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Journal of the Optical Society of America B

Journal of the Optical Society of America B


  • Vol. 19, Iss. 3 — Mar. 1, 2002
  • pp: 477–486

Experimental study of the reversible behavior of modulational instability in optical fibers

Gaetan Van Simaeys, Philippe Emplit, and Marc Haelterman  »View Author Affiliations

JOSA B, Vol. 19, Issue 3, pp. 477-486 (2002)

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We report what is to our knowledge the first clear-cut experimental evidence of the reversibility of modulational instability in dispersive Kerr media. It was possible to perform this experiment with standard telecommunication fiber because we used a specially designed 550-ps square-pulse laser source based on the two-wavelength configuration of a nonlinear optical loop mirror. Our observations demonstrate that reversibility is due to well-balanced and synchronous energy transfer among a significant number of spectral wave components. These results provide what we believe is the first evidence, in the field of nonlinear optics, of the universal Fermi–Pasta–Ulam recurrence phenomenon that has been predicted for a large number of conservative nonlinear systems, including those described by a nonlinear Schrödinger equation that is relevant to the context of the present study.

© 2002 Optical Society of America

OCIS Codes
(060.4370) Fiber optics and optical communications : Nonlinear optics, fibers
(190.3100) Nonlinear optics : Instabilities and chaos
(190.4370) Nonlinear optics : Nonlinear optics, fibers
(190.4380) Nonlinear optics : Nonlinear optics, four-wave mixing

Gaetan Van Simaeys, Philippe Emplit, and Marc Haelterman, "Experimental study of the reversible behavior of modulational instability in optical fibers," J. Opt. Soc. Am. B 19, 477-486 (2002)

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  1. T. B. Benjamin and J. E. Feir, “The disintegration of wave trains on deep water. 1. Theory,” J. Fluid Mech. 27, 417–430 (1967).
  2. T. B. Benjamin, “Instability of periodic wavetrains in nonlinear dispersive systems,” Proc. R. Soc. London Ser. A 299, 59–75 (1967).
  3. B. M. Lake, H. C. Yuen, H. Rungaldier, and W. E. Ferguson, “Nonlinear deep-water waves: theory and experiment. 2. Evolution of a continuous wave train,” J. Fluid Mech. 83, 49–74 (1977).
  4. H. C. Yuen, J. Warren, and E. Ferguson, “Relationship between Benjamin–Feir instability and recurrence in the nonlinear Schrödinger equation,” Phys. Fluids 21, 1275–1278 (1978).
  5. E. Fermi, J. Pasta, and H. C. Ulam, “Studies of nonlinear problems,” in Collected Papers of Enrico Fermi, E. Segrè, ed. (U. Chicago Press, Chicago, Ill., 1965), Vol. 2, pp. 977–988.
  6. T. Taniuti and H. Washimi, “Self-trapping and instability of hydromagnetic waves along the magnetic field in a cold plasma,” Phys. Rev. Lett. 21, 209–212 (1968).
  7. F. D. Tappert and C. N. Judice, “Recurrence of nonlinear ion acousitc waves,” Phys. Rev. Lett. 29, 1308–1311 (1972).
  8. P. Henrotay, “Periodic solutions and recurrence for nonlinear Schrödinger equation: a Fourier-mode approach,” J. Mec. 20, 159–168 (1981).
  9. E. Infeld, “Quantitive theory of the Fermi–Pasta–Ulam recurrence in the nonlinear Schrödinger equation,” Phys. Rev. Lett. 47, 717–718 (1981).
  10. G. Cappellini and S. Trillo, “Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects,” J. Opt. Soc. Am. B 8, 824–838 (1991).
  11. R. H. Stolen and J. E. Bjorkholm, “Parametric amplification and frequency conversion in optical fibers,” IEEE J. Quantum Electron. QE-18, 1062–1072 (1982).
  12. N. N. Akhmediev and V. I. Korneev, “Modulation instability and periodic solutions of the nonlinear Schrödinger equation,” Theor. Math. Phys. 69, 1089–1093 (1986) [ Teor. Mat. Fiz. 69, 189–194 (1986)].
  13. N. N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, “Exact first-order solutions of the nonlinear Schödinger equation,” Theor. Math. Phys. 72, 809–818 (1987) [Teor. Mat. Fiz. 72, 183–196 (1987)].
  14. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Nonlinear dynamics of polarization-modulation instability in optical fiber,” J. Opt. Soc. Am. B 14, 3403–3411 (1997).
  15. S. Trillo and S. Wabnitz, “Dynamics of the nonlinear modulation instability in optical fibers,” Opt. Lett. 16, 986–988 (1991).
  16. M. Haelterman and A. P. Sheppard, “Vector soliton associated with polarization modulational instability in the normal dispersion regime,” Phys. Rev. E 49, 3389–3399 (1994).
  17. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano, “Polarization multiplexing with solitons,” J. Lightwave Technol. 10, 28–35 (1992).
  18. D. Cotter, “Suppression of stimulated Brillouin scattering during transmission of high-power narrowband laser light in monomode fibre,” Electron. Lett. 18, 638–640 (1982).
  19. K. Tai, A. Hasegawa, and A. Tomita, “Observation of modulational instability in optical fibers,” Phys. Rev. Lett. 56, 135–138 (1986).
  20. N. Doran and D. Wood, “Nonlinear-optical loop mirror,” Opt. Lett. 13, 56–58 (1988).
  21. K. J. Blow, N. J. Doran, B. K. Nayar, and B. Nelson, “Two-wavelength operation of the nonlinear fiber loop mirror,” Opt. Lett. 15, 248–250 (1990).
  22. M. Jinno and T. Matsumoto, “Nonlinear Sagnac interferometer switch and its applications,” IEEE J. Quantum Electron. 28, 875–882 (1992).
  23. G. P. Agrawal, Nonlinear Fiber Optics, 2nd ed. (Academic, San Diego, Calif., 1995).
  24. G. Cappellini and S. Trillo, “Energy conversion in degenerate four-photon mixing in birefringent fibers,” Opt. Lett. 16, 895–897 (1991).
  25. S. Wabnitz, “Modulational polarization instability of light in a nonlinear birefringent dispersive medium,” Phys. Rev. A 38, 2018–2021 (1988).
  26. S. G. Murdoch, R. Leonhardt, and J. D. Harvey, “Polarization modulation instability in weakly birefringent fibers,” Opt. Lett. 20, 866–868 (1995).

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