Abstract

An asymptotic method for calculating the collision-induced frequency and timing shifts for quasi-linear pulses in return-to-zero, wavelength-division multiplexed systems with predispersion and postdispersion compensation is developed. Predictions of the asymptotic theory agree well with quadrature and direct numerical simulations. Using this theory, computational savings of many orders of magnitude can be realized over direct numerical simulations.

© 2006 Optical Society of America

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References

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  1. X. Liu, X. Wei, L. Mollenauer, C. J. McKinstrie, and C. Xie, Opt. Lett. 28, 1412 (2003).
    [CrossRef] [PubMed]
  2. L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).
  3. V. S. Grigoryan and A. Richter, J. Catal. 18, 1148 (2000).
  4. M. J. Ablowitz, A. Docherty, and T. Hirooka, Opt. Lett. 28, 1191 (2003).
    [CrossRef] [PubMed]
  5. A. Docherty, "Collision-induced timing shifts in wavelength-division-multiplexed optical fiber com-munication systems," Ph.D. dissertation (University of New South Wales, Sydney, Australia, 2004).
  6. O. V. Sinkin, V. S. Grigoryan, J. Zweck, C. R. Menyuk, A. Docherty, and M. J. Ablowitz, Opt. Lett. 30, 2056 (2005).
    [CrossRef] [PubMed]
  7. M. J. Ablowitz and G. Biondini, Opt. Lett. 23, 1668 (1998).
    [CrossRef]
  8. M. J. Ablowitz, T. Hirooka, and G. Biondini, Opt. Lett. 26, 459 (2001).
    [CrossRef]
  9. M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, 2nd ed. (Cambridge U. Press, 2003).
    [CrossRef]

2005

2003

2001

2000

V. S. Grigoryan and A. Richter, J. Catal. 18, 1148 (2000).

1998

1991

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).

Ablowitz, M. J.

Biondini, G.

Docherty, A.

O. V. Sinkin, V. S. Grigoryan, J. Zweck, C. R. Menyuk, A. Docherty, and M. J. Ablowitz, Opt. Lett. 30, 2056 (2005).
[CrossRef] [PubMed]

M. J. Ablowitz, A. Docherty, and T. Hirooka, Opt. Lett. 28, 1191 (2003).
[CrossRef] [PubMed]

A. Docherty, "Collision-induced timing shifts in wavelength-division-multiplexed optical fiber com-munication systems," Ph.D. dissertation (University of New South Wales, Sydney, Australia, 2004).

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).

Fokas, A. S.

M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, 2nd ed. (Cambridge U. Press, 2003).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).

Grigoryan, V. S.

Hirooka, T.

Liu, X.

McKinstrie, C. J.

Menyuk, C. R.

Mollenauer, L.

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).

Richter, A.

V. S. Grigoryan and A. Richter, J. Catal. 18, 1148 (2000).

Sinkin, O. V.

Wei, X.

Xie, C.

Zweck, J.

J. Catal.

V. S. Grigoryan and A. Richter, J. Catal. 18, 1148 (2000).

J. Low Temp. Phys.

L. F. Mollenauer, S. G. Evangelides, and J. P. Gordon, J. Low Temp. Phys. 9, 362 (1991).

Opt. Lett.

Other

A. Docherty, "Collision-induced timing shifts in wavelength-division-multiplexed optical fiber com-munication systems," Ph.D. dissertation (University of New South Wales, Sydney, Australia, 2004).

M. J. Ablowitz and A. S. Fokas, Complex Variables: Introduction and Applications, 2nd ed. (Cambridge U. Press, 2003).
[CrossRef]

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Figures (1)

Fig. 1
Fig. 1

Total timing shift versus mean collision location z 0 obtained from DNSs of the PNLS equation, numerical integration of Eqs. (3), and asymptotic approximation of Eqs. (3), i.e., using Eqs. (4). Shown are two channels: Ω 0 and 2 Ω 0 .

Equations (7)

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u ± ( z , t ) = α 2 π ( β + i D ̃ ) exp [ ( t t 0 ± Ω D ̃ ) 2 2 ( β + i D ̃ ) ± i Ω t ( i 2 ) Ω 2 D ̃ ] .
Δ Ω ( L + Δ L post ) = A Ω 0 0 L + Δ L post g D ̃ 0 exp [ 2 β Ω 0 2 D ̃ 0 2 ( β 2 + D ̃ 2 ) ] ( β 2 + D ̃ 2 ) 3 2 d z ,
Δ t ( L + Δ L post ) = D ̃ 0 ( L + Δ L post ) Δ Ω ( L + Δ L post ) Δ t res ,
Δ t res ( L + Δ L post ) = A Ω 0 0 L + Δ L post g D ̃ 0 2 exp [ 2 β Ω 0 2 D ̃ 0 2 ( β 2 + D ̃ 2 ) ] ( β 2 + D ̃ 2 ) 3 2 d z .
Δ Ω n + A F n J 1 , n β ϕ n Ω 0 + 3 A F n ϕ n J 2 , n 2 A F n ϕ n J 4 , n 6 β 3 2 ( ϕ n ) 5 2 Ω 0 2 ,
Δ Ω ( L + Δ L post ) A β Ω 0 n = 1 N c [ F n J 1 , n ϕ n + F n ϕ n J 2 , n 2 β 1 2 Ω 0 ( ϕ n ) 5 2 F n ϕ n J 4 , n 3 β 1 2 Ω 0 ( ϕ n ) 5 2 ] + Δ Ω ( p.c. ) ,
Δ t res ( L + Δ L post ) A 2 β 3 2 Ω 0 2 n = 1 N c F n J 2 , n ( ϕ n ) 3 2 + Δ t res ( p.c. ) ,

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