Abstract

An analytical investigation is made of the interplay between dispersion and nonlinearity in the creation of wave breaking in optical fibers. Wave breaking is found to involve two independent processes: (a) overtaking of different parts of the pulse and (b) nonlinear generation of new frequencies during overtaking. Analytical predictions for the distance of wave breaking are obtained and found to be in good agreement with numerical results.

© 1992 Optical Society of America

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References

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  1. D. Grischkowsky and A. C. Balant, Appl. Phys. Lett. 41, 1–3 (1982).
    [Crossref]
  2. B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
    [Crossref]
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    [Crossref]
  4. H. E. Lassen, F. Mengel, B. Tromborg, N. C. Albertsen, and P. L. Christiansen, Opt. Lett. 10, 34–37 (1985).
    [Crossref] [PubMed]
  5. W. J. Tomlinson, R. H. Stolen, and A. M. Johnson, Opt. Lett. 10, 457–459 (1985).
    [Crossref] [PubMed]
  6. J. E. Rothenberg, J. Opt. Soc. Am. B 6, 2392–2401 (1989).
    [Crossref]
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    [Crossref] [PubMed]
  8. F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
    [Crossref]
  9. D. Anderson and M. Lisak, Phys. Rev. 27, 1393–1398 (1983).
    [Crossref]
  10. D. Grishkowsky, Appl. Phys. Lett. 25, 566–568 (1974).
    [Crossref]

1989 (2)

1985 (2)

1984 (1)

1983 (2)

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

D. Anderson and M. Lisak, Phys. Rev. 27, 1393–1398 (1983).
[Crossref]

1982 (1)

D. Grischkowsky and A. C. Balant, Appl. Phys. Lett. 41, 1–3 (1982).
[Crossref]

1974 (1)

D. Grishkowsky, Appl. Phys. Lett. 25, 566–568 (1974).
[Crossref]

1967 (1)

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

Agrawal, G. P.

Albertsen, N. C.

Alfano, R. R.

Anderson, D.

D. Anderson and M. Lisak, Phys. Rev. 27, 1393–1398 (1983).
[Crossref]

Balant, A. C.

D. Grischkowsky and A. C. Balant, Appl. Phys. Lett. 41, 1–3 (1982).
[Crossref]

Baldeck, P. L.

Blow, K. J.

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

Christiansen, P. L.

Cotter, D.

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

De Martini, F.

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

Doran, N. J.

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

Grischkowsky, D.

D. Grischkowsky and A. C. Balant, Appl. Phys. Lett. 41, 1–3 (1982).
[Crossref]

Grishkowsky, D.

D. Grishkowsky, Appl. Phys. Lett. 25, 566–568 (1974).
[Crossref]

Gustavsson, T. K.

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

Johnson, A. M.

Kelley, P. L.

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

Lassen, H. E.

Lisak, M.

D. Anderson and M. Lisak, Phys. Rev. 27, 1393–1398 (1983).
[Crossref]

Mengel, F.

Nelson, B. P.

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

Rothenberg, J. E.

Shank, C. V.

Stolen, R. H.

Tomlinson, W. J.

Townes, C. H.

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

Tromborg, B.

Appl. Phys. Lett. (2)

D. Grischkowsky and A. C. Balant, Appl. Phys. Lett. 41, 1–3 (1982).
[Crossref]

D. Grishkowsky, Appl. Phys. Lett. 25, 566–568 (1974).
[Crossref]

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

B. P. Nelson, D. Cotter, K. J. Blow, and N. J. Doran, Opt. Commun. 48, 292–294 (1983).
[Crossref]

Opt. Lett. (3)

Phys. Rev. (2)

F. De Martini, C. H. Townes, T. K. Gustavsson, and P. L. Kelley, Phys. Rev. 164, 312–323 (1967).
[Crossref]

D. Anderson and M. Lisak, Phys. Rev. 27, 1393–1398 (1983).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

Qualitative plot of the initial chirp variation: a, normal dispersion, weak nonlinearity; b, normal dispersion, strong nonlinearity; c, anomalous dispersion, weak nonlinearity; and d, anomalous dispersion, strong nonlinearity.

Fig. 2
Fig. 2

Comparison of analytical (solid curve) and numerical (dotted curve) results for the wave-breaking distance of an initial Gaussian pulse ψ(0, τ) = A0 exp(−τ2/16), which corresponds to the rms width σ = 2.

Fig. 3
Fig. 3

Numerically calculated pulse shapes: (a) shortly before (2αx02/a02 = 0.4) and (b) shortly after (2αx02/a02 = 0.5) the wave-breaking distance for the initial Gaussian pulse Ψ(0,τ) = 8 exp(−τ2/16).

Fig. 4
Fig. 4

Comparison of analytical (solid curve) and numerical (dotted curve) results for the wave-breaking distance of an initial sech pulse ψ(0, τ) = A0 sech(τπ/481/2), which corresponds to the rms width σ = 2.

Equations (18)

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i ψ x = α 2 ψ τ 2 + κ | ψ | 2 ψ ,
ψ ( x , τ ) = A 0 ( 1 2 i α x / a 0 2 ) 1 / 2 exp [ τ 2 2 a 0 2 ( 1 2 i α x / a 0 2 ) ] .
ω c ( x , τ ) ϕ τ = 2 α x / a 0 2 1 + ( 2 α x / a 0 2 ) 2 τ a 0 2 ,
ω c ( x , τ ) = κ x τ | ψ ( 0 , τ ) | 2 = 2 κ A 0 2 x a 0 2 τ exp ( τ 2 a 0 2 ) .
ω c ( x , τ ) 2 α x a 0 2 τ a 0 2 [ 1 K exp ( τ 2 / a 0 2 ) ] ,
K = κ α a 0 2 A 0 2 = [ exp ( 3 / 2 ) ] / 2 .
Δ τ = x Δ k 0 x k 0 Δ ω x k 0 d ω c d τ Δ τ ,
x wb = 1 2 α d ω c / d τ .
( 2 α x wb a 0 2 ) 2 = 1 G ( τ 2 / a 0 2 ) ,
2 α x wb a 0 2 = 1 ( K K c 1 ) 1 / 2 .
ϕ x = α A τ τ A + α ω c 2 κ A 2 ,
( A 2 ) x = 2 α ( A 2 ω c ) τ ,
ϕ ( x , τ ) ( α A τ τ A + α ω c 2 κ A 2 ) | x = 0 x + ϕ ( 0 , τ ) ,
ω c ( x , τ ) + [ α A τ τ ( 0 , τ ) A ( 0 , τ ) + κ A 2 ( 0 , τ ) ] τ x .
ω c ( x , τ ) = 2 α x a 0 3 ( κ a 0 2 A 0 2 / α 2 ) tanh τ a 0 sech 2 τ a 0 .
( 2 α x wb a 0 2 ) 2 1 2 K 1 H ( sech 2 τ a 0 ) ,
2 α x wb a 0 2 = ( 3 2 K ) 1 / 2 .
{ α [ A τ τ ( 0 , τ ) A ( 0 , τ ) ω c 2 ( 0 , τ ) ] + κ A 2 } τ = f ( τ ) .

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