Abstract

Incomplete collisions in wavelength-division-multiplexed return-to-zero transmission systems are analyzed by asymptotic methods. Formulas for frequency and timing shifts are obtained. The results agree with direct numerical calculations.

© 2003 Optical Society of America

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References

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  1. L. Mollenauer, S. Evangelides, and J. Gordon, J. Lightwave Technol. 9, 362 (1991).
    [CrossRef]
  2. M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
    [CrossRef]
  3. H. Sugahara and A. Maruta, J. Opt. Soc. Am. B 18, 419 (2001).
    [CrossRef]
  4. Y. Kodama and A. Hasegawa, Opt. Lett. 16, 208 (1991).
    [CrossRef] [PubMed]
  5. P. Mamyshev and L. Mollenauer, Opt. Lett. 24, 448 (1999).
    [CrossRef]
  6. C. Xu, C. Xie, and L. Mollenauer, Opt. Lett. 27, 1305 (2002).
  7. R. Mu and C. Menyuk, J. Lightwave Technol. 20, 608 (2002).
    [CrossRef]
  8. M. Ablowitz, T. Hirooka, and G. Biondini, Opt. Lett. 26, 459 (2001).
    [CrossRef]

2002 (3)

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

C. Xu, C. Xie, and L. Mollenauer, Opt. Lett. 27, 1305 (2002).

R. Mu and C. Menyuk, J. Lightwave Technol. 20, 608 (2002).
[CrossRef]

2001 (2)

1999 (1)

1991 (2)

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

Y. Kodama and A. Hasegawa, Opt. Lett. 16, 208 (1991).
[CrossRef] [PubMed]

Ablowitz, M.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

M. Ablowitz, T. Hirooka, and G. Biondini, Opt. Lett. 26, 459 (2001).
[CrossRef]

Biondini, G.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

M. Ablowitz, T. Hirooka, and G. Biondini, Opt. Lett. 26, 459 (2001).
[CrossRef]

Biswas, A.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

Chakravarty, S.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

Docherty, A.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

Evangelides, S.

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

Gordon, J.

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

Hasegawa, A.

Hirooka, T.

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

M. Ablowitz, T. Hirooka, and G. Biondini, Opt. Lett. 26, 459 (2001).
[CrossRef]

Kodama, Y.

Mamyshev, P.

Maruta, A.

Menyuk, C.

R. Mu and C. Menyuk, J. Lightwave Technol. 20, 608 (2002).
[CrossRef]

Mollenauer, L.

C. Xu, C. Xie, and L. Mollenauer, Opt. Lett. 27, 1305 (2002).

P. Mamyshev and L. Mollenauer, Opt. Lett. 24, 448 (1999).
[CrossRef]

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

Mu, R.

R. Mu and C. Menyuk, J. Lightwave Technol. 20, 608 (2002).
[CrossRef]

Sugahara, H.

Xie, C.

C. Xu, C. Xie, and L. Mollenauer, Opt. Lett. 27, 1305 (2002).

Xu, C.

C. Xu, C. Xie, and L. Mollenauer, Opt. Lett. 27, 1305 (2002).

J. Lightwave Technol. (1)

R. Mu and C. Menyuk, J. Lightwave Technol. 20, 608 (2002).
[CrossRef]

J. Lightwave Technol. (1)

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

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

Opt. Lett. (1)

M. Ablowitz, G. Biondini, A. Biswas, A. Docherty, T. Hirooka, and S. Chakravarty, Opt. Lett. 27, 318 (2002).
[CrossRef]

Opt. Lett. (4)

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Figures (2)

Fig. 1
Fig. 1

Total TS versus collision center z0 for a system with length L=25; other parameters are D=0.25, za=0.1, Ω=5, and s=10. The TS, in physical units, is the dimensionless figure multiplied by 12 ps.

Fig. 2
Fig. 2

Maximum TS for an incomplete collision in a QL and DM soliton system versus the dimensionless frequency separation, shown for a system with length L=25; other parameters are D=0.25, za=0.1, and s=10. Inset, maximum TS versus average dispersion D at Ω=10 for a QL system.

Equations (11)

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

iuz+1/2Dzutt+gzu2u=0,
uz,t=α2πβ+iD¯1/2exp-t-ΩD¯22β+iD¯×expiΩt-iD¯Ω2/2,
ΔΩres=AΩ0LgzD¯B3zexp-2βD¯2 Ω2B2zdz,
δtres=AΩ0LgzD¯2B3zexp-2βD¯2Ω2B2zdz,
z˜mj=-Dzam+D¯0+Δ1-Δjθ/2Dza+Δjza,
δtMCWzagz˜mj/2Ω2Δj.
ΔΩedgezc=sgnz˜mj-z˜eWza2βπΩΔjgz˜mj×exp-2βΩΔjza2z˜e-z˜mj2,
ΔΩgzc=2WΓza22βπΩΔ1exp-2βΩΔjza2z˜mj2.
δtresW/2Ω2D
mΔΩedgez˜mj±Wgz˜e/ΔjΩ2D,
δtLW4sΩ2g0L+g0+2ΓzaθL+sD.

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