Abstract

The effect of fifth-order nonlinearity in refractive index on Gaussian pulse propagation in lossy optical fibers is considered. It is shown that fifth-order nonlinearity considerably modifies the pulse propagation, as a result of which the frequency at which the reshaping of the pulse should be done to have a distortionless propagation is reduced significantly (by a factor of about 3 compared with the case of cubic nonlinearity). The peak power for which fifth-order nonlinearity becomes significant is of the same order of magnitude that is required for cubic nonlinearity.

© 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, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  3. A. Hasegawa, Opt. Lett. 8, 650 (1983).
    [CrossRef] [PubMed]
  4. Y. Kodama, A. Hasegawa, Opt. Lett. 7, 339 (1982).
    [CrossRef] [PubMed]
  5. D. Anderson, Proc. Inst. Electr. Eng. 132, 122 (1985).
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    [CrossRef]
  7. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 9, 229 (1984).
    [CrossRef] [PubMed]
  8. D. N. Christodoulides, R. I. Joseph, Opt. Lett. 9, 408 (1984).
    [CrossRef] [PubMed]
  9. D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
    [CrossRef]
  10. A. Hasegawa, Opt. Lett. 9, 288 (1984).
    [CrossRef] [PubMed]
  11. D. Anderson, M. Lisak, Opt. Lett. 9, 468 (1984).
    [CrossRef] [PubMed]
  12. K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
    [CrossRef]
  13. L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
    [CrossRef] [PubMed]
  14. C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).
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    [CrossRef] [PubMed]
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    [CrossRef]
  17. D. Anderson, M. Lisak, P. Anderson, Opt. Lett. 10, 134 (1985).
    [CrossRef] [PubMed]

1985 (3)

1984 (5)

1983 (3)

1982 (3)

Y. Kodama, A. Hasegawa, Opt. Lett. 7, 339 (1982).
[CrossRef] [PubMed]

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

1980 (1)

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

1973 (2)

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Anderson, D.

Anderson, P.

Blow, K. J.

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

Christodoulides, D. N.

Doran, N. J.

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

Fork, R. L.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

Gordon, J. P.

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. S. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

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

Hasegawa, A.

Islam, M. N.

Joseph, R. I.

Kodama, Y.

Lisak, M.

Mollenauer, L. F.

Mollenuer, L. F.

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

Shank, C. V.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

Stolen, R. H.

L. F. Mollenauer, R. H. Stolen, M. N. Islam, Opt. Lett. 10, 229 (1985).
[CrossRef] [PubMed]

L. F. Mollenauer, R. H. Stolen, J. P. Gordon, W. S. Tomlinson, Opt. Lett. 8, 289 (1983).
[CrossRef] [PubMed]

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

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

Tappert, F.

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Tomlinson, W. J.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

Tomlinson, W. S.

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

Appl. Phys. Lett. (2)

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
[CrossRef]

Electron. Lett. (1)

D. N. Christodoulides, R. I. Joseph, Electron. Lett. 20, 659 (1984).
[CrossRef]

Opt. Commun. (2)

K. J. Blow, N. J. Doran, Opt. Commun. 42, 403 (1982).
[CrossRef]

D. Anderson, Opt. Commun. 48, 107 (1983).
[CrossRef]

Opt. Lett. (9)

Phys. Lett. (1)

C. V. Shank, R. L. Fork, R. Yen, R. H. Stolen, W. J. Tomlinson, Phys. Lett. 40, 761 (1982).

Phys. Rev. Lett. (1)

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

Proc. Inst. Electr. Eng. (1)

D. Anderson, Proc. Inst. Electr. Eng. 132, 122 (1985).

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Figures (2)

Fig. 1
Fig. 1

Results of the numerical solution of Eq. (12) for different values of f and λ̃. Solid lines: 1, f = 0.0, λ̃ = 0.0; 2A, f = 1.5, λ̃ = 0.0; 3A, f = 2.0, λ̃ = 0.0; 4A, f = 2.5, λ̃ = 0.0. Dashed lines: 2B, f = 1.5, λ̃ = −0.025; 3B, f = 2.0, λ̃ = −0.025; 4B, f = 2.5, λ̃ = −0.025; 4C, f = 2.5, λ̃ = −0.035.

Fig. 2
Fig. 2

Results of the numerical solution of Eq. (12) for different values of f and λ̃. Solid lines: 1A, f = 2.6, λ̃ = 0.0; 2A, f = 3.0, λ̃ = 0.0; 3A, f = 3.5, λ̃ = 0.0. Dashed lines: 1B, f = 2.6, λ̃ = −0.025; 2B, f = 3.0, λ̃ = −0.025; 3B, f = 3.4, λ̃ = −0.025.

Equations (13)

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n = n 0 ( ω ) + n 2 ψ 2 - n 3 ψ 4 ,
i ( ψ x + γ ψ ) = α 2 ψ τ 2 + κ 0 ψ 2 ψ + λ 0 ψ 4 ψ ,
ψ ( x , τ ) = ϕ ( x , τ ) e - γ x ,
i ϕ x = α 2 ϕ τ 2 + κ 0 e - 2 γ x ϕ 2 ϕ + λ 0 e - 4 γ x ϕ 4 ϕ .
L = i 2 ( ϕ ϕ * x - ϕ * ϕ x ) - α ( ϕ τ ) 2 + κ ( x ) 2 ϕ 4 + λ ( x ) 3 ϕ 6 , κ ( x ) = κ 0 exp ( - 2 γ x ) ,             λ ( x ) = λ 0 exp ( - 4 γ x ) ,
δ L ( ϕ , ϕ * , ϕ x , ϕ * x , ϕ τ , ϕ * τ ) d x d τ = 0 .
ϕ 0 ( 0 , τ ) = A 0 exp ( - τ 2 / 2 a 0 2 ) ,
ϕ ( x , τ ) = A ( x ) exp [ - τ 2 2 a 2 ( x ) + i b ( x ) τ 2 ] ,
δ L d x = 0 ,
L = π 2 [ i a ( A d A * d x - A * d A d x ) + a 3 A 2 d b d x - α a 3 A 2 ( 4 b 2 + 1 a 4 ) + κ ( x ) 2 a A 4 + λ ( x ) 3 a A 6 ] .
d 2 a ( x ) d x 2 = - 4 λ α E 0 2 3 1 a 3 ( x ) + 4 α 2 a 3 ( x ) - 2 α κ ( x ) E 0 a 2 ( x ) ,
d 2 y d x 2 = 2 μ y 3 - 2 λ ˜ e - 4 γ x y 3 - ν e - 2 γ x y 2 ,
μ = 2 α 2 a 0 4 ,             λ ˜ = 2 α λ 0 E 0 2 3 a 0 4 ,             ν = 2 α κ 0 E 0 a 0 3 .

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