Abstract

Transmission control of dark solitons against various perturbations is possible by use of amplifiers with nonlinear gain. Stable propagation of gray and/or black solitons is achieved even in the presence of the Raman effect and mutual interactions between neighboring dark solitons.

© 1995 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  2. V. E. Zakharov, A. B. Shabat, Sov. Phys. JETP 37, 823 (1973).
  3. W. Zhao, E. Bourkoff, Opt. Lett. 14, 703 (1989).
    [CrossRef] [PubMed]
  4. M. Lisak, D. Anderson, B. A. Malomed, Opt. Lett. 16, 1936 (1991).
    [CrossRef] [PubMed]
  5. J. P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
    [CrossRef] [PubMed]
  6. Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
    [CrossRef]
  7. W. Zhao, E. Bourkoff, Opt. Lett. 14, 1371 (1989).
    [CrossRef] [PubMed]
  8. W. Zhao, E. Bourkoff, J. Opt. Soc. Am. B 9, 1134 (1992).
    [CrossRef]
  9. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
    [CrossRef] [PubMed]
  10. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  11. Y. Kodama, Department of Mathematics, Ohio State University, Columbus, Ohio 43210, and A. Maruta, Department of Communication Engineering, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565, Japan (personal communication, 1994).
  12. A. Maruta, Y. Kodama, A. Hasegawa, “Suppression of interaction between adjacent optical dark solitons by means of synchronized phase modulation,” submitted toOpt. Lett.
    [PubMed]
  13. K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.
  14. I. M. Uzunov, V. S. Gerdjikov, Phys. Rev. A 47, 1582 (1993).
    [CrossRef] [PubMed]
  15. Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
    [CrossRef]
  16. N. J. Doran, D. Wood, Opt. Lett. 13, 56 (1988).
    [CrossRef] [PubMed]
  17. M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).
  18. M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
    [CrossRef]

1995

M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
[CrossRef]

1994

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
[CrossRef]

1993

I. M. Uzunov, V. S. Gerdjikov, Phys. Rev. A 47, 1582 (1993).
[CrossRef] [PubMed]

1992

1991

1989

1988

1973

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

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

Allen, K. M.

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.

Anderson, D.

Bourkoff, E.

Doran, N. J.

N. J. Doran, D. Wood, Opt. Lett. 13, 56 (1988).
[CrossRef] [PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.

Emplit, Ph.

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
[CrossRef]

J. P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

Gerdjikov, V. S.

I. M. Uzunov, V. S. Gerdjikov, Phys. Rev. A 47, 1582 (1993).
[CrossRef] [PubMed]

Haelterman, M.

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
[CrossRef]

J. P. Hamaide, Ph. Emplit, M. Haelterman, Opt. Lett. 16, 1578 (1991).
[CrossRef] [PubMed]

Hamaide, J. P.

Hamaide, J.-P.

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
[CrossRef]

Hasegawa, A.

M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
[CrossRef]

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
[CrossRef] [PubMed]

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

A. Maruta, Y. Kodama, A. Hasegawa, “Suppression of interaction between adjacent optical dark solitons by means of synchronized phase modulation,” submitted toOpt. Lett.
[PubMed]

M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).

Haus, H. A.

Ikeda, H.

M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
[CrossRef]

M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).

Kivshar, Yu. S.

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

Yu. S. Kivshar, M. Haelterman, Ph. Emplit, J.-P. Hamaide, Opt. Lett. 19, 9 (1994).
[CrossRef]

Kodama, Y.

Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
[CrossRef] [PubMed]

A. Maruta, Y. Kodama, A. Hasegawa, “Suppression of interaction between adjacent optical dark solitons by means of synchronized phase modulation,” submitted toOpt. Lett.
[PubMed]

Y. Kodama, Department of Mathematics, Ohio State University, Columbus, Ohio 43210, and A. Maruta, Department of Communication Engineering, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565, Japan (personal communication, 1994).

Lai, Y.

Lisak, M.

Malomed, B. A.

Maruta, A.

Y. Kodama, Department of Mathematics, Ohio State University, Columbus, Ohio 43210, and A. Maruta, Department of Communication Engineering, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565, Japan (personal communication, 1994).

A. Maruta, Y. Kodama, A. Hasegawa, “Suppression of interaction between adjacent optical dark solitons by means of synchronized phase modulation,” submitted toOpt. Lett.
[PubMed]

Matsumoto, M.

M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
[CrossRef]

M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).

Mecozzi, A.

Moores, J. D.

Shabat, A. B.

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

Smith, N. J.

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.

Tappert, F.

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

Uda, T.

M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).

Uzunov, I. M.

I. M. Uzunov, V. S. Gerdjikov, Phys. Rev. A 47, 1582 (1993).
[CrossRef] [PubMed]

Williams, J. A. R.

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.

Wood, D.

Yang, X.

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

Zakharov, V. E.

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

Zhao, W.

Appl. Phys. Lett.

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

Electron. Lett.

M. Matsumoto, H. Ikeda, A. Hasegawa, Electron. Lett. 31, 482 (1995).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Lett.

Phys. Rev. A

I. M. Uzunov, V. S. Gerdjikov, Phys. Rev. A 47, 1582 (1993).
[CrossRef] [PubMed]

Phys. Rev. E

Yu. S. Kivshar, X. Yang, Phys. Rev. E 49, 1657 (1994).
[CrossRef]

Sov. Phys. JETP

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

Other

M. Matsumoto, H. Ikeda, T. Uda, A. Hasegawa, “Stable soliton transmission in the system with nonlinear gain,” J. Lightwave Technol. (to be published).

Y. Kodama, Department of Mathematics, Ohio State University, Columbus, Ohio 43210, and A. Maruta, Department of Communication Engineering, Faculty of Engineering, Osaka University, 2-1, Yamada-oka, Suita, Osaka 565, Japan (personal communication, 1994).

A. Maruta, Y. Kodama, A. Hasegawa, “Suppression of interaction between adjacent optical dark solitons by means of synchronized phase modulation,” submitted toOpt. Lett.
[PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, in Nonlinear Guided Waves and Their Applications, Vol. 6 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), pp. 236–238.

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Figures (3)

Fig. 1
Fig. 1

Potential Φ versus the internal phase ϕ for u0 = 1, δ = −0.15, γ1 = 0.4, and γ2 = −0.25 when the Raman effect is not included (σ = 0; solid curve) and when it is included (σ = 0.01; dashed curve).

Fig. 2
Fig. 2

Velocity of a dark soliton versus propagation distance under the influence of the Raman effect (σ = 0.01) with and without the control by nonlinear gain. The solid curves are the numerical results, and the dashed curves are the results of the perturbation analysis.

Fig. 3
Fig. 3

Contour plots for the propagation of a pair of dark solitons with an initial separation of t0= 2. (a) without and (b) with nonlinear gain.

Equations (16)

Equations on this page are rendered with MathJax. Learn more.

i u z - 1 2 2 u t 2 + u 2 u = 0 ,
u ( z , t ) = ( η tanh ζ - i κ ) exp ( i u 0 2 z ) , ζ = η ( t - κ z ) ,             η = u 0 cos ϕ ,             κ = u 0 sin ϕ ,
i u z - 1 2 2 u t 2 + u 2 u = i R ( u ) .
i d a d z + a 2 a = i R ( a ) .
u ( z , t ) = a ( z ) q ( z , t ) ,
i q z - 1 2 2 q t 2 + a 2 ( q 2 - 1 ) q = i R ( a q ) - R ( a ) q a i R .
q ( z , t ) = cos ϕ tanh ζ - i sin ϕ ζ = η ( t - κ z ) ,             η = a cos ϕ ,             κ = a sin ϕ .
P = i 2 - ( q q * t - q * q t ) d t - arg ( q ) t = - t = .
4 cos 2 ϕ d ϕ d z = 2 - Im ( R * ) cos ϕ sech 2 ζ d ζ .
d u 0 d z = δ u 0 + γ 1 u 0 3 + γ 2 u 0 5 .
R = γ 1 u 0 2 ( q 2 - 1 ) q + γ 2 u 0 4 ( q 4 - 1 ) q .
d ϕ d z = - 1 3 γ 1 u 0 2 sin 2 ϕ + 2 15 γ 2 u 0 4 ( 2 cos 2 ϕ - 5 ) sin 2 ϕ .
d Φ d ϕ = - d ϕ d z .
R = γ 1 u 0 2 ( q 2 - 1 ) q + γ 2 u 0 4 ( q 4 - 1 ) q - i σ u 0 2 q 2 t q .
d ϕ d z = - 1 3 γ 1 u 0 2 sin 2 ϕ + 2 15 γ 2 u 0 4 ( 2 cos 2 ϕ - 5 ) × sin 2 ϕ + 4 15 σ u 0 5 cos 3 ϕ .
u ( 0 , t ) = { tanh ( t + t 0 ) ( - < t < 0 ) - tanh ( t - t 0 ) ( 0 t < ) ,

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