Abstract

We discuss the application of importance-sampling techniques to the numerical simulation of transmission impairments induced by amplified spontaneous emission noise in soliton-based optical transmission systems. The method allows one to concentrate numerical simulations on the noise realizations that are most likely to result in transmission errors, thus leading to increases in speed of several orders of magnitude over standard Monte Carlo methods. We demonstrate the technique by calculating the probability distribution function of amplitude and timing fluctuations.

© 2003 Optical Society of America

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  1. D. Marcuse, J. Lightwave Technol. 9, 505 (1991).
    [CrossRef]
  2. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  3. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).
  4. E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).
  5. R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
    [CrossRef]
  6. C. R. Menyuk, Opt. Lett. 20, 270 (1995).
    [CrossRef]
  7. T. Georges, Opt. Commun. 123, 617 (1996).
    [CrossRef]
  8. G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
    [CrossRef]
  9. P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
    [CrossRef]
  10. G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
    [CrossRef]
  11. J. A. C. Weideman and B. M. Herbst, Math. Comp. Simul. 43, 77 (1997).
    [CrossRef]
  12. E. Veach, “Robust Monte Carlo methods for light transport simulation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1997).

2002 (2)

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

2001 (1)

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

1997 (2)

P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
[CrossRef]

J. A. C. Weideman and B. M. Herbst, Math. Comp. Simul. 43, 77 (1997).
[CrossRef]

1996 (1)

T. Georges, Opt. Commun. 123, 617 (1996).
[CrossRef]

1995 (1)

1991 (1)

D. Marcuse, J. Lightwave Technol. 9, 505 (1991).
[CrossRef]

1986 (1)

Biondini, G.

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Falkovich, G. E.

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

Gao, H.

P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
[CrossRef]

Georges, T.

T. Georges, Opt. Commun. 123, 617 (1996).
[CrossRef]

Gordon, J. P.

Grigoryan, V. S.

Hasegawa, A.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

Haus, H. A.

Herbst, B. M.

J. A. C. Weideman and B. M. Herbst, Math. Comp. Simul. 43, 77 (1997).
[CrossRef]

Holzlöhner, R.

Iannone, E.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Kath, W. L.

R. Holzlöhner, V. S. Grigoryan, C. R. Menyuk, and W. L. Kath, J. Lightwave Technol. 20, 389 (2002).
[CrossRef]

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

Kodama, Y.

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

Kolokolov, I.

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

Lebedev, V.

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

Marcuse, D.

D. Marcuse, J. Lightwave Technol. 9, 505 (1991).
[CrossRef]

Matera, F.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Mecozzi, A.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Menyuk, C. R.

Settembre, M.

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

Shafi, M.

P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
[CrossRef]

Smith, P. J.

P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
[CrossRef]

Turitsyn, S. K.

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

Veach, E.

E. Veach, “Robust Monte Carlo methods for light transport simulation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1997).

Weideman, J. A. C.

J. A. C. Weideman and B. M. Herbst, Math. Comp. Simul. 43, 77 (1997).
[CrossRef]

IEEE J. Sel. Areas Commun. (1)

P. J. Smith, M. Shafi, and H. Gao, IEEE J. Sel. Areas Commun. 15, 597 (1997).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

G. Biondini, W. L. Kath, and C. R. Menyuk, IEEE Photon. Technol. Lett. 14, 310 (2002).
[CrossRef]

J. Lightwave Technol. (2)

Math. Comp. Simul. (1)

J. A. C. Weideman and B. M. Herbst, Math. Comp. Simul. 43, 77 (1997).
[CrossRef]

Opt. Commun. (1)

T. Georges, Opt. Commun. 123, 617 (1996).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. E (1)

G. E. Falkovich, I. Kolokolov, V. Lebedev, and S. K. Turitsyn, Phys. Rev. E 63, 25601 (R) (2001).
[CrossRef]

Other (3)

A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

E. Iannone, F. Matera, A. Mecozzi, and M. Settembre, Nonlinear Optical Communication Networks (Wiley, New York, 1998).

E. Veach, “Robust Monte Carlo methods for light transport simulation,” Ph.D. dissertation (Stanford University, Stanford, Calif., 1997).

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Figures (1)

Fig. 1
Fig. 1

pdf of (a) timing and (b) amplitude jitter in a soliton-based transmission system, reconstructed from 50,000 importance-sampled Monte-Carlo simulations. A simple model from soliton perturbation theory provides the expected result in both cases. We provide a considerably larger unbiased Monte Carlo simulation and a Gaussian fit in the case of amplitude jitter to demonstrate the efficiency and accuracy of the biased simulation.

Equations (4)

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iuz+122ut2+u2u=0,
usz,t=A sechAt-T-Ωz×exp iΩt+A2-Ω2z/2+Φ,
P=1Mm=1MIymXm*rXm*,
wz=Lwi/2wtt+2ius2w+ius2w*,

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