Abstract

Bound higher-order solitons, sometimes called breather solitons, can easily be broken apart by small perturbations. We discuss the conditions for breakup of bound solitons and describe a method to determine the details of the soliton breakup. Using this method, we illustrate the breakup of bound solitons by optical filters, by asymmetric FM modulation (not AM or symmetric FM modulation), and by superposition with other optical pulses.

© 1992 Optical Society of America

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References

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  1. Y. Kodama, A. Hasegawa, IEEE J. Quantum Electron. QE-23, 510 (1987).
    [CrossRef]
  2. K. Tai, A. Hasegawa, N. Bekki, Opt. Lett. 13, 392 (1988).
    [CrossRef] [PubMed]
  3. Y. Silberberg, Opt. Lett. 15, 1005 (1990).
    [CrossRef] [PubMed]
  4. V. E. Zahkarov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).
  5. J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
    [CrossRef]
  6. An asymmetric perturbation can be resolved into both symmetric and antisymmetric components.
  7. H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), p. 67.
  8. H. A. Haus, K. Watanabe, Y. Yamamoto, J. Opt. Soc. Am. B 6, 1138 (1989).
    [CrossRef]
  9. S. R. Friberg, Opt. Lett. 16, 1484 (1991).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

1989 (1)

1988 (1)

1987 (1)

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

1974 (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

1972 (1)

V. E. Zahkarov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Bekki, N.

Friberg, S. R.

Hasegawa, A.

K. Tai, A. Hasegawa, N. Bekki, Opt. Lett. 13, 392 (1988).
[CrossRef] [PubMed]

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

Haus, H. A.

H. A. Haus, K. Watanabe, Y. Yamamoto, J. Opt. Soc. Am. B 6, 1138 (1989).
[CrossRef]

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), p. 67.

Kodama, Y.

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

Satsuma, J.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Shabat, A. B.

V. E. Zahkarov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Silberberg, Y.

Tai, K.

Watanabe, K.

Yajima, N.

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Yamamoto, Y.

Zahkarov, V. E.

V. E. Zahkarov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

IEEE J. Quantum Electron. (1)

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

J. Opt. Soc. Am. B (1)

Opt. Lett. (3)

Prog. Theor. Phys. Suppl. (1)

J. Satsuma, N. Yajima, Prog. Theor. Phys. Suppl. 55, 284 (1974).
[CrossRef]

Sov. Phys. JETP (1)

V. E. Zahkarov, A. B. Shabat, Sov. Phys. JETP 34, 62 (1972).

Other (2)

An asymmetric perturbation can be resolved into both symmetric and antisymmetric components.

H. A. Haus, Waves and Fields in Optoelectronics (Prentice-Hall, Englewood Cliffs, N.J., 1984), p. 67.

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Figures (4)

Fig. 1
Fig. 1

Effect of a Fabry–Perot filter on the eigenvalues of an N = 3 soliton. (a) The real part and (b) the imaginary part of the eigenvalues (corresponding to the velocity and the energy, respectively) of the component solitons are plotted as a function of the detuning of the soliton from the center frequency of the filter.

Fig. 2
Fig. 2

Velocity eigenvalues for an N = 3 soliton perturbed by an antisymmetric FM modulation. The eigenvalues are plotted as a function of (a) the modulation depth and (b) the modulation frequency Δm.

Fig. 3
Fig. 3

Propagation of (a) an unperturbed N = 3 soliton and (b) an N = 3 soliton with a superimposed N = 1 soliton. The total propagation distance is five soliton periods.

Fig. 4
Fig. 4

Eigenvalues of the superposition of an N = 3 and N = 1 soliton. (a) The real part and (b) the imaginary part correspond to the velocity and energy of the component solitons, respectively.

Equations (3)

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i ψ 1 t + q ψ 2 = ζ ψ 1 , - i ψ 2 t + q * ψ 1 = ζ ψ 2 .
q n ( t , z ) = 2 η n sech [ 2 η n ( 1.76 t τ 0 - π κ n z z 0 ) ] × exp [ - i 3.52 κ n t τ 0 + i π ( κ n 2 - η n 2 ) z z 0 ] ,
F ( ω ) = ( R - 1 ) exp ( i ω / ω f ) 1 - R exp ( 2 i ω / ω f ) ,

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