Abstract

A new method of controlling optical solitons by means of light wave(s) in fibers is presented. By a proper choice of light wave(s), parametric four-wave mixing can control the soliton shape as well as the soliton parameters (amplitude, frequency, velocity, and position).

© 1995 Optical Society of America

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References

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  1. J. P. Gordon, H. A. Haus, Opt. Lett. 11,665 (1986).
    [CrossRef] [PubMed]
  2. C. Desem, P. L. Chu, in Optical Solitons—Theory and Experiment, J. R. Taylor ed. (Cambridge U. Press, Cambridge, 1992), Chap. 5.
  3. J. P. Gordon, Opt. Lett. 8, 596 (1983).
    [CrossRef] [PubMed]
  4. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
    [CrossRef] [PubMed]
  5. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  6. J. P. Gordon, Opt. Lett. 11,662 (1986).
    [CrossRef] [PubMed]
  7. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]
  8. A. Mecozzi, J. D. Moores, H. A. Haus, Y. Lai, Opt. Lett. 16, 1841 (1991).
    [CrossRef] [PubMed]
  9. Y. Kodama, A. Hasegawa, Opt. Lett. 17,31 (1992).
    [CrossRef] [PubMed]
  10. L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
    [CrossRef]
  11. L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
    [CrossRef] [PubMed]
  12. Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [CrossRef]
  13. M. Matsumoto, H. Ikeda, A. Hasegawa, Opt. Lett. 19, 183 (1994).
    [CrossRef] [PubMed]
  14. M. Matsumoto, A. Hasegawa, Opt. Lett. 18, 897 (1993).
    [CrossRef] [PubMed]
  15. M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
    [CrossRef]
  16. S. Wabnitz, Electron. Lett. 29, 1711 (1993).
    [CrossRef]
  17. V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
    [CrossRef] [PubMed]
  18. J. P. LaSalle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications (Academic, New York, 1961), Chap. 2, pp. 37–41.
  19. M. A. Lavrent’ev, L. A. Lyusternik, The Calculus of Variations, 2nd ed. (Gostechizdat, Moscow, 1950), Chap. 9, p. 265.
  20. V. S. Grigoryan, Phys. Lett. A 149, 371 (1990).
    [CrossRef]

1994

1993

1992

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

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, S. G. Evangelides, Opt. Lett. 17, 1575 (1992).
[CrossRef] [PubMed]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

1991

1990

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

V. S. Grigoryan, Phys. Lett. A 149, 371 (1990).
[CrossRef]

1987

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 12, 355 (1987).
[CrossRef] [PubMed]

1986

1983

Butylkin, V. S.

V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
[CrossRef] [PubMed]

Chronopulo, Yu. G.

V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
[CrossRef] [PubMed]

Chu, P. L.

C. Desem, P. L. Chu, in Optical Solitons—Theory and Experiment, J. R. Taylor ed. (Cambridge U. Press, Cambridge, 1992), Chap. 5.

Desem, C.

C. Desem, P. L. Chu, in Optical Solitons—Theory and Experiment, J. R. Taylor ed. (Cambridge U. Press, Cambridge, 1992), Chap. 5.

Evangelides, S. G.

Gordon, J. P.

Grigoryan, V. S.

V. S. Grigoryan, Phys. Lett. A 149, 371 (1990).
[CrossRef]

Harvey, G. T.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Ikeda, H.

Kaplan, A. E.

V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
[CrossRef] [PubMed]

Kodama, Y.

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

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Kubota, H.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

Lai, Y.

LaSalle, J. P.

J. P. LaSalle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications (Academic, New York, 1961), Chap. 2, pp. 37–41.

Lavrent’ev, M. A.

M. A. Lavrent’ev, L. A. Lyusternik, The Calculus of Variations, 2nd ed. (Gostechizdat, Moscow, 1950), Chap. 9, p. 265.

Lefschetz, S.

J. P. LaSalle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications (Academic, New York, 1961), Chap. 2, pp. 37–41.

Lichtman, E.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Lyusternik, L. A.

M. A. Lavrent’ev, L. A. Lyusternik, The Calculus of Variations, 2nd ed. (Gostechizdat, Moscow, 1950), Chap. 9, p. 265.

Matsumoto, M.

Mecozzi, A.

Mitschke, F. M.

Mollenauer, L. F.

Moores, J. D.

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

Neubelt, M. J.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Nyman, B. M.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Romagnoli, M.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

Wabnitz, S.

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

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Yakubovich, E. I.

V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
[CrossRef] [PubMed]

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

Electron. Lett.

L. F. Mollenauer, E. Lichtman, G. T. Harvey, M. J. Neubelt, B. M. Nyman, Electron. Lett. 28, 792 (1992).
[CrossRef]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1990).
[CrossRef]

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

IEEE J. Quantum Electron.

Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
[CrossRef]

Opt. Lett.

Phys. Lett. A

V. S. Grigoryan, Phys. Lett. A 149, 371 (1990).
[CrossRef]

Other

V. S. Butylkin, A. E. Kaplan, Yu. G. Chronopulo, E. I. Yakubovich, Resonant Nonlinear Interactions of Light with Matter (Springer-Verlag, Berlin, 1989), Chap. 6, p. 152;Chap. 7, p. 206.
[CrossRef] [PubMed]

J. P. LaSalle, S. Lefschetz, Stability by Liapunov’s Direct Method with Applications (Academic, New York, 1961), Chap. 2, pp. 37–41.

M. A. Lavrent’ev, L. A. Lyusternik, The Calculus of Variations, 2nd ed. (Gostechizdat, Moscow, 1950), Chap. 9, p. 265.

C. Desem, P. L. Chu, in Optical Solitons—Theory and Experiment, J. R. Taylor ed. (Cambridge U. Press, Cambridge, 1992), Chap. 5.

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Figures (1)

Fig. 1
Fig. 1

Reshaping of an optical soliton by means of controlling light waves through parametric four-wave interactions. A soliton is seen to be reshaped and constructed from a noisy initial condition. The initial condition for (a) is 1 . 5 sech 12 ( 2 τ / 8 ) exp ( i 5 τ ) with Gaussian noise, whereas that for (b) is only Gaussian noise.

Equations (17)

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ω 1 + ω 2 = 2 ω s ,
i ( z + 1 υ 1 t ) q 1 + d 1 2 2 q 1 t 2 + r 1 [ | q 1 | 2 q 1 + 2 ( | q s | 2 + | q 2 | 2 ) q 1 + q s 2 q 2 * exp ( i Δ k z ) ] = i δ 1 q 1 + t χ 1 ( t t ) q 1 ( z , t ) d t ,
i ( z + 1 υ 2 t ) q 2 + d 2 2 2 q 2 t 2 + r 2 [ | q 2 | 2 q 2 + 2 ( | q s | 2 + | q 1 | 2 ) q 2 + q s 2 q 1 * exp ( i Δ kz ) ] = i δ 2 q 2 + t χ 2 ( t t ) q 2 ( z , t ) d t ,
i ( z + 1 υ s t ) q s + 1 2 2 q s t 2 + | q s | 2 q s + 2 ( | q 1 | 2 + | q 2 | 2 ) q s + 2 q s * q 1 q 2 exp ( i Δ kz ) = i δ s q s + i β 2 q s t 2 ,
| q s | , | q 1 | | q 2 |
i q z + 1 2 2 q τ 2 + | q | 2 q + 2 | q 1 | 2 q + 2 q 1 q 2 q * = i δ s q + i β 2 q τ 2 ,
φ z = 2 A 1 A 2 cos ( 2 φ φ 1 φ 2 ) + D ,
D = 1 A { β ( 2 A τ φ τ + A 2 φ τ 2 ) + 1 2 [ 2 A τ 2 A ( φ τ ) 2 ] } + A 2 + 2 A 1 2
Δ φ = 2 φ φ 1 φ 2 = π 2 + ,
A z = [ δ s + P ( τ ) ] A + β 2 A τ 2 ,
P ( τ ) = 2 A 1 A 2 = 2 A 2 A 1 0 cos ( Ω τ ) = P 0 cos ( Ω τ ) .
U = T 0 / 2 T 0 / 2 { [ δ s + P ( τ ) ] A 2 + β ( A τ ) 2 } d τ .
d U d z = 2 T 0 / 2 T 0 / 2 { [ δ s + P ( τ ) ] A + β 2 A τ 2 } 2 d τ < 0
β 2 y τ 2 + [ δ s + P ( τ ) ] y + λ y = 0
β 2 A τ 2 + [ δ s + P ( τ ) ] A = 0.
A 0 = sech r ( 1 2 Ω τ )
δ s + P ( τ ) = β 2 Ω 2 [ r 2 + r ( r + 1 ) sech 2 ( 1 2 Ω τ ) ]

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