Abstract

An efficient numerical algorithm is presented for massively parallel simulations of dispersion-managed wavelength-division-multiplexed optical fiber systems. The algorithm is based on a weak nonlinearity approximation and independent parallel calculations of fast Fourier transforms on multiple central processor units (CPUs). The algorithm allows one to implement numerical simulations M/2 times faster than a direct numerical simulation by a split-step method, where M is a number of CPUs in a parallel network.

© 2002 Optical Society of America

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References

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  1. F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  5. A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
    [CrossRef]
  6. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
    [CrossRef]
  7. I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
    [CrossRef]
  8. I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861 (1996).
    [CrossRef]
  9. P. M. Lushnikov, Opt. Lett. 26, 1535 (2001).
    [CrossRef]

2001 (1)

2000 (1)

1999 (1)

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

1996 (3)

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef]

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861 (1996).
[CrossRef]

1993 (2)

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

1980 (1)

Audouin, O.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Bennion, I.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Biotteau, B.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Blow, K. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Chraplyvy, A. R.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

Cohen, L. G.

Derosier, R. M.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

Desurvire, E.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Doran, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Favre, F.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Gabitov, I.

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861 (1996).
[CrossRef]

Gabitov, I. R.

Georges, T.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Gnauck, A. H.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

Gripp, J.

Grüner-Nielsen, L.

Hamaide, J.-P.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Knox, F. M.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Kogelnik, H.

Kurtzke, C.

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

Le Lourec, P.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Lin, C.

Lushnikov, P. M.

Mamyshev, P. V.

Mamysheva, N.

Mollenauer, L. F.

Neddam, F.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Neubelt, M. J.

Pinceman, E.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Poignant, P.

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

Smith, N. J.

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

Tkach, R. W.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

Turitsyn, S. K.

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861 (1996).
[CrossRef]

I. R. Gabitov and S. K. Turitsyn, Opt. Lett. 21, 327 (1996).
[CrossRef]

Veng, T.

Electron. Lett. (2)

F. Neddam, P. Le Lourec, B. Biotteau, P. Poignant, E. Pinceman, J.-P. Hamaide, O. Audouin, E. Desurvire, T. Georges, and F. Favre, Electron. Lett. 35, 1093 (1999).
[CrossRef]

N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett. 32, 54 (1996).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, and R. M. Derosier, IEEE Photon. Technol. Lett. 5, 1233 (1993).
[CrossRef]

JETP Lett. (1)

I. Gabitov and S. K. Turitsyn, JETP Lett. 63, 861 (1996).
[CrossRef]

Opt. Lett. (4)

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Figures (2)

Fig. 1
Fig. 1

Schematic of parallel computation algorithm and required number of numerical steps. FFT1, FFT2, represent fast Fourier transforms in the first CPU, second CPU, etc., respectively. The right-hand side shows schematically calculation of vectors bm (see text).

Fig. 2
Fig. 2

Power distributions of five WDM channels after propagation of pseudo-random sequences of Gaussian pulses over 104 km. Only a small part of the total computational interval of 1000 ps is shown.

Equations (9)

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

iAz-12β2zAtt-i6β3zAttt+σzA2A=iGzA,
iuz-12β2zutt-i6β3zuttt+czu2u=0,
ψ^ω,z=ψ^ω,z0+iRψ^ω,z,ω,z,z0,
Rvˆω,z,ω,z,z0=12π2dω1dω2dω3z0zdz×czvˆzω1,zvˆzω2,zvˆ*zω3,zexp-iβz×δω1+ω2-ω-ω3,  vˆzω,zvˆω,zexpiβz.
ψˆω,m+1L=ψˆω,mL+iRψˆω,mL,ω,m+1L,mL+OL/znl2.
ψˆω,m+1L=ψˆω,mL+iRψˆ1ω,z,ω,z,mL+OL/znl3,
ψˆ1ω,zψˆω,mL+iRψˆω,mL,ω,z,mL.
F^-1Rv^ω,ω,z,mL=mLzdzczGzVzt,z,
N4 Log2N+Log2M+Log2MLog2M+1/2N4 Log2N+Log2M22.

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