Abstract

We show that dark solitons are stabilized with respect to amplitude variations when phase-sensitive amplification and spectral filtering are used in combination to compensate for linear loss. In particular, we show that spectral filtering inhibits the sideband instabilities typical of nonlinear pulses and cw waves in periodically amplified systems, whereas phase-sensitive amplification inhibits the destabilization of the constant-intensity background wave caused by the filtering.

© 1996 Optical Society of America

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References

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1995 (1)

1994 (5)

1993 (2)

1992 (1)

1991 (1)

1990 (2)

A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
[CrossRef] [PubMed]

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

1989 (1)

1985 (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Allen, K. M.

K. M. Allen, N. J. Smith, N. J. Doran, J. A. R. Williams, Opt. Lett. 19, 2086 (1994).
[CrossRef] [PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, “Control strategies for temporal dark solitons,” 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.

Bayer, P. W.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Bourkoff, E.

Chamberlin, R. P.

D. J. Richardson, R. P. Chamberlin, L. Dong, D. N. Payne, Electron. Lett. 30, 1326 (1994).
[CrossRef]

Dong, L.

D. J. Richardson, R. P. Chamberlin, L. Dong, D. N. Payne, Electron. Lett. 30, 1326 (1994).
[CrossRef]

Doran, N. J.

K. M. Allen, N. J. Smith, N. J. Doran, J. A. R. Williams, Opt. Lett. 19, 2086 (1994).
[CrossRef] [PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, “Control strategies for temporal dark solitons,” 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, P.

Giannini, J. A.

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

Goedde, C. G.

Haelterman, M.

Hamaide, J.-P.

Hasegawa, A.

Hawegawa, A.

Hile, C. V.

Ikeda, H.

Joseph, R. I.

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

Kath, W. L.

Kivshar, Y. S.

Kodama, Y.

Kumar, P.

Kutz, J. N.

Levenson, M. D.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Li, R.-D.

Matera, F.

Matsumoto, M.

Mecozzi, A.

Payne, D. N.

D. J. Richardson, R. P. Chamberlin, L. Dong, D. N. Payne, Electron. Lett. 30, 1326 (1994).
[CrossRef]

Richardson, D. J.

D. J. Richardson, R. P. Chamberlin, L. Dong, D. N. Payne, Electron. Lett. 30, 1326 (1994).
[CrossRef]

Romagnoli, M.

Settembre, M.

Shelby, R. M.

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Smith, N. J.

K. M. Allen, N. J. Smith, N. J. Doran, J. A. R. Williams, Opt. Lett. 19, 2086 (1994).
[CrossRef] [PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, “Control strategies for temporal dark solitons,” 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.

Williams, J. A. R.

K. M. Allen, N. J. Smith, N. J. Doran, J. A. R. Williams, Opt. Lett. 19, 2086 (1994).
[CrossRef] [PubMed]

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, “Control strategies for temporal dark solitons,” 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.

Yuen, H. P.

Zhao, W.

Electron. Lett. (1)

D. J. Richardson, R. P. Chamberlin, L. Dong, D. N. Payne, Electron. Lett. 30, 1326 (1994).
[CrossRef]

IEEE J. Quantum Electron. (2)

Y. S. Kivshar, IEEE J. Quantum Electron. 29, 250 (1993).
[CrossRef]

J. A. Giannini, R. I. Joseph, IEEE J. Quantum Electron. 26, 2109 (1990).
[CrossRef]

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

Opt. Lett. (9)

Phys. Rev. B (1)

R. M. Shelby, M. D. Levenson, P. W. Bayer, Phys. Rev. B 31, 5244 (1985).
[CrossRef]

Other (1)

K. M. Allen, N. J. Doran, N. J. Smith, J. A. R. Williams, “Control strategies for temporal dark solitons,” 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 (2)

Fig. 1
Fig. 1

Numerical solution of the NLS equation with loss [Eq. (9)] and with phase-insensitive amplification, showing the decay of the constant-intensity background state near a dark soliton.

Fig. 2
Fig. 2

Numerical solution of the NLS equation with loss [Eq. (9)] and with phase-sensitive amplification [Eq. (3b)]. In this case the decay of the constant-intensity background state around the dark soliton has been arrested, leading to a stable dark-soliton-like steady-state pulse solution. Note that the horizontal scale has been magnified by a factor of 2 in comparison with Fig. 1 better to show the approach to the steady state.

Equations (15)

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q Z = - i 2 2 q T 2 + i q 2 q
q = η tanh ( η T ) exp ( i η 2 Z ) .
q Z = i q 2 q - Γ q ,
q + = e - γ [ ( cosh  α ) q - + e i ϕ ( sinh  α ) q - * ] ,
q ( Z ) = a exp [ - Γ Z + i a 2 ( 1 - e - 2 Γ Z ) / 2 Γ + i θ ] .
A 2 = κ + ψ / l ,
tan  θ = - 1 - exp ( α - γ ¯ ) cos  ψ exp ( α - γ ¯ ) sin  ψ ,
cos  ψ = cosh ( γ ¯ ) / cosh  α .
A 2 κ ± Δ α ,
tan  θ ± l exp ( - γ ¯ ) 2 sinh ( γ ¯ ) Δ α ,
Δ α = 2 ( α - γ ¯ ) tanh ( γ ¯ ) / l 2 .
q Z = - i 2 2 q T 2 + i q 2 q - Γ q ,
q ^ out = F ^ ( ω ) q ^ in ,
U ξ = Δ α U + μ 2 U T 2 - 1 4 4 U T 4 - κ 2 U T 2 - κ 2 U + 2 κ U 3 - U 5 + 3 ( 1 + β ) U ( U T ) 2 + ( 2 + β ) U 2 2 U T 2 .
U = η tanh  η T ,             η = ( κ ± Δ α ) 1 / 2 .

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