Abstract

This paper provides a unified framework to the design, performance optimization, and accurate numerical simulation of periodic, dispersion-managed (DM) single-channel long-haul optical transmission systems for nonsoliton on–off keying (OOK) modulation. The focus is on DM terrestrial systems, with identical spans composed of a long transmission fiber compensated at the span end by a linear dispersion compensating module, with pre- and postcompensation fibers at the beginning and end of the link. The framework is based on the dispersion-managed nonlinear Schrödinger equation (DM-NLSE). First, expressions of the DM-NLSE kernel are provided both in the frequency and the time domain, and a novel map strength parameter, appropriate for terrestrial systems, is introduced. It is then shown that the DM-NLSE contains all the basic information needed for system design, as summarized by three parameters: i) nonlinear phase, ii) in-line dispersion, and iii) map strength. Through a large-signal perturbative analysis of the DM-NLSE, the well-known linear relationship between the in-line dispersion and the optimal precompensation is derived, along with the large-signal step response of the DM link, from which the ghost pulses energy growth and a first estimation of the link memory are derived. The DM-NLSE is then linearized around the average signal field to get the amplitude/phase small-signal system matrix of the overall DM link, including pre- and postcompensation. By a singular-value decomposition of the small-signal DM link matrix, a novel expression of the memory of the optimized DM link is finally provided. Knowledge of such a memory is mandatory to run accurate numerical simulations and laboratory measurements with a sufficiently long pseudorandom bit sequence to avoid patterning effects.

© 2008 IEEE

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  2. M. J. Ablowitz, T. Hirooka, "Managing nonlinearity in strongly dispersion-managed optical pulse transmission," J. Opt. Soc. Amer. B, Opt. Phys. 19, 425-439 (2002).
  3. M. J. Ablowitz, T. Hirooka, "Resonant intrachannel pulse interactions in dispersion-managed transmission systems," IEEE J. Sel. Topics Quantum Electron. 8, 603-615 (2002).
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  14. 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).
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  16. Y. Frignac, J.-C. Antona, S. Bigo, "Enhanced analytical engineering rule for fast optimization of dispersion map in 40 Gbit/s-based transmission systems," Proc. OFC '04 (2004).
  17. Y. Frignac, S. Bigo, "Numerical optimization of residual dispersion in dispersion-managed systems at 40 Gbit/s," Proc. OFC '00 (2000) pp. 48-50.
  18. P. Serena, A. Orlandini, A. Bononi, "The memory of optimized dispersion-managed periodic optical links," Proc. ECOC '07 (2007).
  19. L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, A. R. Chraplyvy, "Bit pattern dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).
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  21. M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B, Opt. Phys. 19, 2876-2885 (2002).
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  23. 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).
  24. A. Bononi, G. Bellotti, M. Varani, C. Francia, Optical Networking (Springer, 1999) pp. 383-398.
  25. X. Xiao, S. Gao, Y. Tian, C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightw. Technol. 24, 2038-2043 (2006).
  26. P. Serena, A. Orlandini, A. Bononi, "Scaling laws for weakly-nonlinear WDM dispersion managed OOK systems," Proc. ECOC '06 (2006).
  27. D. Zwillinger, Handbook of Differential Equations (Academic, 1997).
  28. 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).
  29. E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and post-detection filtering," J. Lightw. Technol. 18, 1493-1503 (2000).
  30. A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation," J. Lightw. Technol. 15, 1102-1112 (2002).
  31. P. Serena, A. Orlandini, A. Bononi, "A parametric-gain approach to the analysis of single-channel DPSK/DQPSK systems with nonlinear phase noise," J. Lightw. Technol. 24, 2026-2037 (2006).
  32. X. Wey, "Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links," Opt. Lett. 31, 2544-2546 (2006).
  33. M. J. Potasek, G. P. Agrawal, S. C. Pinault, "Analytic and numerical study of pulse broadening in nonlinear dispersive optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 3, 205-211 (1986).
  34. C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers. Asymptotic Methods and Perturbation Theory (Springer-Verlag, 1999).
  35. P. Johannisson, "Interaction range and generation rate of nonlinear intrachannel signal distortion," J. Opt. Soc. Amer. B, Opt. Phys. 24, 729-738 (2007).
  36. H. Louchet, K. Petermann, A. Robinson, R. Epworth, "Introduction to the concept of nonlinear diffusion bandwidth," Proc. ECOC '05 (2005).
  37. R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1999).

2007 (2)

P. Serena, A. Orlandini, A. Bononi, "Fundamental laws of parametric gain in periodic dispersion-managed optical links," J. Opt. Soc. Amer. B, Opt. Phys. 24, 773-787 (2007).

P. Johannisson, "Interaction range and generation rate of nonlinear intrachannel signal distortion," J. Opt. Soc. Amer. B, Opt. Phys. 24, 729-738 (2007).

2006 (3)

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

X. Wey, "Power-weighted dispersion distribution function for characterizing nonlinear properties of long-haul optical transmission links," Opt. Lett. 31, 2544-2546 (2006).

X. Xiao, S. Gao, Y. Tian, C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightw. Technol. 24, 2038-2043 (2006).

2005 (1)

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, R. Epworth, "Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems," IEEE Photon. Technol. Lett. 17, 2089-2091 (2005).

2004 (1)

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, A. R. Chraplyvy, "Bit pattern dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (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).

A. Cauvin, Y. Frignac, S. Bigo, "Nonlinear impairments at various bit rates in single-channel dispersion-managed systems," Electron. Lett. 39, 1670-1671 (2003).

2002 (5)

M. J. Ablowitz, T. Hirooka, "Managing nonlinearity in strongly dispersion-managed optical pulse transmission," J. Opt. Soc. Amer. B, Opt. Phys. 19, 425-439 (2002).

M. J. Ablowitz, T. Hirooka, "Resonant intrachannel pulse interactions in dispersion-managed transmission systems," IEEE J. Sel. Topics Quantum Electron. 8, 603-615 (2002).

M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B, Opt. Phys. 19, 2876-2885 (2002).

B. Konrad, K. Petermann, J. Berger, R. Ludwig, C. M. Weinert, H. G. Weber, B. Schmauss, "Impact of fiber chromatic dispersion in high-speed TDM transmission systems," J. Lightw. Technol. 20, 2129-2135 (2002).

A. Vannucci, P. Serena, A. Bononi, "The RP method: A new tool for the iterative solution of the nonlinear Schrödinger equation," J. Lightw. Technol. 15, 1102-1112 (2002).

2001 (1)

B. Konrad, K. Petermann, "Optimum fiber dispersion in high-speed TDM systems," IEEE Photon. Technol. Lett. 13, 299-301 (2001).

2000 (3)

R. I. Killey, H. J. Thiele, V. Mikhailov, P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40 Gb/s-based transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (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).

E. Forestieri, "Evaluating the error probability in lightwave systems with chromatic dispersion, arbitrary pulse shape and post-detection 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)

M. J. Ablowitz, G. Biondini, "Multiscale pulse dynamics in communication systems with strong dispersion management," Opt. Lett. 23, 1668-1670 (1998).

1996 (1)

I. R. Gabitov, S. K. Turitsyn, "Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation," Opt. Lett. 21, 327-329 (1996).

1991 (2)

H. A. Haus, "Quantum noise in a soliton like repeater system," J. Opt. Soc. Amer. B, Opt. Phys. 8, 1122-1126 (1991).

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, "Long-distance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightw. Technol. 9, 194-196 (1991).

1986 (1)

M. J. Potasek, G. P. Agrawal, S. C. Pinault, "Analytic and numerical study of pulse broadening in nonlinear dispersive optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 3, 205-211 (1986).

Electron. Lett. (1)

A. Cauvin, Y. Frignac, S. Bigo, "Nonlinear impairments at various bit rates in single-channel dispersion-managed systems," Electron. Lett. 39, 1670-1671 (2003).

IEEE J. Sel. Topics Quantum Electron. (1)

M. J. Ablowitz, T. Hirooka, "Resonant intrachannel pulse interactions in dispersion-managed transmission systems," IEEE J. Sel. Topics Quantum Electron. 8, 603-615 (2002).

IEEE Photon. Technol. Lett. (1)

R. I. Killey, H. J. Thiele, V. Mikhailov, P. Bayvel, "Reduction of intrachannel nonlinear distortion in 40 Gb/s-based transmission over standard fiber," IEEE Photon. Technol. Lett. 12, 1624-1626 (2000).

IEEE Photon. Technol. Lett. (1)

L. K. Wickham, R.-J. Essiambre, A. H. Gnauck, P. J. Winzer, A. R. Chraplyvy, "Bit pattern dependence of intrachannel nonlinearities in pseudolinear transmission," IEEE Photon. Technol. Lett. 16, 1591-1593 (2004).

IEEE Photon. Technol. Lett. (3)

B. Konrad, K. Petermann, "Optimum fiber dispersion in high-speed TDM systems," IEEE Photon. Technol. Lett. 13, 299-301 (2001).

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).

H. Louchet, A. Hodzic, K. Petermann, A. Robinson, R. Epworth, "Simple criterion for the characterization of nonlinear impairments in dispersion-managed optical transmission systems," IEEE Photon. Technol. Lett. 17, 2089-2091 (2005).

J. Lightw. Technol. (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. 15, 1102-1112 (2002).

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, "Long-distance soliton propagation using lumped amplifiers and dispersion shifted fiber," J. Lightw. Technol. 9, 194-196 (1991).

J. Opt. Soc. Amer. B, Opt. Phys. (3)

M. J. Potasek, G. P. Agrawal, S. C. Pinault, "Analytic and numerical study of pulse broadening in nonlinear dispersive optical fibers," J. Opt. Soc. Amer. B, Opt. Phys. 3, 205-211 (1986).

P. Johannisson, "Interaction range and generation rate of nonlinear intrachannel signal distortion," J. Opt. Soc. Amer. B, Opt. Phys. 24, 729-738 (2007).

M. J. Ablowitz, T. Hirooka, T. Inoue, "Higher-order analysis of dispersion-managed transmission systems: Solutions and their characteristics," J. Opt. Soc. Amer. B, Opt. Phys. 19, 2876-2885 (2002).

J. Lightw. Technol. (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).

B. Konrad, K. Petermann, J. Berger, R. Ludwig, C. M. Weinert, H. G. Weber, B. Schmauss, "Impact of fiber chromatic dispersion in high-speed TDM transmission systems," J. Lightw. Technol. 20, 2129-2135 (2002).

J. Lightw. Technol. (3)

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

X. Xiao, S. Gao, Y. Tian, C. Yang, "Analytical optimization of the net residual dispersion in SPM-limited dispersion-managed systems," J. Lightw. Technol. 24, 2038-2043 (2006).

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

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

P. Serena, A. Orlandini, A. Bononi, "Fundamental laws of parametric gain in periodic dispersion-managed optical links," J. Opt. Soc. Amer. B, Opt. Phys. 24, 773-787 (2007).

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

M. J. Ablowitz, T. Hirooka, "Managing nonlinearity in strongly dispersion-managed optical pulse transmission," J. Opt. Soc. Amer. B, Opt. Phys. 19, 425-439 (2002).

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

H. A. Haus, "Quantum noise in a soliton like repeater system," J. Opt. Soc. Amer. B, Opt. Phys. 8, 1122-1126 (1991).

Opt. Lett. (2)

M. J. Ablowitz, G. Biondini, "Multiscale pulse dynamics in communication systems with strong dispersion management," Opt. Lett. 23, 1668-1670 (1998).

I. R. Gabitov, S. K. Turitsyn, "Averaged pulse dynamics in a cascaded transmission system with passive dispersion compensation," Opt. Lett. 21, 327-329 (1996).

Opt. Lett. (1)

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 (13)

A. Bononi, G. Bellotti, M. Varani, C. Francia, Optical Networking (Springer, 1999) pp. 383-398.

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

P. Serena, A. Orlandini, A. Bononi, "Scaling laws for weakly-nonlinear WDM dispersion managed OOK systems," Proc. ECOC '06 (2006).

D. Zwillinger, Handbook of Differential Equations (Academic, 1997).

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers. Asymptotic Methods and Perturbation Theory (Springer-Verlag, 1999).

H. Louchet, K. Petermann, A. Robinson, R. Epworth, "Introduction to the concept of nonlinear diffusion bandwidth," Proc. ECOC '05 (2005).

R. A. Horn, C. R. Johnson, Matrix Analysis (Cambridge Univ. Press, 1999).

J.-C. Antona, S. Bigo, "Nonlinear cumulated phase as a criterion to assess performance of terrestrial WDM systems," Proc. OFC '02 (2002) pp. 365-367.

A. Cauvin, Y. Frignac, S. Bigo, "Single-channel nonlinear impairments at various bit-rate in dispersion-managed systems," Proc. ECOC '03 (2003).

Y. Frignac, J.-C. Antona, S. Bigo, J.-P. Hamaide, "Numerical optimization of pre- and in-line dispersion compensation in dispersion managed systems at 40 Gb/s," Proc. OFC '02 (2002) pp. 612-613.

Y. Frignac, J.-C. Antona, S. Bigo, "Enhanced analytical engineering rule for fast optimization of dispersion map in 40 Gbit/s-based transmission systems," Proc. OFC '04 (2004).

Y. Frignac, S. Bigo, "Numerical optimization of residual dispersion in dispersion-managed systems at 40 Gbit/s," Proc. OFC '00 (2000) pp. 48-50.

P. Serena, A. Orlandini, A. Bononi, "The memory of optimized dispersion-managed periodic optical links," Proc. ECOC '07 (2007).

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