Abstract

Periodically spaced amplifiers along a transoceanic cable provide the phase-matching condition for a four-wave mixing process owing to Kerr nonlinearity. A new kind of sideband instability, shows up in both positive and negative dispersion regimes that is similar to modulation instability. A comparison with the sideband instability that was recently discovered for solitons is carried out.

© 1993 Optical Society of America

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References

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  1. D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
    [CrossRef]
  2. D. Marcuse, J. Lightwave Technol. 9, 356 (1991).
    [CrossRef]
  3. K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
    [CrossRef] [PubMed]
  4. J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
    [CrossRef]
  5. L. F. Mollenauer, K. Smith, J. P. Gordon, C. R. Menyuk, Opt. Lett. 14, 1219 (1989).
    [CrossRef] [PubMed]
  6. N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
    [CrossRef]
  7. S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
    [CrossRef]

1992 (3)

J. P. Gordon, J. Opt. Soc. Am. B 9, 91 (1992).
[CrossRef]

N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

1991 (2)

D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
[CrossRef]

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

1989 (1)

1986 (1)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Andovic, I.

N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Blow, K. J.

N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Chraplyvy, A. R.

D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
[CrossRef]

Gordon, J. P.

Hasegawa, A.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Kelly, S. M. J.

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

Marcuse, D.

D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
[CrossRef]

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

Menyuk, C. R.

Mollenauer, L. F.

Smith, K.

Smith, N. J.

N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

Tai, K.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Tkach, R. W.

D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
[CrossRef]

Tomita, A.

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

Electron. Lett. (1)

S. M. J. Kelly, Electron. Lett. 28, 806 (1992).
[CrossRef]

J. Lightwave Technol. (3)

D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
[CrossRef]

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

N. J. Smith, K. J. Blow, I. Andovic, J. Lightwave Technol. 10, 1329 (1992).
[CrossRef]

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

Opt. Lett. (1)

Phys. Rev. Lett. (1)

K. Tai, A. Hasegawa, A. Tomita, Phys. Rev. Lett. 56, 135 (1986).
[CrossRef] [PubMed]

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Figures (4)

Fig. 1
Fig. 1

Amplitude gain of the parametric process occurring along an amplifier chain, as numerically evaluated after 10,000 km. The group-velocity dispersion coefficient is β″ = −1 ps2/km.

Fig. 2
Fig. 2

Same as Fig. 1, with β″ = 1 ps2/km.

Fig. 3
Fig. 3

Amplitude gain of the parametric process induced by the split-step algorithm. The group-velocity dispersion coefficient is β″ = −16 ps2/km.

Fig. 4
Fig. 4

Same as Fig. 3, with β″ = 16 ps2/km.

Equations (10)

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

z U = Γ U + j β 2 2 t 2 U j γ | U | 2 U .
z u = j β 2 2 t 2 u j γ f ( z ) | u | 2 u ,
f ( z ) = f o ( z ) = exp ( 2 Γ z ) .
d d z a ( z , Ω ) = jKa ( z , Ω ) j γ f ( z ) P o [ a ( z , Ω ) + a * ( z , Ω ) ] ,
f ( z ) = n = c n exp ( j k n z ) ,
d d z b ( z , Ω ) = j ( K k p / 2 + γ P o c o ) b ( z , Ω ) j γ P o c p b * ( z , Ω ) , d d z b * ( z , Ω ) = j ( K k p / 2 + γ P o c o ) b * ( z , Ω ) + j γ P o c p * b ( z , Ω ) .
Ω p = ± ( 2 π p β l 2 γ P o c o β ) 1 / 2 .
| Ω 2 Ω p 2 | < 2 γ P o | c p | | β | = 2 g p | β | .
k r + k s = k p + 2 k o .
f ( z ) = f d ( z ) = m l δ ( z m l ) .

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