Abstract

A method to suppress interactions between adjacent optical dark solitons by means of synchronized phase modulation is presented. Phase modulation with the proper coefficients maintains constant spacing between dark solitons.

© 1995 Optical Society of America

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References

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  1. A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).
  2. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  3. V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)].
  4. J. P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
    [CrossRef] [PubMed]
  5. Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J. P. Hamaide, Opt. Lett. 19, 19 (1994).
    [CrossRef] [PubMed]
  6. W. Zhao, E. Bourkoff, Opt. Lett. 14, 1371 (1989).
    [CrossRef] [PubMed]
  7. H. Ikeda, M. Matsumoto, A. Hasegawa, Opt. Lett. 20, 1113 (1995).
    [CrossRef] [PubMed]
  8. S. Wabnitz, Electron. Lett. 29, 1711 (1993).
    [CrossRef]
  9. N. J. Smith, W. J. Firth, K. J. Blow, K. Smith, Opt. Lett. 19, 16 (1994).
    [CrossRef] [PubMed]

1995 (1)

1994 (2)

1993 (1)

S. Wabnitz, Electron. Lett. 29, 1711 (1993).
[CrossRef]

1991 (1)

1989 (1)

1973 (2)

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

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)].

Blow, K. J.

Bourkoff, E.

Emplit, Ph.

Firth, W. J.

Haelterman, M.

Hamaide, J. P.

Hasegawa, A.

H. Ikeda, M. Matsumoto, A. Hasegawa, Opt. Lett. 20, 1113 (1995).
[CrossRef] [PubMed]

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

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

Ikeda, H.

Kivshar, Yu. S.

Kodama, Y.

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

Matsumoto, M.

Shabat, A. B.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)].

Smith, K.

Smith, N. J.

Tappert, F.

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

Wabnitz, S.

S. Wabnitz, Electron. Lett. 29, 1711 (1993).
[CrossRef]

Zakharov, V. E.

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)].

Zhao, W.

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

S. Wabnitz, Electron. Lett. 29, 1711 (1993).
[CrossRef]

Opt. Lett. (5)

Zh. Eksp. Teor. Fiz. (1)

V. E. Zakharov, A. B. Shabat, Zh. Eksp. Teor. Fiz. 64, 1627 (1973) [Sov. Phys. JETP 37, 823 (1973)].

Other (1)

A. Hasegawa, Y. Kodama, Solitons in Optical Communications (Oxford U. Press, Oxford, 1995).

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Figures (3)

Fig. 1
Fig. 1

Orbits in the T0θ0 plane determined by Eq. (10) for μp = 0.01, η = 1, and ΔT0 = 4.

Fig. 2
Fig. 2

Variation of the pulse separation ΔT versus the normalized distance Z for the initial pulse separation ΔT0 = 4.

Fig. 3
Fig. 3

Maximum magnitude of the variation of the pulse separation, |ΔT − ΔT0|, within 0 < Z < 100 versus the phase-modulation coefficient μp for the initial pulse separation ΔT0 = 4, 5, 6.

Equations (12)

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i q Z - 1 2 2 q T 2 + q 2 q = R ( q , q * ) ,
q ( T , Z ) = η ( Z ) { i cos [ θ 0 ( Z ) 2 ] + sin [ θ 0 ( Z ) 2 ] × tanh [ τ ( Z , T ) ] } exp [ i σ ( Z ) ] ,
d η d Z = d θ 0 d Z = 0 ,             d T 0 d Z = - η cos θ 0 2 ,             d σ d Z = η 2 .
i d d Z - ( q * q T - q q * T ) d T = 2 - ( R * q T + R q * T ) d T .
R ( q , q * ) = μ p cos ( Ω T ) q ,
d θ 0 d Z = μ p 4 p 2 π sin ( Ω T 0 ) 1 cos θ 0 cosech [ p sin ( θ 0 / 2 ) ] ,
T 0 = 1 E 0 - T ( q 2 - η 2 ) d T , E 0 = - ( q 2 - η 2 ) d T .
d T 0 d Z = - η cos θ 0 2 + 1 E 0 - ( T - T 0 ) × [ i ( R * q - R q * ) - 2 η d η d Z ] d T .
d T 0 d Z = - η cos θ 0 2 .
( 3 - p 2 - 2 sin 2 θ 0 2 ) sin θ 0 2 sinh [ p sin ( θ 0 / 2 ) ] - p × sin 2 θ 0 2 cosh [ p sin ( θ 0 / 2 ) ] + p ( p 2 - 3 ) χ [ p sin ( θ 0 / 2 ) ] - 12 μ p p 3 π 2 Ω 2 cos ( Ω T 0 ) = W ,
χ ( x ) cosh x x d x = ln x + 1 2 x 2 2 ! + 1 4 x 4 4 ! + 1 6 x 6 6 ! + .
q ( T , Z = 0 ) = { tanh ( T + Δ T 0 2 ) ( T < 0 ) - tanh ( T - Δ T 0 2 ) ( T 0 ) .

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