Abstract

In optical fiber transmission systems using inline amplifiers, the interaction of a signal and an amplifier noise through the Kerr effect leads to a nonlinear phase noise that can impair detection of phase-modulated signals. The authors show how to minimize the variance of the total phase noise (linear plus nonlinear) by a choice of the number of inline amplifiers N and their spacings and gains, assuming a fixed total system length L and an overall compensation of the fiber loss. In the case of a uniform amplifier spacing and a per-span loss compensation, there exists a finite N that minimizes the total phase noise. This contrasts with the well-known observation that a linear phase noise alone is minimized by a choice of an infinite N. Relaxing the constraints of the uniform spacing and/or the per-span loss compensation leads to further reduction of the total phase noise. The optimization of the spacings and the gains can be approximately formulated as a convex problem. In typical terrestrial and transoceanic systems, the total-phase-noise variance can be reduced by up to 45% and 83%.

© 2006 IEEE

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  1. J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett., vol. 15, no. 23, pp. 1351-1353, Dec. 1990.
  2. A. H. Gnauck, et al. "2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Rama-amplified spans," presented at the Optical Fiber Communication (OFC), San Jose, CA, Postdeadline Paper FC2, 2002.
  3. R. A. Griffin, et al. "10 Gb/s optical differential quadrature phase shift keying (DQPSK) transmission using GaAs/AlGaAs integration," presented at the Optical Fiber Communication (OFC), San Jose, CA, Postdeadline Paper FD6, 2002.
  4. B. Zhu, et al. "Transmission of 3.2 Tb/s (80 × 42.7 Gb/s) over 5200 km of UltraWave fiber with 100-km dispersion-managed spans using RZ-DPSK format," presented at the Eur. Conf. Optical Communication (ECOC), Copenhagen, Denmark,Postdeadline Paper PD4.2, 2003.
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  7. A. Mecozzi, "On the optimization of the gain distribution of transmission lines with unequal amplifier spacing," IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 1033-1035, Jul. 1998.
  8. S. K. Turitsyn, M. P. Fedoruk, V. K. Mezentsev and E. G. Turitsyna, "Theory of optimal power budget in quasi-linear dispersion-managed fibre links," Electron. Lett., vol. 39, no. 1, pp. 29-30, Jan. 2003.
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  13. C. Xu and X. Liu, "Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett., vol. 27, no. 18, pp. 1619-1621, Sep. 2002.
  14. K.-P. Ho and J. M. Kahn, "Detection Technique to Mitigate Kerr Effect Phase Noise,"
  15. G. P. Agrawal, Fiber-Optic Communication Systems, New York: Wiley, 2002.
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  17. K. P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 20, no. 9, pp. 1875-1879, Sep. 2003.
  18. M. Norgia, G. Giuliani and S. Donati, "Noise evolution along optically amplified links in presence of nonlinear parametric gain," J. Lightw. Technol., vol. 17, no. 10, pp. 1750-1757, Oct. 1999.
  19. E. Lichtman, "Optimal amplifier spacing in ultralong lightwave systems," Electron. Lett., vol. 29, no. 23, pp. 2058-2060, Nov. 1993.
  20. J. D. Ania-Castañòn, I. O. Nasieva, S. K. Turitsyn, N. Brochier and E. Pincemin, "Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification," Opt. Lett., vol. 30, no. 1, pp. 23-25, Jan. 2005.
  21. J. P. Gordon and L. F. Mollenauer, "Effects of fiber nonlinearities and amplifier spacing on ultra-long distance transmission," J. Lightw. Technol., vol. 9, no. 2, pp. 170-173, Feb. 1991.
  22. A. Yariv, "Signal-to-noise considerations in fiber links with periodic or distributed optical amplification," Opt. Lett., vol. 15, no. 19, pp. 1064-1066, Oct. 1990.
  23. E. Desurvire, Erbium-Doped Fiber Amplifiers, Device and System Developments, New York: Wiley, 2002.
  24. S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge: U.K.: Cambridge Univ. Press, 2004.

Other (24)

J. P. Gordon and L. F. Mollenauer, "Phase noise in photonic communications systems using linear amplifiers," Opt. Lett., vol. 15, no. 23, pp. 1351-1353, Dec. 1990.

A. H. Gnauck, et al. "2.5 Tb/s (64 × 42.7 Gb/s) transmission over 40 × 100 km NZDSF using RZ-DPSK format and all-Rama-amplified spans," presented at the Optical Fiber Communication (OFC), San Jose, CA, Postdeadline Paper FC2, 2002.

R. A. Griffin, et al. "10 Gb/s optical differential quadrature phase shift keying (DQPSK) transmission using GaAs/AlGaAs integration," presented at the Optical Fiber Communication (OFC), San Jose, CA, Postdeadline Paper FD6, 2002.

B. Zhu, et al. "Transmission of 3.2 Tb/s (80 × 42.7 Gb/s) over 5200 km of UltraWave fiber with 100-km dispersion-managed spans using RZ-DPSK format," presented at the Eur. Conf. Optical Communication (ECOC), Copenhagen, Denmark,Postdeadline Paper PD4.2, 2003.

A. Mecozzi, "Long-distance transmission at zero dispersion: Combined effect of the Kerr nonlinearity and the noise of the in-line amplifiers," J. Opt. Soc. Amer. B, Opt. Phys., vol. 11, no. 3, pp. 462-469, Mar. 1994.

A. R. Charplyvy, "Limitations on lightwave communications imposed by optical-fiber nonlinearities," J. Lightw. Technol., vol. 8, no. 10, pp. 1548-1557, Oct. 1990.

A. Mecozzi, "On the optimization of the gain distribution of transmission lines with unequal amplifier spacing," IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 1033-1035, Jul. 1998.

S. K. Turitsyn, M. P. Fedoruk, V. K. Mezentsev and E. G. Turitsyna, "Theory of optimal power budget in quasi-linear dispersion-managed fibre links," Electron. Lett., vol. 39, no. 1, pp. 29-30, Jan. 2003.

I. Nasieva, J. D. Ania-Castanon and S. K. Turitsyn, "Nonlinearity management in fibre links with distributed amplification," Electron. Lett., vol. 39, no. 11, pp. 856-857, May 2003.

K. P. Ho, "Mid-span compensation of nonlinear phase noise," Opt. Commun., vol. 245, no. 1-6, pp. 391-398, Jan. 2005.

K.-P. Ho, "Statistical properties of nonlinear phase noise," in Advances in Optics and Laser Research, W. T. Arkin, Ed. Hauppauge, NY: Nova Science, 2003,vol. 3.

X. Liu, X. Wei, R. E. Slusher and C. J. McKinstrie, "Improving transmission performance in differential phase-shift-keyed systems by use of lumped nonlinear phase-shift compensation," Opt. Lett., vol. 27, no. 18, pp. 1616-1618, Sep. 2002.

C. Xu and X. Liu, "Postnonlinearity compensation with data-driven phase modulators in phase-shift keying transmission," Opt. Lett., vol. 27, no. 18, pp. 1619-1621, Sep. 2002.

K.-P. Ho and J. M. Kahn, "Detection Technique to Mitigate Kerr Effect Phase Noise,"

G. P. Agrawal, Fiber-Optic Communication Systems, New York: Wiley, 2002.

K. P. Ho, "Impact of nonlinear phase noise to DPSK signals: A comparison of different models," IEEE Photon. Technol. Lett., vol. 16, no. 5, pp. 1403-1405, May 2004.

K. P. Ho, "Probability density of nonlinear phase noise," J. Opt. Soc. Amer. A, Opt. Image Sci., vol. 20, no. 9, pp. 1875-1879, Sep. 2003.

M. Norgia, G. Giuliani and S. Donati, "Noise evolution along optically amplified links in presence of nonlinear parametric gain," J. Lightw. Technol., vol. 17, no. 10, pp. 1750-1757, Oct. 1999.

E. Lichtman, "Optimal amplifier spacing in ultralong lightwave systems," Electron. Lett., vol. 29, no. 23, pp. 2058-2060, Nov. 1993.

J. D. Ania-Castañòn, I. O. Nasieva, S. K. Turitsyn, N. Brochier and E. Pincemin, "Optimal span length in high-speed transmission systems with hybrid Raman-erbium-doped fiber amplification," Opt. Lett., vol. 30, no. 1, pp. 23-25, Jan. 2005.

J. P. Gordon and L. F. Mollenauer, "Effects of fiber nonlinearities and amplifier spacing on ultra-long distance transmission," J. Lightw. Technol., vol. 9, no. 2, pp. 170-173, Feb. 1991.

A. Yariv, "Signal-to-noise considerations in fiber links with periodic or distributed optical amplification," Opt. Lett., vol. 15, no. 19, pp. 1064-1066, Oct. 1990.

E. Desurvire, Erbium-Doped Fiber Amplifiers, Device and System Developments, New York: Wiley, 2002.

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge: U.K.: Cambridge Univ. Press, 2004.

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