Abstract

The asymptotic probability density of nonlinear phase noise, often called the Gordon–Mollenauer effect, is derived analytically when the number of fiber spans is large. Nonlinear phase noise is the summation of infinitely many independently distributed noncentral χ2 random variables with two degrees of freedom. The mean and the standard deviation of those random variables are both proportional to the square of the reciprocal of all odd natural numbers. Nonlinear phase noise can also be accurately modeled as the summation of a noncentral χ2 random variable with two degrees of freedom and a Gaussian random variable.

© 2003 Optical Society of America

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  1. J. P. Gordon and L. F. Mollenauer, Opt. Lett. 15, 1351 (1990).
    [CrossRef] [PubMed]
  2. S. Ryu, J. Lightwave Technol. 10, 1450 (1992).
    [CrossRef]
  3. A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
    [CrossRef]
  4. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
    [CrossRef]
  5. C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 956 (2002), erratum of Ref. .
  6. H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
    [CrossRef]
  7. A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.
  8. R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.
  9. B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.
  10. R. H. Cameron and W. T. Martin, Bull. Am. Math. Soc. 51, 73 (1945).
    [CrossRef]
  11. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).
  12. K.-P. Ho, “Probability density function of Kerr effect phase noise,” January 10, 2003, http://arxiv.org/abs/physics/0301018.
  13. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, San Diego, Calif., 1980).
  14. J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, New York, 2000).

2003 (1)

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

2002 (2)

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 956 (2002), erratum of Ref. .

2000 (1)

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, New York, 2000).

1994 (1)

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

1992 (1)

S. Ryu, J. Lightwave Technol. 10, 1450 (1992).
[CrossRef]

1990 (1)

1984 (1)

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).

1980 (1)

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, San Diego, Calif., 1980).

1945 (1)

R. H. Cameron and W. T. Martin, Bull. Am. Math. Soc. 51, 73 (1945).
[CrossRef]

Agrawal, A.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Banerjee, S.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Baynham, G.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Berry, K.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Cameron, R. H.

R. H. Cameron and W. T. Martin, Bull. Am. Math. Soc. 51, 73 (1945).
[CrossRef]

Carter, A. C.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Chandrasekhar, S.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Doerr, C.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Emori, Y.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Gaarde, P.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Gill, D. M.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Gnauck, A. H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Gordon, J. P.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, San Diego, Calif., 1980).

Griffin, R. A.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Grosz, D.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Gruner-Nielsen, L.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Hall, J.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Ho, K.-P.

K.-P. Ho, “Probability density function of Kerr effect phase noise,” January 10, 2003, http://arxiv.org/abs/physics/0301018.

Hunsche, S.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Jerram, P. A.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Johnstone, R. I.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Kado, S.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Kim, H.

H. Kim and A. H. Gnauck, IEEE Photon. Technol. Lett. 15, 320 (2003).
[CrossRef]

Knudsen, S.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Kung, A.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Leng, L.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Leuthold, J.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Lingle, R. L.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Liu, X.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Marhelyuk, A.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Martin, W. T.

R. H. Cameron and W. T. Martin, Bull. Am. Math. Soc. 51, 73 (1945).
[CrossRef]

Maymar, D.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

McKinstrie, C. J.

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 956 (2002), erratum of Ref. .

C. J. McKinstrie and C. Xie, IEEE J. Sel. Top. Quantum Electron. 8, 616 (2002).
[CrossRef]

Mecozzi, A.

A. Mecozzi, J. Lightwave Technol. 12, 1993 (1994).
[CrossRef]

Mollenauer, L. F.

Movassaghi, M.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Namiki, S.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Nelson, L. E.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, New York, 1984).

Parsons, N. J.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Peckham, D.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Pedersen, M. O.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Proakis, J. G.

J. G. Proakis, Digital Communications, 4th ed. (McGraw-Hill, New York, 2000).

Raybon, G.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Ryu, S.

S. Ryu, J. Lightwave Technol. 10, 1450 (1992).
[CrossRef]

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, San Diego, Calif., 1980).

Stulz, L.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Stulz, S.

B. Zhu, L. Leng, A. H. Gnauck, M. O. Pedersen, D. Peckham, L. E. Nelson, S. Stulz, S. Kado, L. Gruner-Nielsen, R. L. Lingle, S. Knudsen, J. Leuthold, C. Doerr, S. Chandrasekhar, G. Baynham, P. Gaarde, Y. Emori, and S. Namiki, presented at the European Conference on Optical Communication, September 8–12, Copenhagen, Denmark.

Wadsworth, S. D.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Wale, M. J.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Walker, R. G.

R. A. Griffin, R. I. Johnstone, R. G. Walker, J. Hall, S. D. Wadsworth, K. Berry, A. C. Carter, M. J. Wale, P. A. Jerram, and N. J. Parsons, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FD6.

Wei, X.

A. H. Gnauck, G. Raybon, S. Chandrasekhar, J. Leuthold, C. Doerr, L. Stulz, A. Agrawal, S. Banerjee, D. Grosz, S. Hunsche, A. Kung, A. Marhelyuk, D. Maymar, M. Movassaghi, X. Liu, C. Xu, X. Wei, and D. M. Gill, in Optical Fabrication and Testing '02, Vol. 70 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2002), postdeadline paper FC2.

Xie, C.

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Figures (3)

Fig. 1
Fig. 1

p.d.f. of normalized nonlinear phase noise ϕ for SNRs ρ2 of 11, 18, 25: lin., linear.

Fig. 2
Fig. 2

Cumulative tail probabilities as functions of the Q factor.

Fig. 3
Fig. 3

Asymptotic p.d.f. of ϕ compared with the p.d.f.s of N=4,8,16,32,64 fiber spans. The p.d.f. is shown in the inset on a linear scale.

Equations (14)

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ϕNL= γLeffA+n12+A+n1+n22++A+n1++nN2,
ϕNL=κ0LA+Sz2dz,
ϕ=01ρ+bt2dt,
Rbt,s=Ebsb*t=mint,s.
bt=k=1σkxkψkt,
σk=22k-1π,    ψkt=2 sin2k-1π2t.
ϕ=ρ2+22ρk=1σk2Rxk+k=1σk2xk2,
ϕ=k=1σk22ρ+xk2.
Ψ2ρ+xk2jν=11-jν exp2jνρ21-jν.
Ψϕjν=k=111-jνσk2 exp2jνρ2σk21-jνσk2.
Ψϕjν=secjνexpρ2jν tanjν.
σ12σ22+σ32+=2/π21/2-2/π2=4.27,
σ14σ24+σ34+=2/π41/6-2/π4=68.12.
Ψϕjν 11-4jν/π2 exp8jνρ2/π21-4jν/π2×expjν2ρ2+112-4π2-12ν24ρ2+116-16π4

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