Abstract

In this paper, we develop a general first-order perturbation theory of the propagation of a signal in an optical fiber in the presence of amplification and Kerr nonlinearity, valid for arbitrary pulse shapes. We obtain a general expression of the sampled signal after optical filtering, coherent detection, and optimal sampling. We include intrachannel and as well as interchannel nonlinear effects. We obtain simplified expressions in the case in which the accumulated dispersion is high (equivalent to the far-field limit in paraxial optics). This general theory is applied in detail to the special case of spectral-efficient sinc pulses. This exercise shows that the characteristics of the neighboring wavelength-division multiplexed channels are essential in determining the nonlinear impairments.

© 2012 IEEE

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  1. P. J. Winzer, R.-J. Essiambre, "Advanced optical modulation formats," Proc. IEEE. 94, 952-985 (2006).
  2. R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).
  3. A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intra-channel nonlinear effects in highly dispersed pulse transmission in optical fibers," IEEE Photon. Technol. Lett. 12, 392-394 (2000).
  4. A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).
  5. A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).
  6. A. Mecozzi, "A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission," IEEE Photon. J. 2, 728-735 (2010).
  7. K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, "Information capacity of optical fiber channels with zero average dispersion," Phys. Rev. Lett. 91, 203901-1-203901-4 (2003).
  8. M. I. Yousefi, F. R. Kschischang, "On the per-sample capacity of nondispersive optical fibers," IEEE Trans. Inf. Theory 57, 7522-7541 (2011).
  9. A. Mecozzi, "Error probability of amplified IMDD systems at zero dispersion," Electron. Lett. 29, 2136-2137 (1993).
  10. D. Marcuse, "Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion," J. Lightw. Technol. 9, 356-361 (1991).
  11. A. Mecozzi, "Long distance transmission at zero dispersion: The combined effect of Kerr nonlinearity and noise of the inline amplifiers," J. Opt. Soc. Amer. B 11, 462-470 (1994).
  12. A. Mecozzi, "Limits to longhaul coherent transmission set by the Kerr nonlinearity and noise of the inline amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).
  13. A. V. T. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).
  14. R. Hui, K. R. Demarest, C. T. Allen, "Cross-phase modulation in multispan WDM optical fiber systems," J. Lightw. Technol. 17, 1018-1026 (1999).
  15. P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).
  16. R.-J. Essiambre, "Impact of fiber parameters on nonlinear fiber capacity," presented at the Opt. Fiber Commun. Conf. Los AngelesCA Paper OTuJ1.
  17. A. Splett, C. Kurzke, K. Petermann, "Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities," Proc. Eur. Conf. Exhib. Opt. Commun. (1993) pp. 41-44.
  18. G. Bosco, P. Poggiolini, A. Carena, V. Curri, F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," presented at the Eur. Conf. Exhib. Opt. Commun. GenevaSwitzerland (2011) Paper We.7.B.3.
  19. X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).
  20. E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, F. Forghieri, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," presented at the Eur. Conf. Exhib. Opt. Commun. GenevaSwitzerland (2011) Paper We.7.B.2.

2011 (1)

M. I. Yousefi, F. R. Kschischang, "On the per-sample capacity of nondispersive optical fibers," IEEE Trans. Inf. Theory 57, 7522-7541 (2011).

2010 (3)

A. Mecozzi, "A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission," IEEE Photon. J. 2, 728-735 (2010).

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).

2006 (1)

P. J. Winzer, R.-J. Essiambre, "Advanced optical modulation formats," Proc. IEEE. 94, 952-985 (2006).

2003 (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, "Information capacity of optical fiber channels with zero average dispersion," Phys. Rev. Lett. 91, 203901-1-203901-4 (2003).

2001 (2)

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).

2000 (2)

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intra-channel nonlinear effects in highly dispersed pulse transmission in optical fibers," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).

1999 (2)

A. V. T. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).

R. Hui, K. R. Demarest, C. T. Allen, "Cross-phase modulation in multispan WDM optical fiber systems," J. Lightw. Technol. 17, 1018-1026 (1999).

1994 (2)

A. Mecozzi, "Long distance transmission at zero dispersion: The combined effect of Kerr nonlinearity and noise of the inline amplifiers," J. Opt. Soc. Amer. B 11, 462-470 (1994).

A. Mecozzi, "Limits to longhaul coherent transmission set by the Kerr nonlinearity and noise of the inline amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).

1993 (1)

A. Mecozzi, "Error probability of amplified IMDD systems at zero dispersion," Electron. Lett. 29, 2136-2137 (1993).

1991 (1)

D. Marcuse, "Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion," J. Lightw. Technol. 9, 356-361 (1991).

Electron. Lett. (1)

A. Mecozzi, "Error probability of amplified IMDD systems at zero dispersion," Electron. Lett. 29, 2136-2137 (1993).

IEEE Photon. J. (1)

A. Mecozzi, "A unified theory of intra-channel nonlinearity in pseudo-linear phase-modulated transmission," IEEE Photon. J. 2, 728-735 (2010).

IEEE Photon. Technol. Lett. (3)

A. Mecozzi, C. B. Clausen, M. Shtaif, "Analysis of intra-channel nonlinear effects in highly dispersed pulse transmission in optical fibers," IEEE Photon. Technol. Lett. 12, 392-394 (2000).

A. Mecozzi, C. B. Clausen, M. Shtaif, "System impact of intra-channel nonlinear effects in highly dispersed optical pulse transmission," IEEE Photon. Technol. Lett. 12, 1633-1635 (2000).

A. Mecozzi, C. B. Clausen, M. Shtaif, S.-G. Park, A. H. Gnauck, "Cancellation of timing and amplitude jitter in symmetric links using highly dispersed pulses," IEEE Photon. Technol. Lett. 13, 445-447 (2001).

IEEE Trans. Inf. Theory (1)

M. I. Yousefi, F. R. Kschischang, "On the per-sample capacity of nondispersive optical fibers," IEEE Trans. Inf. Theory 57, 7522-7541 (2011).

J. Lightw. Technol. (5)

A. Mecozzi, "Limits to longhaul coherent transmission set by the Kerr nonlinearity and noise of the inline amplifiers," J. Lightw. Technol. 12, 1993-2000 (1994).

A. V. T. Cartaxo, "Cross-phase modulation in intensity modulation-direct detection WDM systems with multiple optical amplifiers and dispersion compensators," J. Lightw. Technol. 17, 178-190 (1999).

R. Hui, K. R. Demarest, C. T. Allen, "Cross-phase modulation in multispan WDM optical fiber systems," J. Lightw. Technol. 17, 1018-1026 (1999).

R.-J. Essiambre, G. Kramer, P. J. Winzer, G. J. Foschini, B. Goebel, "Capacity limits of optical fiber networks," J. Lightw. Technol. 28, 662-701 (2010).

D. Marcuse, "Single-channel operation in very long nonlinear fibers with optical amplifiers at zero dispersion," J. Lightw. Technol. 9, 356-361 (1991).

J. Opt. Soc. Amer. (1)

A. Mecozzi, "Long distance transmission at zero dispersion: The combined effect of Kerr nonlinearity and noise of the inline amplifiers," J. Opt. Soc. Amer. B 11, 462-470 (1994).

Nature (1)

P. P. Mitra, J. B. Stark, "Nonlinear limits to the information capacity of optical fibre communications," Nature 411, 1027-1030 (2001).

Opt. Exp. (1)

X. Chen, W. Shieh, "Closed-form expressions for nonlinear transmission performance of densely spaced coherent optical OFDM systems," Opt. Exp. 18, 19039-19054 (2010).

Phys. Rev. Lett. (1)

K. S. Turitsyn, S. A. Derevyanko, I. V. Yurkevich, S. K. Turitsyn, "Information capacity of optical fiber channels with zero average dispersion," Phys. Rev. Lett. 91, 203901-1-203901-4 (2003).

Proc. IEEE. (1)

P. J. Winzer, R.-J. Essiambre, "Advanced optical modulation formats," Proc. IEEE. 94, 952-985 (2006).

Other (4)

E. Torrengo, R. Cigliutti, G. Bosco, A. Carena, V. Curri, P. Poggiolini, A. Nespola, D. Zeolla, F. Forghieri, "Experimental validation of an analytical model for nonlinear propagation in uncompensated optical links," presented at the Eur. Conf. Exhib. Opt. Commun. GenevaSwitzerland (2011) Paper We.7.B.2.

R.-J. Essiambre, "Impact of fiber parameters on nonlinear fiber capacity," presented at the Opt. Fiber Commun. Conf. Los AngelesCA Paper OTuJ1.

A. Splett, C. Kurzke, K. Petermann, "Ultimate transmission capacity of amplified optical fiber communication systems taking into account fiber nonlinearities," Proc. Eur. Conf. Exhib. Opt. Commun. (1993) pp. 41-44.

G. Bosco, P. Poggiolini, A. Carena, V. Curri, F. Forghieri, "Analytical results on channel capacity in uncompensated optical links with coherent detection," presented at the Eur. Conf. Exhib. Opt. Commun. GenevaSwitzerland (2011) Paper We.7.B.3.

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