Abstract

It is shown that solitons emerging from pulses launched with frequencies at, or close to, the zero-dispersion point in a single-mode optical fiber are ordinary bright solitons corresponding to the nonlinear Schrödinger equation. These solitons are inherently frequency shifted into the anomalous-dispersion regime, where the third-order dispersion acts as a small perturbation. We therefore conclude that an optical-soliton-based communication system should be designed with the carrier frequency in the anomalous-dispersion regime but not too close to the zero-dispersion point, where the formation of an unwanted dispersive-wave component would degrade the system performance.

© 1990 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142171 (1973).
    [Crossref]
  2. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  3. P. K. A. Wai, C. R. Menyuk, H. H. Chen, Y. C. Lee, Opt. Lett. 12, 628 (1987).
    [Crossref] [PubMed]
  4. K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
    [Crossref]
  5. G. R. Boyer, X. F. Carlotti, Opt. Commun. 60, 18 (1986).
    [Crossref]
  6. G. P. Agrawal, M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
    [Crossref] [PubMed]
  7. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [Crossref]
  8. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [Crossref]

1987 (1)

1986 (2)

G. R. Boyer, X. F. Carlotti, Opt. Commun. 60, 18 (1986).
[Crossref]

G. P. Agrawal, M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[Crossref] [PubMed]

1983 (2)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[Crossref]

1981 (1)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

1980 (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

1973 (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142171 (1973).
[Crossref]

Agrawal, G. P.

G. P. Agrawal, M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[Crossref] [PubMed]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

Blow, K. J.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[Crossref]

Boyer, G. R.

G. R. Boyer, X. F. Carlotti, Opt. Commun. 60, 18 (1986).
[Crossref]

Carlotti, X. F.

G. R. Boyer, X. F. Carlotti, Opt. Commun. 60, 18 (1986).
[Crossref]

Chen, H. H.

Cummins, E.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[Crossref]

Doran, N. J.

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[Crossref]

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142171 (1973).
[Crossref]

Kodama, Y.

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

Lee, Y. C.

Menyuk, C. R.

Mollenauer, L. F.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Potasek, M. J.

G. P. Agrawal, M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[Crossref] [PubMed]

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142171 (1973).
[Crossref]

Wai, P. K. A.

Appl. Phys. Lett. (1)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142171 (1973).
[Crossref]

Opt. Commun. (2)

K. J. Blow, N. J. Doran, E. Cummins, Opt. Commun. 48, 181 (1983).
[Crossref]

G. R. Boyer, X. F. Carlotti, Opt. Commun. 60, 18 (1986).
[Crossref]

Opt. Lett. (1)

Phys. Rev. A (2)

G. P. Agrawal, M. J. Potasek, Phys. Rev. A 33, 1765 (1986).
[Crossref] [PubMed]

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[Crossref]

Phys. Rev. Lett. (1)

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
[Crossref]

Proc. IEEE (1)

A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
[Crossref]

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Equations (31)

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i Ψ x = i β 3 Ψ τ 3 + κ | Ψ | 2 Ψ ,
| A | 2 = | 6 β κ | [ 1 5 6 ( 1 Ω a ) 2 ] | Ω | a 2 ,
| 1 Ω a | < 0.24 ,
δ L d τ d x = 0 ,
L = i 2 ( Ψ Ψ * x Ψ * Ψ x ) + κ 2 | Ψ | 4 + β i 2 ( 2 Ψ * τ 2 Ψ τ 2 Ψ τ 2 Ψ * τ ) .
Ψ T ( x , τ ) = A ( x ) sech ( z ) exp { i [ τ U ( x ) ] Ω ( x ) i M ( x ) tanh ( z ) + i b ( x ) z 2 } ,
δ L d x = 0 ,
L = L ( Ψ T ) d τ = i a ( A d A * d x A * d A d x ) + 2 | A | 2 × ( a Ω + 2 3 M ) d U d x + α 1 | A | 2 a ( d b d x 2 b a d a d x ) + 2 3 κ a | A | 4 2 β | A | 2 a ( Ω + 14 15 M a + a 2 Ω 3 + 8 5 M 2 Ω + 2 M Ω 2 a + 16 35 M 3 a ) 12 β | A | 2 a b 2 ( α 1 Ω + α 2 M a )
a | A | 2 = C 0 = const . ,
Ω + 2 3 M a = C 1 / C 0 = const . ,
M 2 + 7 4 M Ω a + 7 8 105 8 b 2 = 0 ,
d a d x = 12 β b a ( Ω + α 2 α 1 M a )
d b d x = κ | A | 2 3 α 1 2 β α 1 1 a 3 [ Ω a + 14 15 M + 6 b 2 ( α 1 Ω a + α 2 M ) ] ,
d U d x = β 1 a 2 [ 1 + 3 ( Ω a ) 2 + 4 M Ω a + 8 5 M 2 + 6 α 1 b 2 ] ,
d d x ( arg A ) = β [ 2 Ω 3 ( 1 1 2 Ω 2 a 2 ) + 4 M Ω 2 a × ( 1 + 2 5 1 Ω a + 2 5 M Ω a + 8 35 M 2 Ω 2 a 2 ) + 6 b 2 a 2 ( α 1 Ω + α 2 M a ) ] 5 6 κ | A | 2 .
I 0 = | Ψ | 2 d τ = const . ,
I 1 = ( Ψ Ψ * τ Ψ * Ψ τ ) d τ = const .
| 1 Ω a | 1
| A | 2 = 6 β κ [ 1 7 15 ( 1 Ω a ) 2 ] Ω a 2 ,
M = 1 2 1 Ω a ,
d U d x = 3 β [ 1 1 3 ( 1 Ω a ) 2 ] Ω 2 ,
d d x ( arg A ) = 2 β [ 1 + ( 1 Ω a ) 2 ] Ω 3 .
1 2 ( d a d x ) 2 + ( a ) = 0 ,
( a ) = 12 β 2 Ω 2 α 1 ( 1 a 2 1 a 0 2 ) 4 β Ω C 0 κ α 1 ( 1 a 1 a 0 ) .
Ψ ( x , τ ) = φ ( x , τ ) exp ( i Ω τ )
i ( φ x + 3 β Ω 2 φ τ ) = β Ω 3 φ + 3 β Ω 2 φ τ 2 + i β 3 φ τ 3 + κ | φ | 2 φ ,
| 3 β Ω 2 φ τ 2 | | β 3 φ τ 3 | ,
Ψ = A 0 sech ( τ u x a ) × exp [ i ( τ u x ) Ω i ( 2 β Ω 3 + κ 2 A 0 2 ) x ] ,
I 0 i = I 0 s + I 0 d , I 1 i = I 1 s + I 1 d ,
Ω = 1 2 i ( Ψ Ψ * τ Ψ * Ψ τ ) d τ / | Ψ | 2 d τ
Ω s Ω d = 1 I 0 i I 0 s .

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