Abstract

The propagation of dispersion-managed solitons in optical fiber links with a random dispersion map has been studied. Two types of randomness are considered: random dispersion magnitudes and random lengths of the spans. By numerical simulations, disintegration of a soliton propagating in such an optical communication line is shown to occur. It is observed that the stability of the soliton propagation is affected more by modulations of the dispersion magnitudes of the spans than by modulations of the span lengths. Results of numerical simulations of the soliton breakup distance confirm theoretical predictions in the averaged dynamics limit.

© 2000 Optical Society of America

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References

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  1. N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
    [CrossRef]
  2. A. Hasegawa, ed., New Trends in Applications of Optical Solitons in Fibers (Kluwer Academic, Dordrecht, The Netherlands, 1998).
  3. M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
    [CrossRef]
  4. D. Anderson, Phys. Rev. A 27, 1393 (1983).
    [CrossRef]
  5. J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).
  6. F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
    [CrossRef]
  7. B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
    [CrossRef]
  8. F. Kh. Abdullaev and J. G. Caputo, Phys. Rev. E 58, 6637 (1998).
    [CrossRef]

1999 (1)

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
[CrossRef]

1998 (2)

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

F. Kh. Abdullaev and J. G. Caputo, Phys. Rev. E 58, 6637 (1998).
[CrossRef]

1997 (1)

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

1993 (1)

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

1983 (1)

D. Anderson, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Abdullaev, F. Kh.

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, Phys. Rev. E 58, 6637 (1998).
[CrossRef]

Anderson, D.

D. Anderson, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Bennion, I.

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

Blow, K. J.

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

Bronski, J.

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
[CrossRef]

Caputo, J. G.

F. Kh. Abdullaev and J. G. Caputo, Phys. Rev. E 58, 6637 (1998).
[CrossRef]

Doran, N.

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

Evangelidis, S. G.

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

Gordon, J. P.

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

Haus, H. A.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Holmes, P.

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

Knox, F.

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

Kutz, J. N.

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

Malomed, B. A.

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

Matsumoto, M.

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

Papanicolaou, G. C.

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
[CrossRef]

Parker, D. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

Smith, N. J.

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

Smyth, N. F.

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

M. Matsumoto and H. A. Haus, IEEE Photon. Technol. Lett. 9, 785 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. N. Kutz, P. Holmes, S. G. Evangelidis, and J. P. Gordon, J. Opt. Soc. Am. 15, 87 (1998).

Phys. Rev. A (1)

D. Anderson, Phys. Rev. A 27, 1393 (1983).
[CrossRef]

Phys. Rev. E (2)

B. A. Malomed, D. F. Parker, and N. F. Smyth, Phys. Rev. E 48, 1418 (1993).
[CrossRef]

F. Kh. Abdullaev and J. G. Caputo, Phys. Rev. E 58, 6637 (1998).
[CrossRef]

Physica D (1)

F. Kh. Abdullaev, J. Bronski, and G. C. Papanicolaou, Physica D 135, 369 (1999).
[CrossRef]

Other (2)

N. J. Smith, F. Knox, N. Doran, K. J. Blow, and I. Bennion, Electron. Lett.32, 54 (1996).
[CrossRef]

A. Hasegawa, ed., New Trends in Applications of Optical Solitons in Fibers (Kluwer Academic, Dordrecht, The Netherlands, 1998).

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Figures (5)

Fig. 1
Fig. 1

Relative mean-squared width of the pulse propagating in a DM line with randomly varying dispersion magnitudes of spans. The dispersion map parameters are D+=26, D-=-24, and z+=z-=0.14. The curves, obtained from Eqs. (5), are averaged over 400 realizations.

Fig. 2
Fig. 2

Growth of the energy H when the dispersion magnitudes of the spans and the span lengths are randomly modulated with standard deviation σ=0.06. The dispersion map parameters are D+=1, D-=-1, z+=1.0, and z-=0.1. The curves, obtained from Eqs. (5), are averaged over 400 realizations.

Fig. 3
Fig. 3

Decay of the normalized pulse amplitude as a result of randomness of the fiber dispersion, according to Eqs. (5). In the DM case, fiber spans are assumed to have D+=1, D-=-1, z+=1.0, z-=0.1, and D+,-, randomly modulated with standard deviation σ=0.06. For the conventional case the fiber dispersion is taken as randomly varying around the corresponding path-averaged value Dav with the same value of σ=0.06. Stochastic equations (5) are averaged over 400 realizations.

Fig. 4
Fig. 4

Mean distance at which a soliton disintegrates, calculated in the averaged dynamics limit and E=1, for different strengths of random modulation of fiber dispersion (according to Eqs. (5), averaged over 400 realizations).

Fig. 5
Fig. 5

Disintegration of a soliton propagating in a DM line with randomly varying dispersion magnitudes of spans. This particular realization is for Eq. (1) with a Gaussian pulse u0,t=2.45 exp-0.427t2. The dispersion map parameters are D+=26, D-=-24, z+=z-=0.14, and σ=0.06.

Equations (7)

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iuz+dz2utt+u2u=0,
d1=0, d1z1d1z2=2σ2δz1-z2,
uz,t=AzFtazexpiϕz+ibzt2,
-u2dt=E=const.
az=2dzab, bz=C1dza4-C2a3-2dzb2,
C1=-F2dτ2-τ2F2dτ, C2=-Fτ4dτ4-τ2F2dτ, τ=ta.
Ld=1σ2E40JAJdJ1.68σ2E4, AJ=JπJ+48π3πJ+23128+448πJ+448π2J2+168π3J3+21π4J4,

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