Abstract

It is demonstrated that the dynamics of small-amplitude dark solitons in optical fibers may be described by the well-known Korteweg–de Vries equation. This approach allows us to explain analytically the temporal self-shift of dark solitons due to the Raman contribution to the nonlinear refractive index, which has been observed experimentally by Weiner et al. [Opt. Lett. 14, 868 (1989)].

© 1990 Optical Society of America

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References

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  1. A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
    [Crossref]
  2. L. F. Mollenauer, R. H. Stolen, J. P. Gordon, Phys. Rev. Lett. 45, 1095 (1980).
    [Crossref]
  3. P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
    [Crossref]
  4. D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
    [Crossref] [PubMed]
  5. A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
    [Crossref] [PubMed]
  6. W. J. Tomlinson, R. J. Hawkins, A. M. Weiner, J. P. Hertiage, R. N. Thurston, J. Opt. Soc. Am. B 6, 329 (1989).
    [Crossref]
  7. S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
    [Crossref]
  8. A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, R. J. Hawkins, Opt. Lett. 14, 868 (1989).
    [Crossref] [PubMed]
  9. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).
  10. V. V. Afanasyev, Yu. S. Kivshar, V. V. Konotop, V. N. Serkin, Opt. Lett. 14, 805 (1989).
    [Crossref] [PubMed]
  11. Yu. S. Kivshar, “Dark-soliton dynamics and shock waves induced by the stimulated Raman effect in optical fibers,” Phys. Rev. A (to be published).
  12. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [Crossref] [PubMed]
  13. L. Gagnon, P. A. Bélanger, Opt. Lett. 15, 466 (1990).
    [Crossref] [PubMed]
  14. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
    [Crossref]
  15. Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
    [Crossref]
  16. W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
    [Crossref] [PubMed]

1990 (2)

S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
[Crossref]

L. Gagnon, P. A. Bélanger, Opt. Lett. 15, 466 (1990).
[Crossref] [PubMed]

1989 (6)

1988 (2)

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

1987 (1)

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

1986 (1)

1980 (1)

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

1973 (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Afanasyev, V. V.

Barthelemy, A.

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Bélanger, P. A.

Bourkoff, E.

Emplit, P.

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Froehly, C.

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Gagnon, L.

Giuliani, G.

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

Gordon, J. P.

Gredeskul, S. A.

S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
[Crossref]

Grisch-kowsky, D.

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

Halas, N. J.

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

Hamaide, J. P.

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Hasegawa, A.

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[Crossref]

Haus, H. A.

Hawkins, R. J.

Heritage, J. P.

A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, R. J. Hawkins, Opt. Lett. 14, 868 (1989).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Hertiage, J. P.

Kirschner, E. M.

A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, R. J. Hawkins, Opt. Lett. 14, 868 (1989).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Kivshar, Yu. S.

S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
[Crossref]

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

V. V. Afanasyev, Yu. S. Kivshar, V. V. Konotop, V. N. Serkin, Opt. Lett. 14, 805 (1989).
[Crossref] [PubMed]

Yu. S. Kivshar, “Dark-soliton dynamics and shock waves induced by the stimulated Raman effect in optical fibers,” Phys. Rev. A (to be published).

Konotop, V. V.

Krökel, D.

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

Leaird, D. E.

A. M. Weiner, R. N. Thurston, W. J. Tomlinson, J. P. Heritage, D. E. Leaird, E. M. Kirschner, R. J. Hawkins, Opt. Lett. 14, 868 (1989).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

Malomed, B. A.

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Mollenauer, L. F.

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

Reynand, E.

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Serkin, V. N.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Stolen, R. H.

R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. Am. B 6, 1159 (1989).
[Crossref]

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

Thurston, R. N.

Tomlinson, W. J.

Weiner, A. M.

Yanovskaya, M. V.

S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
[Crossref]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Zhao, W.

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

Opt. Commun. (1)

P. Emplit, J. P. Hamaide, E. Reynand, C. Froehly, A. Barthelemy, Opt. Commun. 62, 374 (1987).
[Crossref]

Opt. Lett. (5)

Phys. Rev. A (1)

S. A. Gredeskul, Yu. S. Kivshar, M. V. Yanovskaya, Phys. Rev. A 41, 394 (1990).
[Crossref]

Phys. Rev. Lett. (3)

D. Krökel, N. J. Halas, G. Giuliani, D. Grisch-kowsky, Phys. Rev. Lett. 60, 29 (1988).
[Crossref] [PubMed]

A. M. Weiner, J. P. Heritage, R. J. Hawkins, R. N. Thurston, E. M. Kirschner, D. E. Leaird, W. J. Tomlinson, Phys. Rev. Lett. 61, 2445 (1988).
[Crossref] [PubMed]

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

Rev. Mod. Phys. (1)

Yu. S. Kivshar, B. A. Malomed, Rev. Mod. Phys. 61, 763 (1989).
[Crossref]

Sov. Phys. JETP (1)

V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).

Other (2)

A. Hasegawa, Optical Solitons in Fibers (Springer-Verlag, Berlin, 1989).
[Crossref]

Yu. S. Kivshar, “Dark-soliton dynamics and shock waves induced by the stimulated Raman effect in optical fibers,” Phys. Rev. A (to be published).

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Equations (22)

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i u x σ u tt + 2 | u | 2 u = 0 ,
u ( x , t ) = u 0 ( λ ) 2 + exp Z 1 + exp Z exp ( 2 i u 0 2 x ) ,
Z = 2 ν u 0 ( t t 0 2 λ u 0 x ) , λ 2 = 1 ν 2 ,
u ( x , t ) = u 0 tanh ( u 0 t ) exp ( 2 i u 0 2 x ) ,
u ( x , t ) [ u 0 ½ u 0 ν 2 sech 2 ( Z / 2 ) ] × exp [ 2 i u 0 2 x + ( x , t ) ] , φ ( x , t ) = 2 ν / ( 1 + e Z ) ,
Z 2 ν u 0 ( t 2 u 0 x ± u 0 ν 2 x )
u ( x , t ) = [ u 0 + a ( x , t ) ] exp [ 2 i u 0 2 x + ( x , t ) ] .
( a x u 0 φ tt ) ( 2 a t φ t + a φ tt ) = 0 ,
u 0 ( φ x 4 u 0 a ) + a tt + x φ t 2 ( u 0 + a ) 6 u 0 a 2 = 0 ,
C 2 = 4 u 0 2 .
τ = ( t Cx ) , y = 3 x ,
a = 2 a 0 + 4 a 1 + , φ = φ 0 + 3 φ 1 + .
φ 0 τ = ( C / u 0 ) a 0 ,
2 C a 0 y + 24 u 0 a 0 a 0 τ a 0 τττ = 0 .
a 0 = ( κ 2 / 2 u 0 ) sech 2 [ κ ( τ + 2 κ 2 y C ) ] ,
ν u 0 = ∊κ ,
i u x u tt + 2 | u | 2 u = αu ( | u | 2 ) t ,
2 C a 0 y + 24 u 0 a 0 a 0 τ a 0 τττ = 2 ( α / ) u 0 2 a 0 ττ .
d κ d y = 2 C 15 ( α / ) κ 3 .
d ν d x = 2 α 15 C u 0 2 ψ 3 ,
ν 2 = ν 0 2 1 + sgn C ( x / x 0 ) , x 0 1 = 8 15 α u 0 3 ,
u ( 0 , t ) = A tanh t exp ( t 2 / T 2 ) .

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