Abstract

We propose a novel model for a nonlinear optical lumped amplifier. We consider the optimization problem for reshaping of a picosecond soliton by this amplifier. Fixing a value of the gain provided by the amplifier, we demonstrate that there is a set of values of the model’s parameters at which the fraction of dispersive waves (continuous radiation) in the output energy has a well-pronounced minimum. Next we consider a long lossy fiber with periodically installed amplifiers, for which the total amount of dispersive wave generated by all the amplifiers is also demonstrated to have a minimum. The minimum value of the fraction of the radiation energy gradually increases with increasing gain.

© 1996 Optical Society of America

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References

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    [Crossref]
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1995 (2)

I. Gabitov, D. Holm, B. Luce, and A. Mattheus, Opt. Lett. 20, 2490 (1995).
[Crossref]

S. Burtsev, D. J. Kaup, and B. A. Malomed, “Phys. Rev. E 52, 4474 (1995).
[Crossref]

1994 (2)

1993 (1)

1992 (2)

1990 (1)

1988 (1)

1987 (1)

B. A. Malomed, Opt. Commun. 61, 192 (1987).
[Crossref]

1986 (1)

1982 (1)

1971 (1)

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Burtsev, S.

S. Burtsev, D. J. Kaup, and B. A. Malomed, “Phys. Rev. E 52, 4474 (1995).
[Crossref]

Chbat, M. W.

Desurvire, E.

E. Desurvire, Erbium-Doped Fiber Amplifiers (Wiley-Interscience, New York, 1994).

Doran, N. J.

Gabitov, I.

Gordon, J.

Gordon, J. P.

Hasegawa, A.

Haus, H.

Holm, D.

Islam, M. N.

Kaup, D. J.

S. Burtsev, D. J. Kaup, and B. A. Malomed, “Phys. Rev. E 52, 4474 (1995).
[Crossref]

Kodama, Y.

Luce, B.

Malomed, B. A.

S. Burtsev, D. J. Kaup, and B. A. Malomed, “Phys. Rev. E 52, 4474 (1995).
[Crossref]

B. A. Malomed, J. Opt. Soc. Am. B 11, 1261 (1994).
[Crossref]

B. A. Malomed, Opt. Commun. 61, 192 (1987).
[Crossref]

Matsumoto, M.

Mattheus, A.

Pruchal, P. K.

Romagnoli, M.

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

Shabat, A. B.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

Soccolich, C. E.

Wabnitz, S.

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

Wood, D.

Zakharov, V. E.

V. E. Zakharov and A. B. Shabat, Zh. Eksp. Teor. Fiz. 61, 118 (1971) [Sov. Phys. JETP 34, 62 (1972)].

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Figures (2)

Fig. 1
Fig. 1

Three typical examples of the dependences of the gain factor G and the output energy radiation share R on the nonlinear amplification coefficient A1 at a fixed value of the linear attenuation coefficient A0: (a) A0 = 0.20; (b) A0 = 0.35; (c) A0 = 0.75.

Fig. 2
Fig. 2

Dependences (top) of the nonlinear amplification coefficient A1 and (bottom) of the radiation energy shares (asterisks) for the individual amplifier, R, and (circles) for the long fiber with periodically installed amplifiers, ρ [see the definition of ρ in Eqs. (15) and (16)], on the linear attenuation coefficients A0 at different fixed values of the gain G: (a) G = 2.25; (b) G = 4.00; (c) G = 6.25; (d) G = 9.00.

Tables (1)

Tables Icon

Table 1 Minimum Radiation Versus Gain

Equations (16)

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i u z + u τ τ + 2 | u | 2 u = i ( A 0 + A 1 | u | 2 ) u δ ( z ) .
d u d z = ( A 0 u + A 1 | u | 2 u ) δ ( z ) .
| u out ( τ ) | 2 = A 0 | u in ( τ ) | 2 { A 0 exp ( 2 A 0 ) A 1 [ exp ( 2 A 0 ) 1 ] | u in | 2 } 1 ,
| u in ( τ ) | 2 < A 0 A 1 1 exp ( 2 A 0 ) [ exp ( 2 A 0 ) 1 ] 1 ;
u in ( τ ) = 2 η in sech ( 2 η in τ ) ,
A 1 ( A 1 ) max ( A 0 ) ¼ A 0 [ 1 exp ( 2 A 0 ) ] 1 .
ψ τ ( 1 ) + i λ ψ ( 1 ) u ψ ( 2 ) = 0 ,
ψ τ ( 2 ) i λ ψ ( 2 ) u * ψ ( 1 ) = 0 ,
E = + | u ( τ ) | 2 d τ ,
E = 2 A 0 A 1 { [ exp ( 2 A 0 ) 1 ] [ ( A 0 4 A 1 ) × exp ( 2 A 0 ) + 4 A 1 ] } 1 / 2 × cot 1 { ( A 0 4 A 1 ) exp ( 2 A 0 ) + 4 A 1 4 A 1 [ exp ( 2 A 0 ) 1 ] } .
i u z + u τ τ + 2 | u | 2 u = i γ u ,
E ( z ) = E ( 0 ) exp ( 2 γ z ) .
η ( z ) = η ( 0 ) exp ( 2 γ z ) .
exp ( 4 γ L ) = G .
ρ = n = 0 R exp [ ( 2 γ L + 2 A 0 ) n ] = R { 1 exp [ 2 ( γ L + A 0 ) ] } 1 ,
ρ = R [ 1 exp ( 2 A 0 ) G 1 / 2 ] 1 .

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