Abstract

The evolution of a linearly chirped pulse into a soliton is studied. Even under severe chirping, a soliton can be generated if the initial amplitude is high enough. However, the resulting soliton will always be broader than in the unchirped case.

© 1986 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. A. Hasegawa, Y. Kodama, Proc. IEEE 69, 1145 (1981).
    [CrossRef]
  3. H. E. Lassen, F. Mengel, B. Tromborg, N. C. Albertsen, P. L. Christiansen, Opt. Lett. 10, 34 (1985).
    [CrossRef] [PubMed]
  4. D. Anderson, M. Lisak, P. Anderson, Opt. Lett. 10, 134 (1985).
    [CrossRef] [PubMed]
  5. Z. V. Lewis, Phys. Lett. 112A, 99 (1985).
  6. V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); Sov. Phys. JETP 34, 62 (1972).
  7. J. Satsuma, N. Yajima, Prog. Teor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  8. J. N. Elgin, D. J. Kaup, Opt. Commun. 43, 233 (1982).
    [CrossRef]
  9. J. N. Elgin, Phys. Lett. 110A, 441 (1985).
  10. A. Hasegawa, Appl. Opt. 23, 3302 (1984).
    [CrossRef] [PubMed]

1985

1984

1982

J. N. Elgin, D. J. Kaup, Opt. Commun. 43, 233 (1982).
[CrossRef]

1981

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

1974

J. Satsuma, N. Yajima, Prog. Teor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

1973

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

1971

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); Sov. Phys. JETP 34, 62 (1972).

Albertsen, N. C.

Anderson, D.

Anderson, P.

Christiansen, P. L.

Elgin, J. N.

J. N. Elgin, Phys. Lett. 110A, 441 (1985).

J. N. Elgin, D. J. Kaup, Opt. Commun. 43, 233 (1982).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Appl. Opt. 23, 3302 (1984).
[CrossRef] [PubMed]

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Kaup, D. J.

J. N. Elgin, D. J. Kaup, Opt. Commun. 43, 233 (1982).
[CrossRef]

Kodama, Y.

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

Lassen, H. E.

Lewis, Z. V.

Z. V. Lewis, Phys. Lett. 112A, 99 (1985).

Lisak, M.

Mengel, F.

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Teor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); Sov. Phys. JETP 34, 62 (1972).

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Tromborg, B.

Yajima, N.

J. Satsuma, N. Yajima, Prog. Teor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); Sov. Phys. JETP 34, 62 (1972).

Appl. Opt.

Appl. Phys. Lett.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Opt. Commun.

J. N. Elgin, D. J. Kaup, Opt. Commun. 43, 233 (1982).
[CrossRef]

Opt. Lett.

Phys. Lett.

J. N. Elgin, Phys. Lett. 110A, 441 (1985).

Z. V. Lewis, Phys. Lett. 112A, 99 (1985).

Proc. IEEE

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

Prog. Teor. Phys. Suppl.

J. Satsuma, N. Yajima, Prog. Teor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Zh. Eksp. Teor. Fiz.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971); Sov. Phys. JETP 34, 62 (1972).

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Figures (3)

Fig. 1
Fig. 1

The imaginary part of the eigenvalues η as a function of magnitude of the initial chirp ϕ.

Fig. 2
Fig. 2

The evolution of a positive chirped pulse into a soliton. ϕ = 0.25 and A = 1.

Fig. 3
Fig. 3

Peak amplitude variation of the chirped pulses as they propagate along a fiber: 1 and 2 show ϕ = −0.12, 0.12; 3 and 4 show ϕ = −0.25, 0.25. Straight lines denote the asymptotic values obtained from the eigenvalues.

Equations (5)

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i q t + 1 2 2 q x 2 + q 2 q = 0 ,
q ( x , t ) = η sech [ η ( x - ξ t ) ] exp [ i ξ x + i ( η 2 - ξ 2 ) t / 2 ] ,
v / x + i ξ v = q u , u / x - i ξ u = - q * v ,
q ( x , 0 ) = A sech ( x ) exp ( - i ϕ x 2 ) ,
- [ η sech ( η x ) ] 2 d x - q ( x , 0 ) 2 d x = η A 2 .

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