Abstract

We develop an analytical description of the evolution of square pulses in nonlinear fiber transmissions operating in the normal dispersion regime. The theory is in excellent agreement with numerical simulations. We also show that signal distortion may be compensated by initial periodic phase modulation.

© 1995 Optical Society of America

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References

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  1. See, e.g.,N. S. Bergano, C. R. Davidson, in Optical Amplifiers and Their Applications, Vol. 14 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper PD7.
  2. D. Marcuse, A. R. Chraplyvy, R. W. Tkach, J. Lightwave Technol. 9, 121 (1991).
    [CrossRef]
  3. D. Anderson, Phys. Rev. A 27, 3135 (1983).
    [CrossRef]
  4. D. Marcuse, J. Lightwave Technol. 10, 17 (1992).
    [CrossRef]
  5. P. A. Belanger, N. Belanger, Opt. Commun. 117, 56 (1995).
    [CrossRef]
  6. L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
    [CrossRef]
  7. A. Hasegawa, Y. Kodama, Opt. Lett. 15, 1443 (1990).
    [CrossRef] [PubMed]
  8. G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), p. 113.
  9. Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
    [CrossRef]
  10. Y. Kodama, S. Wabnitz, Electron. Lett. 31, 1761 (1995).
    [CrossRef]

1995 (2)

P. A. Belanger, N. Belanger, Opt. Commun. 117, 56 (1995).
[CrossRef]

Y. Kodama, S. Wabnitz, Electron. Lett. 31, 1761 (1995).
[CrossRef]

1992 (2)

D. Marcuse, J. Lightwave Technol. 10, 17 (1992).
[CrossRef]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

1991 (2)

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

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

1990 (1)

1983 (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Belanger, N.

P. A. Belanger, N. Belanger, Opt. Commun. 117, 56 (1995).
[CrossRef]

Belanger, P. A.

P. A. Belanger, N. Belanger, Opt. Commun. 117, 56 (1995).
[CrossRef]

Bergano, N. S.

See, e.g.,N. S. Bergano, C. R. Davidson, in Optical Amplifiers and Their Applications, Vol. 14 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper PD7.

Chraplyvy, A. R.

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

Davidson, C. R.

See, e.g.,N. S. Bergano, C. R. Davidson, in Optical Amplifiers and Their Applications, Vol. 14 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper PD7.

Evangelides, S. G.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Hasegawa, A.

Haus, H. A.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Kodama, Y.

Y. Kodama, S. Wabnitz, Electron. Lett. 31, 1761 (1995).
[CrossRef]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

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

Marcuse, D.

D. Marcuse, J. Lightwave Technol. 10, 17 (1992).
[CrossRef]

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

Mollenauer, L. F.

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

Romagnoli, M.

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Tkach, R. W.

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

Wabnitz, S.

Y. Kodama, S. Wabnitz, Electron. Lett. 31, 1761 (1995).
[CrossRef]

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Whitham, G. B.

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), p. 113.

Electron. Lett. (2)

Y. Kodama, M. Romagnoli, S. Wabnitz, Electron. Lett. 28, 1981 (1992).
[CrossRef]

Y. Kodama, S. Wabnitz, Electron. Lett. 31, 1761 (1995).
[CrossRef]

J. Lightwave Technol. (3)

L. F. Mollenauer, S. G. Evangelides, H. A. Haus, J. Lightwave Technol. 9, 194 (1991).
[CrossRef]

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

D. Marcuse, J. Lightwave Technol. 10, 17 (1992).
[CrossRef]

Opt. Commun. (1)

P. A. Belanger, N. Belanger, Opt. Commun. 117, 56 (1995).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 3135 (1983).
[CrossRef]

Other (2)

G. B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974), p. 113.

See, e.g.,N. S. Bergano, C. R. Davidson, in Optical Amplifiers and Their Applications, Vol. 14 of 1994 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1994), paper PD7.

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Figures (4)

Fig. 1
Fig. 1

Numerically propagated square pulse (solid curve) and its analytical approximation (crosses). Dotted– dashed curve, the initial pulse.

Fig. 2
Fig. 2

Numerical (solid curves) and analytical (crosses) pulses at 10 Mm for (a) 200-ps, 0.25-mW and (b) 400-ps, 1-mW initial super-Gaussian pulses (dotted–dashed curves).

Fig. 3
Fig. 3

Dependence of the pulse-widening factor W (at 10 Mm) on the input pulse power for different input time widths and dispersion.

Fig. 4
Fig. 4

Pulses at 10 Mm (solid curves) and initial profiles (dotted–dashed curves) of phase-modulated pulses as in Fig. 2, with initial modulation amplitude M.

Equations (10)

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i Q Z - k 2 Q t t + γ Q 2 Q = 0.
i q Z - β 2 q T T + q 2 q = 0.
q ( T , Z ) = ρ ( T , Z ) exp [ i T u ( T , Z ) d T ] ,
Z ( ρ u ) ( β u β ρ 1 β u ) T ( ρ u ) .
r ± Z = λ ± r ± T ,
ρ ( T , Z ) = u ( T , Z ) = 0             for  T > T p 1 ( Z ) , ρ ( T , Z ) = min [ ρ 0 , 1 9 ( 2 ρ 0 - T - T p β Z ) 2 ]             for  0 < T < T p 1 ( Z ) , u ( T , Z ) = - max [ 0 , 2 3 β ( ρ 0 + T - T p β Z ) ]             for 0 < T < T p 1 ( Z ) ,
q ( T , Z = 0 ) = ρ 0 2 [ tanh ( T + T p T r ) - tanh ( T - T p T r ) ] ,
q ( T , Z = 0 ) = q s ( T ) ρ 0 exp [ - 1 2 ( T T w ) n ] ,
W 1 + 2 β ρ 0 Z T p ,
q ( T , Z = 0 ) = q s ( T ) exp [ - i Φ ( T ) ] ,

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