Abstract

We analyze the role of third-order dispersion on the propagation, stability, and interactions of solitons in optical fiber transmission links and fiber lasers.

© 1994 Optical Society of America

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References

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  1. H. A. Haus, J. D. Moores, L. E. Nelson, Opt. Lett. 18, 51 (1993).
    [Crossref] [PubMed]
  2. Y. Kodama, J. Stat. Phys. 39, 597 (1985).
    [Crossref]
  3. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [Crossref]
  4. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [Crossref]
  5. A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
    [Crossref] [PubMed]
  6. Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [Crossref]
  7. Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993); Opt. Lett. 18, 1311 (1993).
    [Crossref] [PubMed]
  8. see P. K. A. Wai, C. R. Menyuk, Y. C. Lee, H. H. Chen, Opt. Lett. 11, 464 (1986); J. N. Elgin, Opt. Lett. 17, 1409 (1992).
    [Crossref] [PubMed]
  9. M. L. Dennis, I. N. Duling, Appl. Phys. Lett. 62, 2911 (1993).
    [Crossref]
  10. P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
    [Crossref]
  11. Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
    [Crossref] [PubMed]

1993 (2)

M. L. Dennis, I. N. Duling, Appl. Phys. Lett. 62, 2911 (1993).
[Crossref]

H. A. Haus, J. D. Moores, L. E. Nelson, Opt. Lett. 18, 51 (1993).
[Crossref] [PubMed]

1992 (2)

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[Crossref]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

1991 (2)

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993); Opt. Lett. 18, 1311 (1993).
[Crossref] [PubMed]

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[Crossref] [PubMed]

1987 (2)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[Crossref] [PubMed]

1986 (1)

1985 (2)

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[Crossref]

Y. Kodama, J. Stat. Phys. 39, 597 (1985).
[Crossref]

Chen, H. H.

Chu, P. L.

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[Crossref]

Dennis, M. L.

M. L. Dennis, I. N. Duling, Appl. Phys. Lett. 62, 2911 (1993).
[Crossref]

Desem, C.

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[Crossref]

Duling, I. N.

M. L. Dennis, I. N. Duling, Appl. Phys. Lett. 62, 2911 (1993).
[Crossref]

Gordon, J. P.

Hasegawa, A.

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[Crossref] [PubMed]

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

Haus, H. A.

Kodama, Y.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[Crossref] [PubMed]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993); Opt. Lett. 18, 1311 (1993).
[Crossref] [PubMed]

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[Crossref] [PubMed]

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

Y. Kodama, J. Stat. Phys. 39, 597 (1985).
[Crossref]

Lee, Y. C.

Menyuk, C. R.

Moores, J. D.

Nelson, L. E.

Nozaki, K.

Romagnoli, M.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

Wabnitz, S.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993); Opt. Lett. 18, 1311 (1993).
[Crossref] [PubMed]

Wai, P. K. A.

Appl. Phys. Lett. (1)

M. L. Dennis, I. N. Duling, Appl. Phys. Lett. 62, 2911 (1993).
[Crossref]

Electron. Lett. (3)

P. L. Chu, C. Desem, Electron. Lett. 21, 228 (1985).
[Crossref]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[Crossref]

Y. Kodama, S. Wabnitz, Electron. Lett. 27, 1931 (1991); Y. Kodama, S. Wabnitz, Electron. Lett. 29, 226 (1993); Opt. Lett. 18, 1311 (1993).
[Crossref] [PubMed]

IEEE J. Quantum Electron. (1)

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[Crossref]

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

J. Stat. Phys. (1)

Y. Kodama, J. Stat. Phys. 39, 597 (1985).
[Crossref]

Opt. Lett. (3)

Phys. Rev. Lett. (1)

A. Hasegawa, Y. Kodama, Phys. Rev. Lett. 66, 161 (1991).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Contour plot of soliton pulse propagation with β3 = −0.2.

Fig. 2
Fig. 2

Soliton resonances with periodic amplification and β3 = −1/30: (a) soliton spectrum and resonance sidebands, (b) numerical value of the resonance sideband shift ft (points) and theoretical prediction (solid curve) versus the sideband order N.

Fig. 3
Fig. 3

Initial frequency shifts of the two-soliton solution versus the pulse separation X0.

Fig. 4
Fig. 4

Suppression of two-soliton interactions with X0 = 4: (a) β = 3δ = 0.15, β3 = 0; (b) δ = β = 0, β3 = −0.2; (c) β = 3δ = 0.15, β3 = −0.2; (d) β = 0.15, δ = 0.02, γ = 0.045, β3 = −0.2.

Equations (10)

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q Z i 2 q T T i | q | 2 q = δ q + β q T T + γ | q | 2 q β 3 q T T T .
Q = q 3 i β 3 [ q T + 2 q T | q ( T ) | 2 d T ] ,
Q Z i 2 Q T T i | Q | 2 Q + β 3 ( Q T T T + 6 | Q | 2 Q ) = 0 .
Q ( Z , T ) = η sech [ η ( T Z / v s θ 0 ) ] × exp ( i κ T + i k s Z i σ 0 ) ,
v s 1 = κ + β 3 ( η 2 3 κ 2 ) ,
k s = ( η 2 κ 2 ) / 2 + β 3 κ ( 3 η 2 κ 2 ) .
Δ ζ = κ / 2 = β 3 Γ [ q 0 ( 1 ) * ψ 1 2 ( ζ ) q 0 ( 1 ) ψ 2 2 ( ζ ) ] d T = β 3 η 2
2 π N Z a = k s k r = ( 1 2 + 4 β 3 2 8 β 3 4 ) ( Ω 2 2 β 3 Ω 3 ) .
q ˆ 0 ( T , Z = 0 ) = sech ( T X 0 ) + sech ( T + X 0 )
Δ ζ l = κ l / 2 = β 3 Γ i [ q ˆ 0 ( 1 ) * ψ 1 2 ( ζ l ) q ˆ 0 ( 1 ) ψ 2 2 ( ζ l ) ] d T , l = 1 , 2 ,

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