Abstract

In optical fiber transmission systems near the zero-dispersion wavelength that use in-line erbium-doped fiber amplifiers (EDFA’s), the enhancement of optical amplifier noise caused by four-wave mixing (FWM) in transmission fibers degrades signal-to-noise ratio (SNR) excessively. We theoretically show that the enhancement of amplifier noise by the FWM in transmission fibers can be effectively eliminated by implementing in-line phase-sensitive amplifiers (PSA’s). Small-signal analysis of the nonlinear Schrödinger equation shows that the transmission distance limited by the SNR of an in-line PSA system is expanded four times more than that of an in-line EDFA system.

© 1997 Optical Society of America

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References

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1995 (1)

S. Saito and A. Naka, Electron. Commun. Jpn. 78, 11 (1995).
[CrossRef]

1994 (3)

1993 (1)

K. Kikuchi, IEEE Photon. Technol. Lett. 5, 221 (1993).
[CrossRef]

1992 (1)

1991 (1)

D. Marcuse, IEEE J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

1990 (1)

A. Mecozzi and P. Tombesi, Opt. Commun. 75, 256 (1990).
[CrossRef]

1982 (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

1976 (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Abram, I.

Caves, C. M.

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Deutsch, I. H.

Fukada, Y.

M. Murakami, Y. Fukada, and T. Imai, in European Conference on Optical Communication ’94 (Institute Internazionale delle Comunicuzioni, Firenze, Italy, 1994), p. 613.

Goedde, C. G.

Imai, T.

M. Murakami, Y. Fukada, and T. Imai, in European Conference on Optical Communication ’94 (Institute Internazionale delle Comunicuzioni, Firenze, Italy, 1994), p. 613.

Kath, W. L.

C. G. Goedde, W. L. Kath, and P. Kumar, Opt. Lett. 19, 2077 (1994).
[CrossRef] [PubMed]

R.-D. Li, P. Kumar, and W. L. Kath, IEEE J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

Kikuchi, K.

K. Kikuchi, IEEE Photon. Technol. Lett. 5, 221 (1993).
[CrossRef]

Kumar, P.

R.-D. Li, P. Kumar, and W. L. Kath, IEEE J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

C. G. Goedde, W. L. Kath, and P. Kumar, Opt. Lett. 19, 2077 (1994).
[CrossRef] [PubMed]

Li, R.-D.

R.-D. Li, P. Kumar, and W. L. Kath, IEEE J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

Marcuse, D.

D. Marcuse, IEEE J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

Mecozzi, A.

A. Mecozzi and P. Tombesi, Opt. Commun. 75, 256 (1990).
[CrossRef]

Murakami, M.

M. Murakami, Y. Fukada, and T. Imai, in European Conference on Optical Communication ’94 (Institute Internazionale delle Comunicuzioni, Firenze, Italy, 1994), p. 613.

Naka, A.

S. Saito and A. Naka, Electron. Commun. Jpn. 78, 11 (1995).
[CrossRef]

Saito, S.

S. Saito and A. Naka, Electron. Commun. Jpn. 78, 11 (1995).
[CrossRef]

Tombesi, P.

A. Mecozzi and P. Tombesi, Opt. Commun. 75, 256 (1990).
[CrossRef]

Yuen, H. P.

Electron. Commun. Jpn. (1)

S. Saito and A. Naka, Electron. Commun. Jpn. 78, 11 (1995).
[CrossRef]

IEEE J. Lightwave Technol. (2)

D. Marcuse, IEEE J. Lightwave Technol. 9, 356 (1991).
[CrossRef]

R.-D. Li, P. Kumar, and W. L. Kath, IEEE J. Lightwave Technol. 12, 541 (1994).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

K. Kikuchi, IEEE Photon. Technol. Lett. 5, 221 (1993).
[CrossRef]

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

Opt. Commun. (1)

A. Mecozzi and P. Tombesi, Opt. Commun. 75, 256 (1990).
[CrossRef]

Opt. Lett. (2)

Phys. Rev. A (1)

H. P. Yuen, Phys. Rev. A 13, 2226 (1976).
[CrossRef]

Phys. Rev. D (1)

C. M. Caves, Phys. Rev. D 26, 1817 (1982).
[CrossRef]

Other (1)

M. Murakami, Y. Fukada, and T. Imai, in European Conference on Optical Communication ’94 (Institute Internazionale delle Comunicuzioni, Firenze, Italy, 1994), p. 613.

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Figures (3)

Fig. 1
Fig. 1

In-line amplifier light-wave system and noise propagation.

Fig. 2
Fig. 2

Calculated noise spectra after 5000-km transmission, where a fiber nonlinear coefficient γ of 2.16 W-1 km-1 and a fiber dispersion D of (a) -0.1 ps/nm/km and (b) 0.1 ps/nm/km are assumed.

Fig. 3
Fig. 3

SNR as a function of the number of amplifiers. A receiver bandwidth B of 40 GHz, fiber nonlinear coefficient γ of 2.16 W-1 km-1, and fiber dispersion D of -0.1 and 0.1 ps/nm/km are assumed.

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

Ez,t=A0z+az,ωcosωtcosω0t+bz,ωcosωtsinω0t,
aL,ωbL,ω=exp-αL2FL,ωa0,ωb0,ω,
FL,ω=cosκωL-ξωsinκωLξ-1ωsinκωLcosκωL,
κω=β2ω22β2ω22+2γP¯01/2,
ξω=β2ω22β2ω22+2γP¯01/2,
aoutjL,ω=GainjL,ω, boutjL,ω=GbinjL,ω,
aiNL,ωbiNL,ω=FL,ωN-iaiiL,ωbiiL,ω,
aoutjL,ω=GainjL,ω, boutjL,ω=1/GbinjL,ω.
aiNL,ωbiNL,ω=100G-1FL,ωN-i×aiiL,ωbiiL,ω.
12a2NL,ω=12i=1Nai2NL,ω,
12b2NL,ω=12i=1Nbi2NL,ω.
ai2iL,ω=bi2iL,ω=2ω0G-1.
αΔaˆ12α=¼G, αΔaˆ22α=1/4G,
ai2iL,ω=ω0G, bi2iL,ω=ω0/G.

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