Abstract

Starting from a model of random nonlinear polarization rotations for the effect of cross-polarization modulation in DWDM systems, we derive the mean distribution of the time-dependent polarization states at an arbitrary location within an optical link. We show that this distribution is fully parameterized by the degree of polarization of the particular wavelength channel, and we derive expressions to approximate this parameter for general optical links consisting of multiple optically amplified and dispersion-compensated spans, as well as related power thresholds. From the analytical expressions we derive a method to significantly reduce the detrimental effects.

© 2009 IEEE

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  1. M. A. Duguay, J. W. Hansen, "An ultrafast light gate," Appl. Phys. Lett. 15, 192-194 (1969).
  2. R. H. Stolen, A. Ashkin, "Optical Kerr effect in glass waveguide," Appl. Phys. Lett. 22, 294-296 (1973).
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  8. D. van den Borne, "Reduction of nonlinear penalties through polarization interleaving in 2$\,\times\,$10 Gb/s polarization-multiplexed transmission," IEEE Photon. Technol. Lett. 17, 1337-1339 (2005).
  9. M. R. Phillips, S. L. Woodward, "Cross-polarization modulation: Theory and measurement of a two-channel WDM system," IEEE Photon. Technol. Lett. 17, 2086-2088 (2005).
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  18. C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).
  19. R. P. Feynman, "An operator calculus having applications in quantum electrodynamics," Phys. Rev. 84, 108-128 (1951).
  20. W. Magnus, "On the exponential solution of differential equations for a linear operator," Commun. Pure and Appl. Math. 7, 649-673 (1954).
  21. N. Korneev, "Application of Magnus series for polarization evolution in fibers," Revista mexicana de física 48, 250-254 (2002).
  22. P. H. Roberts, H. D. Ursell, "Random walk on a sphere and on a Riemannian manifold," Philos. Trans. Roy. Soc. London, Ser. A 252, 317-356 (1960).
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  24. M. Karlsson, "Long-term measurement of PMD and polarization drift in installed fibers," J. Lightwave Technol. 18, 941-951 (2000).
  25. T. Ueda, W. L. Kath, "Dynamics of optical pulses in randomly birefringent fibers," Physica D 55, 166-181 (1992).
  26. J. P. Gordon, Polarization Mode Dispersion (Springer, 2005) pp. 52-69.
  27. H. Kogelnik, Optical Fiber Telecommunications IV B (Academic Press, 2002) pp. 725-861.

2007 (2)

C. J. McKinstrie, "Stokes-space derivations of generalized Schrödinger equations for wave propagation in various fibers," Opt. Expr. 15, 10 964-10 983 (2007).

S. Chandrasekhar, X. Liu, "Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid," IEEE Photon. Technol. Lett. 19, 1801-1803 (2007).

2006 (3)

2005 (2)

D. van den Borne, "Reduction of nonlinear penalties through polarization interleaving in 2$\,\times\,$10 Gb/s polarization-multiplexed transmission," IEEE Photon. Technol. Lett. 17, 1337-1339 (2005).

M. R. Phillips, S. L. Woodward, "Cross-polarization modulation: Theory and measurement of a two-channel WDM system," IEEE Photon. Technol. Lett. 17, 2086-2088 (2005).

2004 (1)

Q. Lin, G. P. Agrawal, "Vector theory of cross-phase modulation: Role of nonlinear polarization rotation," IEEE J. Quantum Electron. 40, 958-964 (2004).

2003 (2)

2002 (1)

N. Korneev, "Application of Magnus series for polarization evolution in fibers," Revista mexicana de física 48, 250-254 (2002).

2000 (3)

M. Karlsson, "Long-term measurement of PMD and polarization drift in installed fibers," J. Lightwave Technol. 18, 941-951 (2000).

B. C. Collings, L. Boivin, "Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems," IEEE Photon. Technol. Lett. 12, 1582-1584 (2000).

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. National Academy of Sciences of the United States of America 97, 4541-4550 (2000).

1999 (1)

C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).

1997 (1)

D. Marcuse, "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).

1996 (1)

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

1992 (2)

S. G. Evangelides, "Polarization multiplexing with solitons," J. Lightwave Technol. 10, 28-35 (1992).

T. Ueda, W. L. Kath, "Dynamics of optical pulses in randomly birefringent fibers," Physica D 55, 166-181 (1992).

1973 (1)

R. H. Stolen, A. Ashkin, "Optical Kerr effect in glass waveguide," Appl. Phys. Lett. 22, 294-296 (1973).

1969 (1)

M. A. Duguay, J. W. Hansen, "An ultrafast light gate," Appl. Phys. Lett. 15, 192-194 (1969).

1960 (1)

P. H. Roberts, H. D. Ursell, "Random walk on a sphere and on a Riemannian manifold," Philos. Trans. Roy. Soc. London, Ser. A 252, 317-356 (1960).

1954 (1)

W. Magnus, "On the exponential solution of differential equations for a linear operator," Commun. Pure and Appl. Math. 7, 649-673 (1954).

1951 (1)

R. P. Feynman, "An operator calculus having applications in quantum electrodynamics," Phys. Rev. 84, 108-128 (1951).

Appl. Phys. Lett. (2)

M. A. Duguay, J. W. Hansen, "An ultrafast light gate," Appl. Phys. Lett. 15, 192-194 (1969).

R. H. Stolen, A. Ashkin, "Optical Kerr effect in glass waveguide," Appl. Phys. Lett. 22, 294-296 (1973).

Commun. Pure and Appl. Math. (1)

W. Magnus, "On the exponential solution of differential equations for a linear operator," Commun. Pure and Appl. Math. 7, 649-673 (1954).

IEEE J. Quantum Electron. (1)

Q. Lin, G. P. Agrawal, "Vector theory of cross-phase modulation: Role of nonlinear polarization rotation," IEEE J. Quantum Electron. 40, 958-964 (2004).

IEEE Photon. Technol. Lett. (4)

B. C. Collings, L. Boivin, "Nonlinear polarization evolution induced by cross-phase modulation and its impact on transmission systems," IEEE Photon. Technol. Lett. 12, 1582-1584 (2000).

D. van den Borne, "Reduction of nonlinear penalties through polarization interleaving in 2$\,\times\,$10 Gb/s polarization-multiplexed transmission," IEEE Photon. Technol. Lett. 17, 1337-1339 (2005).

M. R. Phillips, S. L. Woodward, "Cross-polarization modulation: Theory and measurement of a two-channel WDM system," IEEE Photon. Technol. Lett. 17, 2086-2088 (2005).

S. Chandrasekhar, X. Liu, "Impact of channel plan and dispersion map on hybrid DWDM transmission of 42.7-Gb/s DQPSK and 10.7-Gb/s OOK on 50-GHz grid," IEEE Photon. Technol. Lett. 19, 1801-1803 (2007).

J. Eng. Math. (1)

C. R. Menyuk, "Application of multiple-length-scale methods to the study of optical fiber transmission," J. Eng. Math. 36, 113-136 (1999).

J. Lightwave Technol. (8)

Opt. Expr. (1)

C. J. McKinstrie, "Stokes-space derivations of generalized Schrödinger equations for wave propagation in various fibers," Opt. Expr. 15, 10 964-10 983 (2007).

Opt. Lett. (1)

Philos. Trans. Roy. Soc. London, Ser. A (1)

P. H. Roberts, H. D. Ursell, "Random walk on a sphere and on a Riemannian manifold," Philos. Trans. Roy. Soc. London, Ser. A 252, 317-356 (1960).

Phys. Rev. (1)

R. P. Feynman, "An operator calculus having applications in quantum electrodynamics," Phys. Rev. 84, 108-128 (1951).

Physica D (1)

T. Ueda, W. L. Kath, "Dynamics of optical pulses in randomly birefringent fibers," Physica D 55, 166-181 (1992).

Proc. National Academy of Sciences of the United States of America (1)

J. P. Gordon, H. Kogelnik, "PMD fundamentals: Polarization mode dispersion in optical fibers," Proc. National Academy of Sciences of the United States of America 97, 4541-4550 (2000).

Revista mexicana de física (1)

N. Korneev, "Application of Magnus series for polarization evolution in fibers," Revista mexicana de física 48, 250-254 (2002).

Other (3)

J. P. Gordon, Polarization Mode Dispersion (Springer, 2005) pp. 52-69.

H. Kogelnik, Optical Fiber Telecommunications IV B (Academic Press, 2002) pp. 725-861.

D. van den Borne, "Cross phase modulation induced depolarization penalties in 2$\,\times\,$10 Gbit/s polarization-multiplexed transmission," 30th European Conf. Optical Communication (ECOC) (2004).

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