Abstract

The effect of delayed Raman response on soliton collisions in wavelength division multiplexing (WDM) transmission systems is investigated. Taking into account the stochastic nature of pulse sequences in different frequency channels and the Raman-induced cross talk, it is shown that the soliton amplitude is a random variable with a log-normal distribution. Moreover, the Raman-induced self-frequency shift and cross-frequency shift are also random variables with log-normal-like distributions. These results imply that fluctuations in soliton amplitude and frequency induced by soliton collisions in the presence of delayed Raman response play an important role in massive WDM transmission.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Hasegawa and Y. Kodama, Solitons in Optical Communications (Clarendon, Oxford, 1995).
  2. F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  3. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  4. S. Chi and S. Wen, Opt. Lett. 14, 1216 (1989).
    [CrossRef] [PubMed]
  5. B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
    [CrossRef] [PubMed]
  6. S. Kumar, Opt. Lett. 23, 1450 (1998).
    [CrossRef]
  7. T. L. Lakoba and D. J. Kaup, Opt. Lett. 24, 808 (1999).
    [CrossRef]
  8. The dimensionless z in Eq. (1) is z=β2x/2τ0, where x is the actual position, τ0 is the soliton width, and β2 is the second-order dispersion coefficient. The dimensionless retarded time is t=τ/τ0, where τ is the retarded time. The spectral width is ν0=1/π2τ0, and the channel spacing is Δν=πΩν0/2. The dimensionless Raman coefficient is ∊R=0.00594/τ0, where τ0 is in picoseconds.
  9. A. Peleg, M. Chertkov, and I. Gabitov, J. Opt. Soc. Am. B 21, 18 (2004).
    [CrossRef]
  10. J. N. Elgin, Phys. Lett. A 110, 441 (1985).
    [CrossRef]
  11. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  12. E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
    [CrossRef]
  13. L. F. Mollenauer and P. V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998).
    [CrossRef]

2004 (1)

1999 (1)

1998 (2)

S. Kumar, Opt. Lett. 23, 1450 (1998).
[CrossRef]

L. F. Mollenauer and P. V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

1992 (1)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

1991 (1)

B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
[CrossRef] [PubMed]

1989 (1)

1986 (3)

1985 (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Chertkov, M.

Chi, S.

Dianov, E. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Elgin, J. N.

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Gabitov, I.

Gordon, J. P.

Hasegawa, A.

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

Haus, H. A.

Kaup, D. J.

Kodama, Y.

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

Kumar, S.

Lakoba, T. L.

Luchnikov, A. V.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Malomed, B. A.

B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
[CrossRef] [PubMed]

Mamyshev, P. V.

L. F. Mollenauer and P. V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

L. F. Mollenauer and P. V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

F. M. Mitschke and L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
[CrossRef] [PubMed]

Peleg, A.

Pilipetskii, A. N.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Prokhorov, A. M.

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

Wen, S.

Appl. Phys. B (1)

E. M. Dianov, A. V. Luchnikov, A. N. Pilipetskii, and A. M. Prokhorov, Appl. Phys. B 54, 175 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

L. F. Mollenauer and P. V. Mamyshev, IEEE J. Quantum Electron. 34, 2089 (1998).
[CrossRef]

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

Opt. Lett. (6)

Phys. Lett. A (1)

J. N. Elgin, Phys. Lett. A 110, 441 (1985).
[CrossRef]

Phys. Rev. A (1)

B. A. Malomed, Phys. Rev. A 44, 1412 (1991).
[CrossRef] [PubMed]

Other (2)

The dimensionless z in Eq. (1) is z=β2x/2τ0, where x is the actual position, τ0 is the soliton width, and β2 is the second-order dispersion coefficient. The dimensionless retarded time is t=τ/τ0, where τ is the retarded time. The spectral width is ν0=1/π2τ0, and the channel spacing is Δν=πΩν0/2. The dimensionless Raman coefficient is ∊R=0.00594/τ0, where τ0 is in picoseconds.

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Probability of observing values of η0, which are larger than or equal to η0th=2, as a function of disorder strength D. The solid curve is the result Prη0η0th [Eq. (7)], which is based on the accurate log-normal statistics of η0. The dashed curve is the result PrGη0η0th [Eq. (8)], which is based on a Gaussian approximation for the statistics of η0.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

izΨ+t2Ψ+2Ψ2Ψ=-RΨtΨ2.
Δη0=2η0ηΩ sgnΩR.
ΔΩ0=-4η02ηΩΩ-1R.
Δη0Δzcz=zi=2 sgnΩRη0zi-1ζ˜iΔzc,
η0z=exp2 sgnΩR0zdzξz,
Fη0=πD-1/2η0-1 exp-ln2η0/D,
Prη0η0thD4πln η0th21/2 exp-ln2 η0thD,
PrGη0η0thD4πη0th-121/2×exp-η0th-12D.
R0sz=dΩ0s/dz=-8Rη04z/15,
dΩ0c/dz=-4RξzΩ-1η02z.
GΩ0c=exp-ln21-ΩΩ0c/4D4πD1/2Ω0c-1/Ω.
Δη0Δzc1z=zi=2Rη0zi-1Δzc1k0 sgnΩkm=ki-1+1kiζ˜mk,
ξKz=1Δzc1k0 sgnΩkm=ki-1+1kiζ˜mk.

Metrics