Abstract

The amplification of wavelength division multiplexed (WDM) data in fiber-optical parametric amplifiers give rise to cross-gain saturation and four-wave mixing crosstalk. This crosstalk affects the data quality, especially at higher input powers. The statistics in this regime are nontrivial to obtain and we present, for the first time, a model based on a combination of theory and numerics that gives accurate statistics at a highly reduced computational cost. This model is obtained from an exact solution of WDM data being amplified in the strictly nonlinear regime which is derived in this paper. Using this model, predictions of the bit-error rate (BER) can be obtained even at very low rates impossible to reach by numerical methods alone. We show that there exists no trivial relationship between the BER and the commonly used quality measure, the Q-value. We also study how different amplifier parameters affect the statistics and suggest design rules to reduce channel crosstalk.

© 2008 IEEE

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  8. T. Torounidis, M. Karlsson, P. A. Andrekson, "Fiber optical parametric amplifier pulse source: Theory and experiments," IEEE Photon. Technol. Lett. 23, 4067-4073 (2005).
  9. Q. Lin, R. Jiang, C. F. Marki, C. J. McKinstrie, R. Jopson, J. Ford, G. P. Agrawal, S. Radic, "40-Gbs optical switching and wavelength multicasting in a two-pump parametric device," IEEE Photon. Technol. Lett. 17, 2376-2378 (2005).
  10. M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, "High-performance optical-fiber-nonlinearity-based optical waveform monitoring," J. Lightw. Technol. 23, 2012-2022 (2005).
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  12. P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Correction to noise characteristics of fiber optical parametric amplifiers," J. Lightw. Technol. 23, 2192 (2005).
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  24. P. Kylemark, J. Ren, M. Karlsson, S. Radic, C. J. McKinstrie, P. A. Andrekson, "Noise in dual-pumped fiber-optical parametric amplifiers: Theory and experiments," J. Lightw. Technol. 25, 2837-2846 (2007).
  25. R. M. Jopson, R. E. Tench, "Polarization-independent phase conjugation of lightwave signals," Electron. Lett. 29, 2216-2227 (1993).
  26. P. Kylemark, Noise and Saturation Properties of Fiber Optical Parametric Amplifiers (Chalmers Univ. of Technol., 2006).
  27. M. Matsumoto, "Performance improvement of phase-shift-keying signal transmission by means of optical limiters using four-wave mixing in fibers," J. Lightw. Technol. 23, 2696-2701 (2005).

2007

P. Kylemark, M. Karlsson, T. Torounidis, P. A. Andrekson, "Noise statistics in fiber optical parametric amplifiers," J. Lightw. Technol. 25, 612-620 (2007).

N. Alic, R. M. Jopson, J. Ren, E. Myslivets, R. Jiang, A. H. Gnauck, S. Radic, "Impairments in deeply-saturated optical parametric amplifiers for amplitude- and phase-modulated signals," Opt. Express 15, 8997-9008 (2007).

P. Kylemark, J. Ren, M. Karlsson, S. Radic, C. J. McKinstrie, P. A. Andrekson, "Noise in dual-pumped fiber-optical parametric amplifiers: Theory and experiments," J. Lightw. Technol. 25, 2837-2846 (2007).

J. M. C. Boggio, J. D. Marconi, S. R. Bickham, H. L. Fragnito, "Spectrally flat and broadband fiber optical parametric amplifiers," Opt. Express 15, 5288-5309 (2007).

2006

J. M. Chavez Boggio, J. D. Marconi, H. L. Fragnito, "Crosstalk in double-pumped fiber optic parametric amplifiers for wavelength division multiplexing systems," Opt. Commun. 259, 94-103 (2006).

P. Kylemark, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Semi-analytic saturation theory of fiber optical parametric amplifiers," J. Lightw. Technol. 24, 3471-3479 (2006).

2005

T. Torounidis, M. Karlsson, P. A. Andrekson, "Fiber optical parametric amplifier pulse source: Theory and experiments," IEEE Photon. Technol. Lett. 23, 4067-4073 (2005).

Q. Lin, R. Jiang, C. F. Marki, C. J. McKinstrie, R. Jopson, J. Ford, G. P. Agrawal, S. Radic, "40-Gbs optical switching and wavelength multicasting in a two-pump parametric device," IEEE Photon. Technol. Lett. 17, 2376-2378 (2005).

M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, "High-performance optical-fiber-nonlinearity-based optical waveform monitoring," J. Lightw. Technol. 23, 2012-2022 (2005).

P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Correction to noise characteristics of fiber optical parametric amplifiers," J. Lightw. Technol. 23, 2192 (2005).

A. Bogris, D. Syvridis, P. Kylemark, P. A. Andrekson, "Noise characteristics of dual-pump fiber-optic parametric amplifiers," J. Lightw. Technol. 23, 2788-2795 (2005).

M. Matsumoto, "Performance improvement of phase-shift-keying signal transmission by means of optical limiters using four-wave mixing in fibers," J. Lightw. Technol. 23, 2696-2701 (2005).

2004

2003

T. Torounidis, H. Sunnerud, P. O. Hedekvist, P. A. Andrekson, "Amplification of WDM signals in fiber-based optical parametric amplifiers," IEEE Photon. Technol. Lett. 15, 1061-1063 (2003).

2002

C. J. McKinstrie, S. Radic, A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8, 538-547 (2002).

C. J. McKinstrie, S. Radic, A. R. Chraplyvy, "Correction to parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8, 956 (2002).

2001

A. T. Clausen, L. Oxenlowe, C. Peucheret, H. N. Poulsen, P. Jeppesen, S. N. Knudsen, L. Gruner-Nielsen, "10-GHz return-to-zero pulse source tunable in wavelength with a single- or multiwavelength output based on four-wave mixing in a newly developed highly nonlinear fiber," IEEE Photon. Technol. Lett. 13, 70-72 (2001).

J. Hansryd, P. A. Andrekson, "Broad-band continuous-wave pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).

1993

R. M. Jopson, R. E. Tench, "Polarization-independent phase conjugation of lightwave signals," Electron. Lett. 29, 2216-2227 (1993).

1991

G. Cappellini, S. Trillo, "Third-order three-wave mixing in single-mode fibers: exact solution and spatial instability effects," J. Opt. Soc. Amer. B. 8, 824-838 (1991).

1990

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).

1982

R. H. Stolen, J. E. Bjorkholm, "Parametric amplificaton and frequency conversion in optical fibers," IEEE J. Quantum Electron. JQE-18, 1062-1072 (1982).

Electron. Lett.

R. M. Jopson, R. E. Tench, "Polarization-independent phase conjugation of lightwave signals," Electron. Lett. 29, 2216-2227 (1993).

IEEE J. Quantum Electron.

R. H. Stolen, J. E. Bjorkholm, "Parametric amplificaton and frequency conversion in optical fibers," IEEE J. Quantum Electron. JQE-18, 1062-1072 (1982).

IEEE J. Sel. Top. Quantum Electron.

C. J. McKinstrie, S. Radic, A. R. Chraplyvy, "Parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8, 538-547 (2002).

C. J. McKinstrie, S. Radic, A. R. Chraplyvy, "Correction to parametric amplifiers driven by two pump waves," IEEE J. Sel. Top. Quantum Electron. 8, 956 (2002).

IEEE Photon. Technol. Lett.

A. T. Clausen, L. Oxenlowe, C. Peucheret, H. N. Poulsen, P. Jeppesen, S. N. Knudsen, L. Gruner-Nielsen, "10-GHz return-to-zero pulse source tunable in wavelength with a single- or multiwavelength output based on four-wave mixing in a newly developed highly nonlinear fiber," IEEE Photon. Technol. Lett. 13, 70-72 (2001).

IEEE Photon. Technol. Lett.

J. Hansryd, P. A. Andrekson, "Broad-band continuous-wave pumped fiber optical parametric amplifier with 49-dB gain and wavelength-conversion efficiency," IEEE Photon. Technol. Lett. 13, 194-196 (2001).

T. Torounidis, H. Sunnerud, P. O. Hedekvist, P. A. Andrekson, "Amplification of WDM signals in fiber-based optical parametric amplifiers," IEEE Photon. Technol. Lett. 15, 1061-1063 (2003).

T. Torounidis, M. Karlsson, P. A. Andrekson, "Fiber optical parametric amplifier pulse source: Theory and experiments," IEEE Photon. Technol. Lett. 23, 4067-4073 (2005).

Q. Lin, R. Jiang, C. F. Marki, C. J. McKinstrie, R. Jopson, J. Ford, G. P. Agrawal, S. Radic, "40-Gbs optical switching and wavelength multicasting in a two-pump parametric device," IEEE Photon. Technol. Lett. 17, 2376-2378 (2005).

J. Lightw. Technol.

D. Marcuse, "Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers," J. Lightw. Technol. 8, 1816-1823 (1990).

J. Opt. Soc. Amer. B.

G. Cappellini, S. Trillo, "Third-order three-wave mixing in single-mode fibers: exact solution and spatial instability effects," J. Opt. Soc. Amer. B. 8, 824-838 (1991).

J. Lightw. Technol.

P. Kylemark, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Semi-analytic saturation theory of fiber optical parametric amplifiers," J. Lightw. Technol. 24, 3471-3479 (2006).

M. Westlund, P. A. Andrekson, H. Sunnerud, J. Hansryd, J. Li, "High-performance optical-fiber-nonlinearity-based optical waveform monitoring," J. Lightw. Technol. 23, 2012-2022 (2005).

P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Noise characteristics of fiber optical parametric amplifiers," J. Lightw. Technol. 22, 409-416 (2004).

P. Kylemark, P.-O. Hedekvist, H. Sunnerud, M. Karlsson, P. A. Andrekson, "Correction to noise characteristics of fiber optical parametric amplifiers," J. Lightw. Technol. 23, 2192 (2005).

A. Bogris, D. Syvridis, P. Kylemark, P. A. Andrekson, "Noise characteristics of dual-pump fiber-optic parametric amplifiers," J. Lightw. Technol. 23, 2788-2795 (2005).

P. Kylemark, M. Karlsson, T. Torounidis, P. A. Andrekson, "Noise statistics in fiber optical parametric amplifiers," J. Lightw. Technol. 25, 612-620 (2007).

P. Kylemark, J. Ren, M. Karlsson, S. Radic, C. J. McKinstrie, P. A. Andrekson, "Noise in dual-pumped fiber-optical parametric amplifiers: Theory and experiments," J. Lightw. Technol. 25, 2837-2846 (2007).

M. Matsumoto, "Performance improvement of phase-shift-keying signal transmission by means of optical limiters using four-wave mixing in fibers," J. Lightw. Technol. 23, 2696-2701 (2005).

Opt. Commun.

J. M. Chavez Boggio, J. D. Marconi, H. L. Fragnito, "Crosstalk in double-pumped fiber optic parametric amplifiers for wavelength division multiplexing systems," Opt. Commun. 259, 94-103 (2006).

Opt. Express

N. Alic, R. M. Jopson, J. Ren, E. Myslivets, R. Jiang, A. H. Gnauck, S. Radic, "Impairments in deeply-saturated optical parametric amplifiers for amplitude- and phase-modulated signals," Opt. Express 15, 8997-9008 (2007).

Opt. Express

Opt. Lett.

Other

P. Kylemark, Noise and Saturation Properties of Fiber Optical Parametric Amplifiers (Chalmers Univ. of Technol., 2006).

A. Leon Garcia, Probability and Random Processes for Electrical Engineering (Addison-Wesley, 1994).

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

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