Abstract

Nonlinear intrachannel interactions responsible for timing shifts in a transmission system with strong periodic dispersion management are investigated. Formulas describing the evolution of the timing shift are obtained for general bit patterns. When average dispersion is negligible, the timing shift is shown to grow linearly in distance in a system with loss and lumped amplification, whereas in a lossless system the timing shift is sufficiently small at every chirp-free point. The analysis agrees with direct numerical simulations.

© 2001 Optical Society of America

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References

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    [CrossRef]
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  5. R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
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  6. P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
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2001 (2)

2000 (1)

1999 (2)

R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

P. V. Mamyshev and N. A. Mamysheva, Opt. Lett. 24, 1454 (1999).
[CrossRef]

1995 (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

1993 (1)

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

Ablowitz, M. J.

Abramov, A. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Anderson, D.

Bergano, N. S.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Berntson, A.

Biondini, G.

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Corbett, P. C.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Danielsson, A.

Darcie, J. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Davidson, C. R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Essiambre, R. J.

R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Evangelides, S. G.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Golovchenko, E.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Hirooka, T.

Johannisson, P.

Kidorf, H. D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Kurtzke, C.

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

Lisak, M.

Ma, M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Mamyshev, P. V.

Mamysheva, N. A.

Martensson, J.

Menges, R.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Mikkelsen, B.

R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Mills, M. A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Peckham, D.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Pedersen, B.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Pillipetskii, A.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Raybon, G.

R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

Rottwitt, K.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Vengsarkar, A. M.

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

Westlund, M.

Electron. Lett. (1)

R. J. Essiambre, B. Mikkelsen, and G. Raybon, Electron. Lett. 35, 1576 (1999).
[CrossRef]

IEEE J. Lightwave Technol. (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, and R. M. Derosier, IEEE J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

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

Opt. Lett. (4)

Other (1)

N. S. Bergano, C. R. Davidson, M. Ma, A. Pillipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar, in Optical Fiber Communication Conference (OFC), Vol. 2 of 1998 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1998), postdeadline paper PD12.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of a two-step dispersion map.

Fig. 2
Fig. 2

Growth of timing shifts of the signals centered at t=-TΔt-1, t=0Δt0, and t=2TΔt2 in a 1 1 0 1 bit pattern in a lossy case Γ=10. The solid lines are the results of direct numerical simulation of Eq.  (1), and the dashed lines are the results obtained from Eq.  (8) with Eqs.  (12) and (13). The dotted curve shows the timing shift, Δt-1, when G=0 is obtained from direct numerical simulation.

Fig. 3
Fig. 3

Growth rate of the timing shift versus map strength s for m-n=-1,1, 2, calculated from Eq.  (12) with Eq.  (13) (solid curves) and with approximation (14) (dashed curves).

Equations (14)

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iuz+Dz22ut2+gzu2u=0.
iumz+Dz22umt2+gzum2+2un2um=0.
dΩm,ndz=2gz-um2un2tdt-um2dt,
dtm,ndz=DzΩm,nz.
Δtm,nz=0zDz0zdΩm,ndzdzdz=0zdΩm,ndzzzDzdzdz=0zdΩm,ndzD¯z-D¯zdz=δtm,n1z+δtm,n2z,
δtm,n1z=D¯zΩm,nz,
δtm,n2z=0z-dΩm,ndzD¯zdz.
δtm,n2z=P̅m,nz.
ukz,t=α2πξzexp-t-kT22ξz,ξz=β+iCz,
dΩm,ndz=-gzα2βm-nT2πξz3exp-βm-n2T22ξz2.
P¯m,nsgnCα2βm-nT2πza0zagzC2z×exp-βm-n2T22C2zdz.
P¯m,n=g041-exp-2GAm,nIm,n,
Im,n=1s1/sexp-Gsx+exp-2GexpGsx×exp-βm-n2T22x2dx,
Im,nGs21+exp-2Gπλ2-1G-1-exp-2GlogλG-γ2+J++exp-2GJ-,λ1,

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