Abstract

We analytically and numerically analyze the occurrence of modulational instability in fibers with periodic changes in the group-velocity dispersion. For small variations, a set of resonances occurs in the gain spectrum. However, large dispersion variations eliminate these resonances and restrict the bandwidth of the fundamental gain spectrum. This research has been motivated by the adoption of dispersion management techniques in long-haul optical communications.

© 1996 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. C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
    [CrossRef]
  3. R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
    [CrossRef]
  4. G. P. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).
  5. F. Matera, A. Mecozzi, M. Romagnoli, M. Settembre, Opt. Lett. 18, 1499 (1993).
    [CrossRef] [PubMed]

1995 (1)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

1993 (2)

1991 (1)

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).

Chraplyvy, A. R.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

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

Derosier, R. M.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Forghieri, F.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Gnauck, A. H.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

Kurtzke, C.

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

Marcuse, D.

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

Matera, F.

Mecozzi, A.

Romagnoli, M.

Settembre, M.

Tkach, R. W.

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

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

IEEE Photon. Technol. Lett. (1)

C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
[CrossRef]

J. Lightwave Technol. (2)

R. W. Tkach, A. R. Chraplyvy, F. Forghieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
[CrossRef]

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

Opt. Lett. (1)

Other (1)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, Orlando, Fla., 1989).

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Figures (3)

Fig. 1
Fig. 1

Dispersion profile used in the numerical simulations. Values of the parameters β̈1 and β̈2 can be found in Table 1.

Fig. 2
Fig. 2

Modulational instability gain over 2000 km of dispersion maps A, D, E, F, and G, showing progressive reduction in the cutoff frequency and peak gains. Top, numerical integration; bottom, analytical theory.

Fig. 3
Fig. 3

Modulational instability gain over 2000 km of dispersion maps A–D, showing the creation and suppression of sideband resonances.

Tables (1)

Tables Icon

Table 1 Choice of Fiber Dispersions Used in Numerical Simulations A–G

Equations (11)

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i u z = ½ [ β ¨ av + β ¨ fl ( z ) ] 2 u t 2 - γ u 2 u
a ( z , t ) = [ a ( z , Ω ) exp ( i Ω t ) + a ( z , - Ω ) exp ( - i Ω t ) ] / 2.
i d a ( z , t ) d z = - ½ [ β ¨ av + β ¨ fl ( z ) ] Ω 2 a ( z , Ω ) - γ P 0 [ a ( z , Ω ) + a * ( z , - Ω ) ] .
a ( z , Ω ) = b ( z , Ω ) exp [ - ½ i Ω 2 0 z β ¨ fl ( z ) d z ] .
i d b ( z , Ω ) d z = - ½ β ¨ av ( z ) Ω 2 b ( z , Ω ) - γ P 0 × { b ( z , Ω ) + b * ( z , - Ω ) exp [ i Ω 2 0 z β ¨ fl ( z ) d z ] } .
f ( z ) exp [ i Ω 2 0 z β ¨ fl ( z ) d z ] = n c n exp ( - i n k z ) .
i d g ( z , Ω ) d z = - ( p k 2 + β ¨ av Ω 2 2 + γ P 0 ) g ( z , Ω ) - γ P 0 c p g * ( z , - Ω ) .
f ( z ) = J 0 ( β ¨ p Ω 2 k p ) + 2 m = 1 J 2 m ( β ¨ p Ω 2 k p ) cos ( 2 m k p z ) + 2 i m = 0 J 2 m + 1 ( β ¨ p Ω 2 k p ) sin [ ( 2 m + 1 ) k p z ] ,
d g ( z , Ω ) d z = - i ( β ¨ av Ω 2 / 2 + γ P 0 ) g ( z , Ω ) + i γ P 0 J 0 ( β ¨ p Ω 2 / k p ) g * ( z , - Ω ) .
K 2 = - β ¨ av Ω 2 ( γ P 0 + β ¨ av Ω 2 / 4 ) + γ 2 P 0 2 [ J 0 2 ( β ¨ p Ω 2 / k p ) - 1 ] .
Ω = [ ( p k - 2 γ P 0 ) / β ¨ av ] ½ .

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