Abstract

Nonadiabatic effects caused by lumped amplifiers in fiber soliton transmission systems are reduced by the use of dispersion-decreasing fibers between amplifiers. As a practical application, we consider a stepwise dispersion-decreasing fiber with M steps and show that the increase in M is almost equivalent to the reduction of amplifier spacing, Za, to Za/M in reducing collision-induced jitters in soliton-based wavelength-division multiplexing systems.

© 1996 Optical Society of America

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References

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  1. L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  2. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990 );Phys. Rev. Lett. 66, 161 (1991).
    [CrossRef] [PubMed]
  3. A. J. Stentz, R. W. Boyd, A. F. Evans, Opt. Lett. 20, 1770 (1995).
    [CrossRef] [PubMed]
  4. W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
    [CrossRef] [PubMed]
  5. W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
    [CrossRef]
  6. A. Hasegawa, Y. Kodama, S. Kumar, “Adiabatic soliton transmission in fibers with lumped amplifiers,” submitted to Opt. Lett.
  7. A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press,Oxford, 1995), p. 181.

1995 (1)

1994 (2)

W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
[CrossRef]

W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
[CrossRef] [PubMed]

1991 (1)

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

1990 (1)

Boyd, R. W.

Doran, N. J.

W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
[CrossRef] [PubMed]

W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
[CrossRef]

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Evans, A. F.

Forysiak, W.

W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
[CrossRef] [PubMed]

W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
[CrossRef]

Gordon, J. P.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990 );Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, S. Kumar, “Adiabatic soliton transmission in fibers with lumped amplifiers,” submitted to Opt. Lett.

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press,Oxford, 1995), p. 181.

Knox, F. M.

W. Forysiak, F. M. Knox, N. J. Doran, Opt. Lett. 19, 174 (1994).
[CrossRef] [PubMed]

W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
[CrossRef]

Kodama, Y.

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990 );Phys. Rev. Lett. 66, 161 (1991).
[CrossRef] [PubMed]

A. Hasegawa, Y. Kodama, S. Kumar, “Adiabatic soliton transmission in fibers with lumped amplifiers,” submitted to Opt. Lett.

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press,Oxford, 1995), p. 181.

Kumar, S.

A. Hasegawa, Y. Kodama, S. Kumar, “Adiabatic soliton transmission in fibers with lumped amplifiers,” submitted to Opt. Lett.

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

Stentz, A. J.

J. Lightwave Technol. (2)

L. F. Mollenauer, S. G. Evangelides, J. P. Gordon, J. Lightwave Technol. 9, 362 (1991).
[CrossRef]

W. Forysiak, F. M. Knox, N. J. Doran, J. Lightwave Technol. 12, 1330 (1994).
[CrossRef]

Opt. Lett. (3)

Other (2)

A. Hasegawa, Y. Kodama, S. Kumar, “Adiabatic soliton transmission in fibers with lumped amplifiers,” submitted to Opt. Lett.

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press,Oxford, 1995), p. 181.

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Figures (5)

Fig. 1
Fig. 1

Stepwise dispersion profile with fiber sections equally spaced in Z′ (solid curves) and ideal exponential dispersion profile (dashed curves).

Fig. 2
Fig. 2

Frequency shift ΔK(∞) versus steps M for the case of fiber sections equally spaced in Z′ (solid curve) and in Z (dashed curve). Za = 2.45, Γ = 0.185, and ΔB = 5.0.

Fig. 3
Fig. 3

Absolute amplitude |q| as a function of distance Z and time T with no dispersion management. The slower soliton is artificially removed at Z = 9.8 to clarify the mean position of the faster soliton.

Fig. 4
Fig. 4

Same as Fig. 3 but with dispersion management. Fiber sections are equally spaced in Z′; M = 4.

Fig. 5
Fig. 5

Mean position of the faster soliton versus distance for different values of M. Fiber sections are equally spaced in Z′.

Equations (12)

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i u Z ' + 1 2 2 u T 2 + a 1 2 ( Z ) d ( Z ) | u | 2 u = 0.
a 1 ( Z ) = a 1 ( 0 ) exp [ Γ ( Z n Z a ) ] , n Z a < Z < ( n + 1 ) Z a ,
a 1 ( 0 ) = [ 2 Γ Z a 1 exp ( 2 Γ Z a ) ] 1 / 2 .
Z ' = 0 Z d ( Z ) d Z .
i u Z ' + 1 2 2 u T 2 + a M 2 ( Z ) | u | 2 u = 0 ,
Δ K ( ) = 1 Δ B d Z ' d a M 2 ( Z ) d Z ' × sec h ( T + Δ B Z ' 2 ) sec h ( T Δ B Z ' 2 ) d T = Im { 32 π 2 n = 1 Z a B n 2 π n ( π 2 n / Z a Δ B ) 4 [ sinh ( π 2 n / Z a Δ B ) ] 2 } ,
B n = 1 Z a 0 Z a d Z a 1 2 ( Z ) exp ( 2 π n i Z ' Z a ) .
Z ' ( Z l + 1 ) Z ' ( Z l ) = Z a / M ,    l = 0 , 1 , ... M 1.
D l = 1 Z l + 1 Z l Z l Z l + 1 a 1 2 ( 0 ) exp ( 2 Γ Z ) d Z ,
Z l = 1 2 Γ ln { 1 l [ 1 exp ( 2 Γ Z a ) ] M } ,
D l = Z a M ( Z l + 1 Z l ) .
B n = a 1 ( 0 ) 2 M exp ( i π n / M ) m 0 M 1 exp ( i 2 π n m / M ) × [ 2 i ( M m α ) sin ( n π / M ) ] + α exp ( i π n / M ) Γ Z a + i π n D m ,

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