Abstract

This paper investigates the evolution of kurtosis of the input Gaussian amplified spontaneous emission (ASE) noise in a nonlinear fiber with negligible dispersion. The nonlinear Schrodinger equation (NLSE) describing propagation in optical fibers is simplified such that the fiber represents a zero memory nonlinear (ZMNL) system, and this approximation allows the development of analytical formulas for the statistical moments of the output noise. It is possible to calculate moments of all integer orders and the explicit expressions for the first four moments are given. The investigations show that the ASE noise does not preserve its Gaussian character when Kerr nonlinearity is significant. This observation proves that the common assumption of the Gaussian output ASE is not necessarily valid. Numerical simulations are provided to support the derivation. Kurtosis deviating significantly from the value typical for Gaussian noise is also an indicator that BER calculation in the coherent systems based on the assumption that ASE is Gaussian is likely to be inaccurate.

© 2008 IEEE

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2007 (2)

J. Hongo, K. Kasai, M. Yoshida, M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).

E. Vanin, G. Jacobsen, A. Berntson, "Nonlinear phase noise separation method for on-off keying transmission system modeling with non-Gaussian noise generation in optical fibers," Opt. Lett. 32, 1740-1742 (2007).

2006 (3)

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, K. Kikuchi, "Bismuth-oxide-based nonlinear fiber with a high SBS threshold and its application to four wave-mixing wavelength conversion using a pure continuous wave pump," J. Lightw. Technol. 24, 22-28 (2006).

S. Watanabe, "Optical signal processing using nonlinear fibers," J. Opt. Fiber Commun. Rep. 3, 1-24 (2006).

S. Camatel, V. Ferrero, "Homodyne coherent detection of ASK and PSK signals performed by a subcarrier optical phase-locked loop," IEEE Photon. Technol. Lett. 18, 142-144 (2006).

2004 (3)

J. Wang, J. M. Kahn, "Accurate bit-error-ratio computation in nonlinear CRZ-OOK and CRZ-DPSK systems," IEEE Photon. Technol. Lett. 16, 2165-2167 (2004).

K. Kikuchi, K. Taira, T. Tanemura, "All-optical signal processing using nonlinear fibers," Proc. SPIE Active and Passive Optical Components for WDM Communications IV 291-301 (2004).

A. Mecozzi, "Probability density functions of the nonlinear phase noise," Opt. Lett. 29, 673-675 (2004).

2003 (2)

K.-P. Ho, "Performance degradation of phase-modulated systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 1213-1215 (2003).

K.-P. Ho, "Asymptotic probability density of nonlinear phase noise," Opt. Lett. 28, 1350-1352 (2003).

2002 (1)

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

2000 (1)

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical method for the BER evaluation in optical systems affected by parametric gain," IEEE Photon. Technol. Lett. 12, 152-154 (2000).

1994 (2)

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

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. Am. B 11, 462-469 (1994).

1990 (1)

IEEE Photon. Technol. Lett. (1)

J. Hongo, K. Kasai, M. Yoshida, M. Nakazawa, "1-Gsymbol/s 64-QAM coherent optical transmission over 150 km," IEEE Photon. Technol. Lett. 19, 638-640 (2007).

IEEE Photon. Technol. Lett. (2)

K.-P. Ho, "Performance degradation of phase-modulated systems due to nonlinear phase noise," IEEE Photon. Technol. Lett. 15, 1213-1215 (2003).

J. Wang, J. M. Kahn, "Accurate bit-error-ratio computation in nonlinear CRZ-OOK and CRZ-DPSK systems," IEEE Photon. Technol. Lett. 16, 2165-2167 (2004).

IEEE Photon. Technol. Lett. (2)

S. Camatel, V. Ferrero, "Homodyne coherent detection of ASK and PSK signals performed by a subcarrier optical phase-locked loop," IEEE Photon. Technol. Lett. 18, 142-144 (2006).

G. Bosco, A. Carena, V. Curri, R. Gaudino, P. Poggiolini, S. Benedetto, "A novel analytical method for the BER evaluation in optical systems affected by parametric gain," IEEE Photon. Technol. Lett. 12, 152-154 (2000).

J. Lightw. Technol. (3)

J. H. Lee, T. Nagashima, T. Hasegawa, S. Ohara, N. Sugimoto, K. Kikuchi, "Bismuth-oxide-based nonlinear fiber with a high SBS threshold and its application to four wave-mixing wavelength conversion using a pure continuous wave pump," J. Lightw. Technol. 24, 22-28 (2006).

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

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

J. Opt. Fiber Commun. Rep. (1)

S. Watanabe, "Optical signal processing using nonlinear fibers," J. Opt. Fiber Commun. Rep. 3, 1-24 (2006).

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

Opt. Lett. (4)

Proc. SPIE Active and Passive Optical Components for WDM Communications IV (1)

K. Kikuchi, K. Taira, T. Tanemura, "All-optical signal processing using nonlinear fibers," Proc. SPIE Active and Passive Optical Components for WDM Communications IV 291-301 (2004).

Other (8)

J. W. Goodman, Statistical Optics (Wiley, 2000).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, 2000).

M. Abramowitz, I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (Dover, 1972).

A. Stuart, J. K. Ord, Kendall's Advanced Theory of Statistics (Charles Griffin & Co., 1987).

E. Vanin, G. Jacobsen, A. Berntson, "Correlated noise generation in high-speed transmission fiber links," Proc. 12th Eur. Conf. Netw. Opt. Commun. NOC (2007) pp. 184-191.

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

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2007).

S. Primak, V. Kontorovitch, V. Lyandres, Stochastic Methods and their Applications to Communications (Wiley, 2005).

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