W 1 + d S j , 2 W 2 = 0 , j = 1 n ,
W 1 2 + W 2 2 = 1 .
W 1 = ± R ( P + λ ) 2 + R 2 ,
W 2 = ( P + λ ) ( P + λ ) 2 + R 2 ,
P = j = 1 n ( d S j , 1 ) 2 ,
Q = j = 1 n ( d S j , 2 ) 2 ,
R = j = 1 n ( d S j , 1 d S j , 2 ) ,
λ ± = ( P + Q ) ± ( P Q ) 2 + 4 R 2 2 .
V i ( ω ) = [ S ̂ i ( ω ) W ̂ ] W ̂ + S ̂ i ( ω ) ,
V r ( ω ) = [ S ̂ r ( ω ) W ̂ ] W ̂ + S ̂ r ( ω ) .
d ω < π c 2 L Δ n
g ( Δ n ) = j = 1 n S ̂ r , e ( ω j ) S ̂ r ( ω j ) 2 .
g ( Δ n ) = j = 1 n l j 2 ( Δ x j 2 + Δ y j 2 ) ,
l j 2 = 1 W ̂ S ̂ i ( ω j ) ,
Δ x j 2 = cos ( 2 ω j Δ n L c ) cos [ 2 ϕ ( ω j ) ] 2 ,
Δ y j 2 = sin ( 2 ω j Δ n L c ) sin [ 2 ϕ ( ω j ) ] 2 .
( cos [ 2 ϕ ( ω j ) ] sin [ 2 ϕ ( ω j ) ] ) = ( L T L ) 1 L T [ S ̂ r ( ω j ) KM r S ̂ i ( ω j ) ] ,
A i r = ( M i M i 1 M 1 ) t ( M i M i 1 M 1 ) A i ,
A ̃ i r = R i 1 D i 2 R i A ̃ i i ,
M ̃ i = M i M 1 ,
δ λ < λ 2 4 Δ n L max ,
Δ λ > λ 2 Δ ϕ min 4 π Δ n L min ,
h ( z ) = exp [ 1 ln 2 ( π n δ λ z 2 λ 0 2 ) 2 ] .
S ̂ r , e ( ω j ) = L ( cos ( 2 ω j Δ n L c ) sin ( 2 ω j Δ n L c ) ) + KM r S ̂ i ( ω j ) ,
S ̂ r ( ω j ) = L ( cos [ 2 ϕ j ( ω j ) ] sin [ 2 ϕ j ( ω j ) ] ) + KM r S ̂ i ( ω j ) ,
L = [ W 2 2 S 1 i W 1 W 2 S 2 i W 2 S 3 i W 1 W 2 S 1 i + W 1 2 S 2 i W 1 S i 2 S 3 i W 2 S 1 i W 1 S 2 i ] ,
K = [ W 1 2 W 1 W 2 0 W 1 W 2 W 2 2 0 0 0 0 ] .
g ( Δ n ) = j = 1 n L ( cos ( 2 ω j Δ n L c ) cos [ 2 ϕ j ( ω j ) ] sin ( 2 ω j Δ n L c ) sin [ 2 ϕ j ( ω j ) ] ) 2 .
g ( Δ n ) = j = 1 n l j 2 ( Δ x j 2 + Δ y j 2 ) ,
l j 2 = 1 W ̂ S ̂ i ( ω j ) ,
Δ x j 2 = cos ( 2 ω j Δ n L c ) cos [ 2 ϕ ( ω j ) ] 2 ,
Δ y j 2 = sin ( 2 ω j Δ n L c ) sin [ 2 ϕ ( ω j ) ] 2 .

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