Abstract

Dispersion-managed optical transmission lines, with dispersion periodically switched between the normal and anomalous regimes, offer significantly better performance than transmission lines with constant dispersion by reducing the dispersion penalty and spectral broadening owing to self-phase modulation. We analyze the evolution of plane waves in a dispersion-managed transmission line, using Floquet theory, and show them to be modulationally stable, provided that the average dispersion is zero or negative (normal dispersion) and that the switching is fast enough, and to be unstable when anomalous dispersion dominates. These results indicate that the transition regions between 1’s and 0’s are primarily responsible for pulse deformations.

© 1996 Optical Society of America

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References

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  1. N. S. Bergano, C. R. Davidson, in Optical Fiber Communication, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD19.
  2. A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
    [CrossRef]
  3. A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
    [CrossRef]
  4. C. Kurtzke, IEEE Photon. Technol. Lett. 5, 1250 (1993).
    [CrossRef]
  5. R. W. Tkach, A. R. Chraplyvy, F. Forguieri, A. H. Gnauck, R. M. Derosier, J. Lightwave Technol. 13, 841 (1995).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).
  7. A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, New York, 1979).
  8. C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).
  9. Y. Kodama, S. Wabnitz, Opt. Lett. 20, 2291 (1995).
    [CrossRef] [PubMed]
  10. J. C. Bronski, J. N. Kutz, Physica D (to be published).

1995

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

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

Y. Kodama, S. Wabnitz, Opt. Lett. 20, 2291 (1995).
[CrossRef] [PubMed]

1993

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

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

Bender, C. M.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).

Bergano, N. S.

N. S. Bergano, C. R. Davidson, in Optical Fiber Communication, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD19.

Bronski, J. C.

J. C. Bronski, J. N. Kutz, Physica D (to be published).

Chraplyvy, A. R.

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

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

Davidson, C. R.

N. S. Bergano, C. R. Davidson, in Optical Fiber Communication, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD19.

Derosier, R. M.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

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

Ferguson, G. A.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

Forguieri, F.

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

Giles, C. R.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

Gnauck, A. H.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

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

Kodama, Y.

Kurtzke, C.

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

Kutz, J. N.

J. C. Bronski, J. N. Kutz, Physica D (to be published).

Mook, D. T.

A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, New York, 1979).

Nayfeh, A. H.

A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, New York, 1979).

Nyman, B. M.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

Orszag, S. A.

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).

Sulhoff, J. W.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

Tkach, R. W.

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

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

Wabnitz, S.

Zyskind, J. L.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

IEEE Electron. Lett.

A. H. Gnauck, A. R. Chraplyvy, R. W. Tkach, R. M. Derosier, IEEE Electron. Lett. 31, 277 (1995).
[CrossRef]

IEEE Photon. Technol. Lett.

A. R. Chraplyvy, A. H. Gnauck, R. W. Tkach, R. M. Derosier, C. R. Giles, B. M. Nyman, G. A. Ferguson, J. W. Sulhoff, J. L. Zyskind, IEEE Photon. Technol. Lett. 7, 98 (1995).
[CrossRef]

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

J. Lightwave Technol.

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

Opt. Lett.

Other

J. C. Bronski, J. N. Kutz, Physica D (to be published).

N. S. Bergano, C. R. Davidson, in Optical Fiber Communication, Vol. 8 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), paper PD19.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, San Diego, Calif., 1989).

A. H. Nayfeh, D. T. Mook, Nonlinear Oscillations (Wiley, New York, 1979).

C. M. Bender, S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers (McGraw-Hill, New York, 1978).

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Figures (3)

Fig. 1
Fig. 1

Typical NRZ bit-stream pattern.

Fig. 2
Fig. 2

Approximate depiction of the dispersion map and its cumulative dispersion, as given by Ref. 2.

Fig. 3
Fig. 3

Floquet discriminant Δ versus η for (a) P = 2 and (b) P = 3, given L± = P/2 and β± = ±2.5. For P < Pc ≈ 2.14 the plane waves are modulationally stable since |Δ| < 2.

Equations (11)

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i Q Z + σ ( Z ) 2 2 Q T 2 + α | Q | 2 Q = 0 .
α = 2 π n 2 | E 0 | 2 Z NL λ 0 A eff = 1 ,
Z NL = λ 0 A eff 2 π n 2 | E 0 | 2 = 3729 km .
T 0 = ( Z NL λ 0 2 D 0 2 π c ) 1 / 2 = 69 ps .
σ ( Z ) = { β + 0 < Z < L + β L + < Z < P = L + + L ,
σ ( Z ) = 0 P σ ( Z ) d Z = β + L + + β L .
Q ( Z , T ) = [ 1 + δ ψ ( Z , T ) ] exp { i [ ω T k ( Z ) ] } ,
i ψ Z + i ω σ ( Z ) ψ T + σ ( Z ) 2 2 ψ T 2 + ψ + ψ * = 0 ,
i ψ Z + σ ( Z ) 2 2 ψ t 2 + ψ + ψ * = 0 .
i d d Z ( ψ ˆ ψ ˆ * ) = [ η 2 σ ( Z ) 2 1 1 1 1 η 2 σ ( Z ) 2 ] ( ψ ˆ ψ ˆ * ) ,
Δ ( η ) = 2 cos ( γ + L + ) cos ( γ L ) + [ β + β η 4 + 2 ( β + β ) η 2 2 γ + γ ] × sin ( γ + L + ) sin ( γ L ) ,

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