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Evolution of Optical Pulses in Fiber Lines with Lumped Nonlinear Devices as a Mapping Problem

Abstract

We analyze the steady-state propagation of optical pulses in fiber transmission systems with lumped nonlinear optical devices (NODs) placed periodically in the line. For the first time to our knowledge, a theoretical model is developed to describe the transmission regime with a quasilinear pulse evolution along the transmission line and the point action of NODs. We formulate the mapping problem for pulse propagation in a unit cell of the line and show that in the particular application to nonlinear optical loop mirrors, the steady-state pulse characteristics predicted by the theory accurately reproduce the results of direct numerical simulations.

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REFERENCES

  1. 1.

    A. Hasegawa and Y. Kodama, Opt. Lett., 15, 1443–1445 (1990).

  2. 2.

    I. Gabitov and S. K. Turitsyn, Opt. Lett., 21, 327–329 (1996).

  3. 3.

    N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion, Electron. Lett., 32, 54–55 (1996).

  4. 4.

    J. H. B. Nijhof, N. J. Doran, W. Forysiak, and A. Berntson, Electron. Lett., 34, 481–482 (1998).

  5. 5.

    S. Boscolo, J. H. B. Nijhof, and S. K. Turitsyn, Opt. Lett., 25, 1240–1242 (2000).

  6. 6.

    S. Boscolo, S. K. Turitsyn, and K. J. Blow, IEEE Photon. Technol. Lett., 14, 30–32 (2002).

  7. 7.

    D. Rouvillain, P. Brindel, E. Seguineau, L. Pierre, O. Leclerc, H. Choumane, G. Aubin, and J. L. Oudar, Electron. Lett., 38, 1113–1114 (2002).

  8. 8.

    B. S. Kerner and V. V. Osipov, Autosolitons [in Russian], Nauka, Moscow (1991); English transl.: Autosolitons: A New Approach to Problems of Self-Organization and Turbulence, Kluwer, Dordrecht (1994).

  9. 9.

    J. D. Logan, Applied Mathematics: A Contemporary Approach, Wiley, New York (1987).

  10. 10.

    N. J. Smith and N. J. Doran, J. Opt. Soc. Am. B, 12, 1117–1125 (1995).

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 277–289, August, 2005.

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Boscolo, S., Derevyanko, S.A., Turitsyn, S.K. et al. Evolution of Optical Pulses in Fiber Lines with Lumped Nonlinear Devices as a Mapping Problem. Theor Math Phys 144, 1117–1127 (2005). https://doi.org/10.1007/s11232-005-0140-8

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Keywords

  • dispersive systems with point nonlinearity
  • mapping problem
  • autosolitons