Abstract

The intrinsic evolution of a high-order soliton described by the nonlinear Schrödinger equation is initiated by a self-four-wave mixing effect (or modulational instability) and recurs neatly every soliton period. We show that when there is noise such as amplified spontaneous emission, however, a high-order soliton evolves randomly and independently and is distorted because the evolution is initiated by noise. Thus the time and the frequency coherence of a soliton pulse train are both greatly degraded.

© 1999 Optical Society of America

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References

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  1. R. R. Alfano, ed., The Super Continuum Laser Sources (Springer-Verlag, Berlin, 1989).
    [CrossRef]
  2. C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
    [CrossRef]
  3. K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.
  4. T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
    [CrossRef]
  5. M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
    [CrossRef]
  6. M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
    [CrossRef] [PubMed]
  7. J. P. Gordon and H. A. Haus, Opt. Lett. 11, 665 (1986).
    [CrossRef] [PubMed]

1996 (1)

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

1989 (1)

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

1986 (1)

1982 (1)

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Fork, R. L.

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Gordon, J. P.

Haus, H. A.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

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

Kamatani, O.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Kanamori, T.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Kawanishi, S.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Kubota, H.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
[CrossRef]

Mori, K.

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.

Morioka, T.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.

Nakazawa, M.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
[CrossRef]

Ono, H.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Saruwatari, M.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.

Shank, C. V.

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Stolen, R. H.

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Suzuki, K.

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

Takahashi, H.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Takara, H.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.

Takiguchi, K.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Tamura, K.

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
[CrossRef]

Uchiyama, K.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Yamada, M.

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Yen, R.

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Yoshida, E.

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
[CrossRef]

Appl. Phys. Lett. (1)

C. V. Shank, R. L. Fork, R. Yen, and R. H. Stolen, Appl. Phys. Lett. 40, 761 (1982).
[CrossRef]

Electron. Lett. (1)

T. Morioka, H. Takara, S. Kawanishi, O. Kamatani, K. Takiguchi, K. Uchiyama, M. Saruwatari, H. Takahashi, M. Yamada, T. Kanamori, and H. Ono, Electron. Lett. 32, 906 (1996).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

M. Nakazawa, K. Suzuki, H. Kubota, and H. A. Haus, Phys. Rev. A 39, 5768 (1989).
[CrossRef] [PubMed]

Other (3)

R. R. Alfano, ed., The Super Continuum Laser Sources (Springer-Verlag, Berlin, 1989).
[CrossRef]

M. Nakazawa, K. Tamura, H. Kubota, and E. Yoshida, Opt. Fiber Technol.4, 215 (1998).
[CrossRef]

K. Mori, T. Morioka, H. Takara, and M. Saruwatari, presented at the Meeting on Optical Amplifiers and Their Applications, Yokohama, Japan, July 4–6, 1993.

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Figures (4)

Fig. 1
Fig. 1

Evolution of high-order solitons (a) without and (b) with random noise. The GVD of the fiber is 0.2  ps/(km  nm), the pulse width is 3  ps, and the soliton number N is set at 10.

Fig. 2
Fig. 2

Random evolution of a high-order soliton in the presence of a small amount of amplitude noise. (a) The intrinsic evolution of an N=12.8 soliton; (b), (c) the evo-lution with different random noise patterns. The noise power level is 5.2×10-6 below the soliton power within the 3-dB bandwidth.

Fig. 3
Fig. 3

Evolution of nonlinear pulses in the normal GVD region (a) with and (b) without random amplitude noise.

Fig. 4
Fig. 4

Spectral profiles of the SC and corresponding coherence degradation in (a) DDF and (b) DSF.

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