Abstract

Whenever a bright soliton is superimposed onto a much longer pulse or a continuous wave at the input of an optical fiber, its nonlinear propagation in the anomalous dispersion regime of the fiber critically depends on the relative phase at input of the two pulses. Whenever the relative phase between the pulses is in the range [−π/2, π/2], a stable solitonlike waveform is formed. Otherwise the soliton pulse rapidly decays into dispersive waves. We describe the potential of this effect for coherent-phase detection of solitons, optical-pulse compression, and all-optical switching. We also discuss the influence on the propagation of solitons plus a background of perturbations such as modulational instability and the Raman self-scattering effect.

© 1992 Optical Society of America

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References

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  1. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988), and references therein.
    [CrossRef]
  3. A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 171 (1973).
    [CrossRef]
  4. A. Hasegawa, Y. Kodama, Opt. Lett. 7, 285 (1982).
    [CrossRef] [PubMed]
  5. V. I. Bespalov, V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].
  6. A. Hasegawa, Opt. Lett. 9, 288 (1974).
    [CrossRef]
  7. N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].
  8. Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).
  9. N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
    [CrossRef]
  10. H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
    [CrossRef]
  11. Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
    [CrossRef] [PubMed]
  12. E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].
  13. F. M. Mitschke, L. F. Mollenauer, Opt. Lett. 11, 659 (1986).
    [CrossRef] [PubMed]
  14. J. P. Gordon, Opt. Lett. 11, 662 (1986).
    [CrossRef] [PubMed]
  15. R. H. Stolen, J. P. Gordon, W. J. Tomlinson, H. A. Haus, J. Opt. Soc. of Am. B 6, 1159 (1989).
    [CrossRef]
  16. K. J. Blow, D. Wood, IEEE J. Quantum Electron. QE-25, 2665 (1989).
    [CrossRef]

1989 (2)

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

K. J. Blow, D. Wood, IEEE J. Quantum Electron. QE-25, 2665 (1989).
[CrossRef]

1988 (2)

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

L. F. Mollenauer, K. Smith, Opt. Lett. 13, 675 (1988), and references therein.
[CrossRef]

1987 (2)

Y. Kodama, K. Nozaki, Opt. Lett. 12, 1038 (1987).
[CrossRef] [PubMed]

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
[CrossRef]

1986 (2)

1985 (1)

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

1982 (1)

1979 (1)

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

1974 (1)

1973 (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

1966 (1)

V. I. Bespalov, V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Akhmediev, N. N.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
[CrossRef]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Bespalov, V. I.

V. I. Bespalov, V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Blow, K. J.

K. J. Blow, D. Wood, IEEE J. Quantum Electron. QE-25, 2665 (1989).
[CrossRef]

Dianov, E. M.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Eleonskii, V. M.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
[CrossRef]

Eleonsky, V. M.

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Fomichev, A. A.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Gordon, J. P.

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

J. P. Gordon, Opt. Lett. 11, 662 (1986).
[CrossRef] [PubMed]

Hadachihara, H.

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

Hasegawa, A.

A. Hasegawa, Y. Kodama, Opt. Lett. 7, 285 (1982).
[CrossRef] [PubMed]

A. Hasegawa, Opt. Lett. 9, 288 (1974).
[CrossRef]

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

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

Haus, H. A.

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

Karasik, A. Ya.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Kodama, Y.

Kulagin, N. E.

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
[CrossRef]

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Ma, Y. C.

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

Mamyshev, P. A.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

McLaughlin, D. W.

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

Mitschke, F. M.

Mollenauer, L. F.

Moloney, J. V.

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

Newell, A. C.

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

Nozaki, K.

Prokhorov, A. M.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Serkin, V. N.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Smith, K.

Stel’markh, M. F.

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

Stolen, R. H.

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

Talanov, V. I.

V. I. Bespalov, V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Tappert, F.

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

Tomlinson, W. J.

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

Wood, D.

K. J. Blow, D. Wood, IEEE J. Quantum Electron. QE-25, 2665 (1989).
[CrossRef]

Appl. Phys. Lett. (2)

A. Hasegawa, F. Tappert, Appl. Phys. Lett. 23, 142 (1973).
[CrossRef]

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

IEEE J. Quantum Electron. (1)

K. J. Blow, D. Wood, IEEE J. Quantum Electron. QE-25, 2665 (1989).
[CrossRef]

J. Math. Phys. (1)

H. Hadachihara, D. W. McLaughlin, J. V. Moloney, A. C. Newell, J. Math. Phys. 29, 63 (1988).
[CrossRef]

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

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

Opt. Lett. (6)

Pis’ma Zh. Eksp. Teor. Fiz. (1)

V. I. Bespalov, V. I. Talanov, Pis’ma Zh. Eksp. Teor. Fiz. 3, 471 (1966) [JETP Lett. 3, 307 (1966)].

Stud. Appl. Math. (1)

Y. C. Ma, Stud. Appl. Math. 60, 43 (1979).

Teor. Mat. Fiz. (1)

N. N. Akhmediev, V. M. Eleonskii, N. E. Kulagin, Teor. Mat. Fiz. 72, 183 (1987) [Theor. Math. Phys. 72, 809 (1987)].
[CrossRef]

Zh. Eksp. Teor. Fiz. (1)

N. N. Akhmediev, V. M. Eleonsky, N. E. Kulagin, Zh. Eksp. Teor. Fiz. 89, 1542 (1985) [Sov. Phys. JETP 62, 894 (1985)].

Other (1)

E. M. Dianov, A. Ya. Karasik, P. A. Mamyshev, A. M. Prokhorov, V. N. Serkin, M. F. Stel’markh, A. A. Fomichev, Pis’ma Zh. Eksp. Teor. Fiz.41, 242 [JETP Lett. 41, 295 (1985)].

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Figures (10)

Fig. 1
Fig. 1

Trajectory of the middle point of the soliton on the complex plane of the field (dashed circle) for a = 0.25. The solid circle indicates the set of initial conditions corresponding to Eq. (6).

Fig. 2
Fig. 2

Evolution of a soliton on a cw background with a = 0.1.

Fig. 3
Fig. 3

Same as Fig. 2, with a = 0.25. One period of the solution is shown.

Fig. 4
Fig. 4

Same as in Fig. 3, with a = 0.45.

Fig. 5
Fig. 5

Evolution of the superposition of a bright pulse plus the cw background for a = 0.25 and various initial relative phases: (a) relative phase Δϕ = π/8, (b) Δϕ = 5π/8, (c) Δϕ = 7π/8, (d) Δϕ = 9π/8, (e) Δϕ = 3π/2, (f) Δϕ = 7π/4.

Fig. 6
Fig. 6

As in Fig. 5(c), with a = 0.45. The relative phase is again Δϕ = 7π/8.

Fig. 7
Fig. 7

Instability of the finite-width background pulse. Here a = 0.4, whereas the relative phase Δϕ = π.

Fig. 8
Fig. 8

Evolutions of initially modulated ( = 0.01, Ω = 21/2a) solitons on a background with (a) a = 0.1, (b) a = 0.25.

Fig. 9
Fig. 9

Intensity profile of the soliton as in Fig. 8(b) with weak initial modulation (curve 1). Curves 2 and 3 show the calculated intensity profiles at the distances ξ = 2Λ/3 and ξ = 2Λ, respectively.

Fig. 10
Fig. 10

Effects of Raman self-scattering on a soliton on a Gaussian background with a = 0.25 and for an initial one-soliton pulse time width of tFWHM = 215 fs.

Equations (14)

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n = n 0 + n 2 E 2 ,
i u ξ + 1 2 2 u τ 2 + u 2 u = 0 ,
ξ = k z / q 2 ,             τ = ( t - z / V ) / q , u = A ( 2 π n 2 / λ c A eff k ) 1 / 2 q .
u = a 1 / 2 exp ( i a ξ + i ϕ 1 ) ,
u = i p cosh ( p τ ) exp ( i p 2 2 ξ + i ϕ 2 ) .
u ( ξ = 0 ) = [ a 1 / 2 + i p cosh ( p τ ) exp ( i Δ ϕ ) ] exp ( i ϕ 1 )
u = [ a 1 / 2 + 2 1 / 2 μ μ cos ( μ ξ ) + i sin ( μ ξ ) ( 2 a ) 1 / 2 cos ( μ ξ ) + cosh ( p τ ) ] × exp ( i a ξ + ϕ 1 ) ,
u = 2 ( 1 - a ) cos [ μ ( ξ - ξ 0 ) ] + ( 2 a ) 1 / 2 cosh [ p ( τ - τ 0 ) ] + i 2 μ sin [ μ ( ξ - ξ 0 ) ] 2 a 1 / 2 cos [ μ ( ξ - ξ 0 ) ] + 2 1 / 2 cosh [ p ( τ - τ 0 ) ] exp ( a ξ + ϕ 1 ) ,
u ( ξ = 0 ) = ( a 1 / 2 ± i p cosh p τ ) exp ( i ϕ 1 ) ,
[ Re ( u ) + a 1 / 2 ] 2 + [ Im ( u ) ] 2 = 2.
[ Re ( u ) - a 1 / 2 ] 2 + [ Im ( u ) ] 2 = p 2 .
u ( ξ = 0 ) = [ a 1 / 2 + i p sech ( p τ ) exp ( i Δ ϕ ) ] × exp ( i ϕ 1 ) + cos Ω τ .
i u ξ + 1 2 2 u τ 2 + α u u 2 + ( 1 - α ) u - τ f ( τ - s ) u ( s ) 2 d s = 0 ,
f ( s ) = τ 1 2 + τ 2 2 τ 1 τ 2 2 exp ( - s / τ 2 ) sin ( t / τ 1 ) ,

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