Abstract

We present a novel perturbation method for the nonlinear Schrödinger equation (NLSE) that governs the propagation of light in optical fibers. We apply this method to study signal-noise interactions in amplified multispan fiber-optic systems. Being based on a combination of the regular perturbation (RP) and logarithmic perturbation, the method is especially suitable for modeling the simultaneous presence of nonlinear and dispersive effects. Even after linearization, it retains the contribution of the quadratic perturbation terms of the NLSE, thereby achieving higher accuracy than an RP with comparable complexity. We revise parametric gain and nonlinear phase-noise effects under the new theory. We finally consider several examples and evaluate the probability density function of the optical or postdetection signal and the bit-error rate of an NRZ–OOK system. All of the results are compared with other models and with multicanonical Monte Carlo simulations.

© 2009 IEEE

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  1. G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).
  2. O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).
  3. M. Karlsson, "Modulational instability in lossy optical fibers," J. Opt. Soc. Amer. B 12, 2071-2077 (1995).
  4. A. V. T. Cartaxo, "Small-signal analysis for nonlinear and dispersive optical fibres, and its application to design of dispersion supported transmission systems with optical dispersion compensation," Proc. Inst. Elect. Eng., Optoelectron. 146, 213-222 (1999).
  5. A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).
  6. E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).
  7. E. Forestieri, M. Secondini, Optical Communication Theory and Techniques (Springer, 2004) pp. 3-11.
  8. R. Hui, M. O'Sullivan, A. Robinson, M. Taylor, "Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments," J. Lightw. Technol. 15, 1071-1082 (1997).
  9. A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "New analytical results on fiber parametric gain and its effects on ASE noise," IEEE Photon. Technol. Lett. 9, 535-537 (1997).
  10. R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, L. a. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).
  11. P. Serena, A. Bononi, J.-C. Antona, S. Bigo, "Parametric gain in the strongly nonlinear regime and its impact on 10-Gb/s NRZ systems with forward-error correction," J. Lightw. Technol. 23, 2352-2363 (2005).
  12. M. Secondini, E. Forestieri, C. R. Menyuk, "A novel perturbation method for signal-noise interaction in nonlinear dispersive fibers," OFC AnaheimCA (2006) paper OThD3.
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  15. K.-P. Ho, "Impact of nonlinear phase noise to DPSK signals: A comparison of different models," IEEE Photon. Technol. Lett 16, 1403-1405 (2004).
  16. B. A. Berg, "Algorithmic aspects of multicanonical simulations," Nucl. Phys. B (Proc. Suppl.) 63A-C, 982-984 (1998).
  17. R. Holzlöhner, C. R. Menyuk, "Use of multicanonical monte carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).
  18. L. Gerardi, M. Secondini, E. Forestieri, "Pattern perturbation method for multicanonical Monte Carlo simulations in optical communications," IEEE Photon. Technol. Lett. 19, 1934-1936 (2007).
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  23. E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).
  24. J.-S. Lee, C.-S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).
  25. G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical approach to the evaluation of the impact of fiber parametric gain on the bit error rate," IEEE Trans. Commun. 49, 2154-2163 (2001).
  26. P. Serena, A. Orlandini, A. Bononi, "Parametric gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).
  27. E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).

2009 (1)

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).

2007 (1)

L. Gerardi, M. Secondini, E. Forestieri, "Pattern perturbation method for multicanonical Monte Carlo simulations in optical communications," IEEE Photon. Technol. Lett. 19, 1934-1936 (2007).

2006 (1)

P. Serena, A. Orlandini, A. Bononi, "Parametric gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

2005 (2)

E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).

P. Serena, A. Bononi, J.-C. Antona, S. Bigo, "Parametric gain in the strongly nonlinear regime and its impact on 10-Gb/s NRZ systems with forward-error correction," J. Lightw. Technol. 23, 2352-2363 (2005).

2004 (1)

K.-P. Ho, "Impact of nonlinear phase noise to DPSK signals: A comparison of different models," IEEE Photon. Technol. Lett 16, 1403-1405 (2004).

2003 (2)

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

R. Holzlöhner, C. R. Menyuk, "Use of multicanonical monte carlo simulations to obtain accurate bit error rates in optical communications systems," Opt. Lett. 28, 1894-1896 (2003).

2002 (2)

A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, L. a. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).

2001 (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical approach to the evaluation of the impact of fiber parametric gain on the bit error rate," IEEE Trans. Commun. 49, 2154-2163 (2001).

2000 (1)

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).

1999 (1)

A. V. T. Cartaxo, "Small-signal analysis for nonlinear and dispersive optical fibres, and its application to design of dispersion supported transmission systems with optical dispersion compensation," Proc. Inst. Elect. Eng., Optoelectron. 146, 213-222 (1999).

1998 (1)

B. A. Berg, "Algorithmic aspects of multicanonical simulations," Nucl. Phys. B (Proc. Suppl.) 63A-C, 982-984 (1998).

1997 (2)

R. Hui, M. O'Sullivan, A. Robinson, M. Taylor, "Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments," J. Lightw. Technol. 15, 1071-1082 (1997).

A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "New analytical results on fiber parametric gain and its effects on ASE noise," IEEE Photon. Technol. Lett. 9, 535-537 (1997).

1995 (1)

M. Karlsson, "Modulational instability in lossy optical fibers," J. Opt. Soc. Amer. B 12, 2071-2077 (1995).

1994 (1)

J.-S. Lee, C.-S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).

1993 (1)

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

1990 (1)

1947 (1)

M. Kac, A. J. F. Siegert, "On the theory of noise in radio receivers with square law detectors," J. Appl. Phys. 18, 383-397 (1947).

Electron. Lett. (1)

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

IEEE Photon. Technol. Lett (1)

K.-P. Ho, "Impact of nonlinear phase noise to DPSK signals: A comparison of different models," IEEE Photon. Technol. Lett 16, 1403-1405 (2004).

IEEE Photon. Technol. Lett. (3)

E. Ciaramella, E. Forestieri, "Analytical approximation of nonlinear distortions," IEEE Photon. Technol. Lett. 17, 91-93 (2005).

A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "New analytical results on fiber parametric gain and its effects on ASE noise," IEEE Photon. Technol. Lett. 9, 535-537 (1997).

L. Gerardi, M. Secondini, E. Forestieri, "Pattern perturbation method for multicanonical Monte Carlo simulations in optical communications," IEEE Photon. Technol. Lett. 19, 1934-1936 (2007).

IEEE Trans. Commun. (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical approach to the evaluation of the impact of fiber parametric gain on the bit error rate," IEEE Trans. Commun. 49, 2154-2163 (2001).

J. Appl. Phys. (1)

M. Kac, A. J. F. Siegert, "On the theory of noise in radio receivers with square law detectors," J. Appl. Phys. 18, 383-397 (1947).

J. Lightw. Technol. (9)

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and pre- and postdetection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).

J.-S. Lee, C.-S. Shim, "Bit-error-rate analysis of optically preamplified receivers using an eigenfunction expansion method in optical frequency domain," J. Lightw. Technol. 12, 1224-1229 (1994).

P. Serena, A. Orlandini, A. Bononi, "Parametric gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).

E. Forestieri, M. Secondini, "On the error probability evaluation in lightwave systems with optical amplification," J. Lightw. Technol. 27, 706-717 (2009).

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, L. a. Kath, "Accurate calculation of eye diagrams and bit error rates in optical transmission systems using linearization," J. Lightw. Technol. 20, 389-400 (2002).

P. Serena, A. Bononi, J.-C. Antona, S. Bigo, "Parametric gain in the strongly nonlinear regime and its impact on 10-Gb/s NRZ systems with forward-error correction," J. Lightw. Technol. 23, 2352-2363 (2005).

O. V. Sinkin, R. Holzlöhner, J. Zweck, C. R. Menyuk, "Optimization of the split-step Fourier method in modeling optical-fiber communications systems," J. Lightw. Technol. 21, 61-68 (2003).

A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation," J. Lightw. Technol. 20, 1102-1112 (2002).

R. Hui, M. O'Sullivan, A. Robinson, M. Taylor, "Modulation instability and its impact in multispan optical amplified IMDD systems: Theory and experiments," J. Lightw. Technol. 15, 1071-1082 (1997).

J. Opt. Soc. Amer. B (1)

M. Karlsson, "Modulational instability in lossy optical fibers," J. Opt. Soc. Amer. B 12, 2071-2077 (1995).

Nucl. Phys. B (Proc. Suppl.) (1)

B. A. Berg, "Algorithmic aspects of multicanonical simulations," Nucl. Phys. B (Proc. Suppl.) 63A-C, 982-984 (1998).

Opt. Lett. (2)

Proc. Inst. Elect. Eng., Optoelectron. (1)

A. V. T. Cartaxo, "Small-signal analysis for nonlinear and dispersive optical fibres, and its application to design of dispersion supported transmission systems with optical dispersion compensation," Proc. Inst. Elect. Eng., Optoelectron. 146, 213-222 (1999).

Other (6)

G. P. Agrawal, Nonlinear Fiber Optics (Academic Press, 1995).

M. Secondini, E. Forestieri, C. R. Menyuk, "A novel perturbation method for signal-noise interaction in nonlinear dispersive fibers," OFC AnaheimCA (2006) paper OThD3.

E. Forestieri, M. Secondini, Optical Communication Theory and Techniques (Springer, 2004) pp. 3-11.

E. Forestieri, Opt. Netw. (Springer-Verlag, 1999) pp. 364-382.

A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions (Dover, 1972).

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