Abstract

The superposition of spontaneous emission noise on a train of soliton pulses produces a random change of the center frequency of the soliton spectrum that causes a change of the group velocity of individual solitons, which in long-light-wave systems translates into a random jitter of the position of the pulses at the receiver. This phenomenon is known as the Gordon–Haus effect. If uncontrolled, the Gordon–Haus effect sets a definite limit on the permissible data rate or on the length of soliton-based light-wave systems. Recently Kodama and Hasegawa [Opt. Lett. 17, 31 (1992)] have shown that the Gordon–Haus effect can be suppressed by placing filters along the fiber that reduce the frequency jitter and the concomitant group-velocity changes. We demonstrate the reduction of the Gordon–Haus effect by computer simulations.

© 1992 Optical Society of America

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References

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  1. A. Hasegawa, F. D. Tappert, Appl. Phys. Lett. 23, 142 (1973).
    [CrossRef]
  2. G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).
  3. Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).
  4. N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. QE-19, 1883 (1983).
    [CrossRef]
  5. A. Hasegawa, Appl. Opt. 23, 3302 (1984).
    [CrossRef] [PubMed]
  6. L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
    [CrossRef]
  7. D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass., 1991), Chap. 9.
  8. J. P. Gordon, A. H. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]
  9. M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
    [CrossRef]
  10. M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
    [CrossRef] [PubMed]
  11. M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
    [CrossRef]
  12. Y. Kodama, A. Hasegawa, Opt. Lett. 17, 31 (1992).
    [CrossRef] [PubMed]
  13. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  14. D. Marcuse, “An alternative derivation of the Gordon–Haus effect,”IEEE Photon. Technol. Lett. (to be published).

1992 (1)

1991 (2)

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

1990 (2)

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

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

1986 (2)

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

J. P. Gordon, A. H. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

1984 (1)

1983 (1)

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. QE-19, 1883 (1983).
[CrossRef]

1973 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Blow, K. J.

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. QE-19, 1883 (1983).
[CrossRef]

Doran, N. J.

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. QE-19, 1883 (1983).
[CrossRef]

Gordon, J. P.

J. P. Gordon, A. H. Haus, Opt. Lett. 11, 665 (1986).
[CrossRef] [PubMed]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

Hasegawa, A.

Haus, A. H.

Islam, M. N.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

Kodama, Y.

Kubota, H.

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Kurokawa, K.

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Marcuse, D.

D. Marcuse, “An alternative derivation of the Gordon–Haus effect,”IEEE Photon. Technol. Lett. (to be published).

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass., 1991), Chap. 9.

Mollenauer, L. F.

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

Nakazawa, M.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Shen, Y. R.

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

Suzuki, K.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

Tappert, F. D.

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

Yamada, E.

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

M. Nakazawa, H. Kubota, K. Kurokawa, E. Yamada, J. Opt. Soc. Am. B 8, 1811 (1991).
[CrossRef]

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

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

Electron. Lett. (1)

M. Nakazawa, E. Yamada, H. Kubota, K. Suzuki, Electron. Lett. 27, 1270 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

N. J. Doran, K. J. Blow, IEEE J. Quantum Electron. QE-19, 1883 (1983).
[CrossRef]

L. F. Mollenauer, J. P. Gordon, M. N. Islam, IEEE J. Quantum Electron. QE-22, 157 (1986).
[CrossRef]

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

Opt. Lett. (3)

Phys. Rev. Lett. (1)

M. Nakazawa, K. Kurokawa, H. Kubota, E. Yamada, Phys. Rev. Lett. 65, 1881 (1990).
[CrossRef] [PubMed]

Other (4)

D. Marcuse, Theory of Dielectric Optical Waveguides, 2nd ed. (Academic, Boston, Mass., 1991), Chap. 9.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, New York, 1989).

Y. R. Shen, Principles of Nonlinear Optics (Wiley, New York, 1984).

D. Marcuse, “An alternative derivation of the Gordon–Haus effect,”IEEE Photon. Technol. Lett. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Soliton pulses that in the absence of noise maintain their shape indefinitely.

Fig. 2
Fig. 2

Eye diagram of a noiseless soliton pulse train. Simulated electrical bandwidth Bel = 2.5 GHz. The vertical scale corresponds to the average optical power in milliwatts.

Fig. 3
Fig. 3

Eye diagram of received solitons in the presence of spontaneous emission noise. The pulse position jitter apparent is the Gordon–Haus effect. Fiber length L = 9000 km, simulated electrical bandwidth Bel = 2.5 GHz. The vertical scale corresponds to the average optical power in milliwatts.

Fig. 4
Fig. 4

Eye diagram of received solitons in the presence of spontaneous emission noise reduced by in-line Fabry–Perot filters with filter width B = 157 GHz, which have succeeded in suppressing most of the pulse position jitter apparent in Fig. 3. Fiber length L = 9000 km, simulated electrical bandwidth Bel = 2.5 GHz. The vertical scale corresponds to the average optical power in milliwatts.

Equations (3)

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Q = G α L amp G 1 ,
σ = [ 1 . 763 N sp N 2 D h ( G 1 ) L 3 9 t s A eff L amp Q ] 1 / 2 .
H FP = 1 1 + i 2 ( f f 0 ) B .

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