Abstract

We have systematically investigated soliton amplification and reshaping by a nonlinear optical amplifier consisting of an active second-harmonic-generating element and a piece of passive dechirping fiber with a dispersion different from that in the system fiber. In the active element the fundamental harmonic is damped by enhanced losses, whereas the second harmonic is amplified through the external pumping. By selecting the length of the dechirping fiber we find it possible to achieve practically ideal soliton amplification, viz., low-power input (fundamental) solitons are amplified and then released into the system fiber as virtually unchirped high-power fundamental solitons. We have found that a power gain for the soliton of as much as 20–25 dB can be readily achieved; the length or the dispersion of the dechirping fiber is not critical for the degree of soliton amplification. The dispersion of this fiber can be merely twice that of the standard system fiber, and its length can be <10 km. Moreover, we have found that the dechirping fiber is not always needed, although the effective power gain in these cases is smaller, 10–12 dB. We have further investigated the influence of a random amplitude noise added to the input soliton. We found that the soliton amplification and reshaping scheme proposed is reasonably stable against this noise, especially when the dechirping fiber is not used.

© 1998 Optical Society of America

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References

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    [CrossRef] [PubMed]
  2. A. Hasegawa and Y. Kodama, Solitons In Optical Communications (Oxford U. Press, Oxford, 1995).
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    [CrossRef]
  4. M. Matsumoto, H. Ikeda, and A. Hasegawa, Opt. Lett. 19, 183 (1994); Electron. Lett. 31, 482 (1995); H. Ikeda, M. Matsumoto, and A. Hasegawa, Opt. Lett. OPLEDP 20, 1113 (1995).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  7. B. A. Malomed, G. D. Peng, and P. L. Chu, Opt. Lett. 21, 330 (1996).
    [CrossRef] [PubMed]
  8. P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
  11. G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
    [CrossRef]

1997

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 140, 289 (1997).
[CrossRef]

1996

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

S. Burtsev, D. J. Kaup, and B. A. Malomed, J. Opt. Soc. Am. B 13, 888 (1996).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, Opt. Lett. 21, 330 (1996).
[CrossRef] [PubMed]

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
[CrossRef]

1994

1988

1987

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

1986

Burtsev, S.

Chu, P. L.

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 140, 289 (1997).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, Opt. Lett. 21, 330 (1996).
[CrossRef] [PubMed]

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
[CrossRef]

Doran, N.

Gordon, J. P.

Hagan, D. J.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Hasegawa, A.

Haus, H. A.

Kaup, D. J.

Kodama, Y.

Malomed, B. A.

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 140, 289 (1997).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
[CrossRef]

S. Burtsev, D. J. Kaup, and B. A. Malomed, J. Opt. Soc. Am. B 13, 888 (1996).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, Opt. Lett. 21, 330 (1996).
[CrossRef] [PubMed]

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

Matsumoto, M.

Peng, G. D.

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 140, 289 (1997).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
[CrossRef]

B. A. Malomed, G. D. Peng, and P. L. Chu, Opt. Lett. 21, 330 (1996).
[CrossRef] [PubMed]

Stegeman, G. I.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Torner, L.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Wood, D.

J. Opt. Soc. Am. B

Opt. Commun.

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

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 128, 76 (1996).
[CrossRef]

P. L. Chu, B. A. Malomed, and G. D. Peng, Opt. Commun. 140, 289 (1997).
[CrossRef]

Opt. Lett.

Opt. Quantum Electron.

G. I. Stegeman, D. J. Hagan, and L. Torner, Opt. Quantum Electron. 28, 1691 (1996).
[CrossRef]

Other

A. Hasegawa and Y. Kodama, Solitons In Optical Communications (Oxford U. Press, Oxford, 1995).

M. Matsumoto, H. Ikeda, and A. Hasegawa, Opt. Lett. 19, 183 (1994); Electron. Lett. 31, 482 (1995); H. Ikeda, M. Matsumoto, and A. Hasegawa, Opt. Lett. OPLEDP 20, 1113 (1995).
[CrossRef] [PubMed]

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Figures (11)

Fig. 1
Fig. 1

(a) Output power and (b) net change of the FH phase versus the input power, as obtained by numerical integration of Eqs. (4)–(7). Loss and gain parameters are γ=2 and Γ=1; the length of the active SHG element is L=π. The plots are given for two different values of the mismatch, β.

Fig. 2
Fig. 2

OVI characteristics as in Fig. 1 for two different values of the loss parameter Γ. Here the gain is γ=2, the amplifier length is L=π/2, and the mismatch is β=0.5.

Fig. 3
Fig. 3

Optimum dispersion versus input peak power. The length of the active SHG section is (a) L=π and (b) L=π/2. In (a) the gain and loss parameters are γ=2 and Γ=1, respectively, and the values of the mismatch β are indicated. In (b) the gain parameter is γ=2 and the mismatch β is 0.5. The values of the loss parameters Γ are indicated. In (a) and (b) a dashed horizontal line indicates Dopt=1.

Fig. 4
Fig. 4

Examples of the amplified pulse directly released into the system fiber, without use of the dechirping pulse. (a) Dopt =1.0001, (b) Dopt=1.0093. The input peak power and the mismatch are (a) Pin=0.15 and β=0.5, (b) Pin=0.22 and β=0.05; the corresponding output powers Pout are 1.6 and 3.5. The other parameters are γ=2, Γ=1, and L=π.

Fig. 5
Fig. 5

Example of the amplified pulse released into the system fiber in the form of a persistent breather. Here the length ZD of the dechirping segment is chosen arbitrarily. Inset, the breather’s peak power as a function of propagation distance z. The values of the parameters are γ=2, Γ=1, β=0.05, L=π, D =2, and ZD=0.15π; the peak power of the input soliton is Pin =0.244.

Fig. 6
Fig. 6

Maximum and minimum powers of the output breather versus normalized length ZD/π of the dechirping fiber. The powers were measured after the output pulse was released into the system fiber and allowed to propagate over a distance equal to four soliton periods. The mismatch coefficient and input pulse’s power are (a) β=0.5 and Pin=0.175, (b) β=0.05 and Pin=0.243. The values of the other parameters are γ=2, Γ =1, L=π, and D=2.

Fig. 7
Fig. 7

Amplified pulse released into the system fiber when length ZD of the dechirping segment is chosen to correspond to the overlapping points in Fig. 6(b) at (a) ZD=0.08π, (b) ZD=0.23π. The arrangement of this figure is similar to that of Fig. 5.  

Fig. 8
Fig. 8

Effect produced on soliton amplification by the noise when the dechirping fiber is employed. Here a random noise with relative intensity 4% (in terms of the peak power) was added to the input soliton.

Fig. 9
Fig. 9

Noise effect on soliton amplification when the dechirping fiber is employed. (a), (b) maximum and minimum peak powers, respectively, for six different realizations of the random noise. All parameters and relative noise intensity are the same as in Fig. 8. Horizontal lines, corresponding maximum and minimum peak powers when the input is noise free.

Fig. 10
Fig. 10

Noise effect on soliton amplification when the dechirping fiber is not employed. (a), (b) same values of the parameters as in Fig. 4, except that random noise with a relative intensity 4% (in terms of the peak power) was added to the input soliton. For comparison, the same noise realization as in Fig. 8 are used.

Fig. 11
Fig. 11

Noise effect on soliton amplification when the dechirping fiber is not employed. (a), (b) maximum and minimum peak powers, respectively, for six different realizations of the random noise. Here all the values of the parameters and the relative noise intensity are the same as in Fig. 10. For comparison, the same noise realizations as in Fig. 9 are used.

Equations (12)

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i dudζ+u*v=-iΓu,
i dvdζ+12 u2-βv=iγv,
u2p cos θ exp[(i/2)(ϕ+ψ)],
vp sin θ exp[i(ϕ-ψ)],
dpdζ=½(γ-Γ)p-½(γ+Γ)p cos(2θ),
dθdζ=-p cos θ sin(2ψ)+½(γ+Γ)sin(2θ),
dψdζ=-p 3 cos2 θ-2sin θ cos(2ψ)+β.
ddζ [½(ϕ+ψ)]=p sin θ cos(2ψ).
iuz+½Duττ+|u|2u=0,
u(z, τ)=P sechτWexp12 iPz,WD/P.
Dopt=PW2.
Greshaping10 log(Pout/Pin),

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