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

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 Schrodinger equation that is relevant to the context of the present study.

[1]  H. Washimi,et al.  Self-Trapping and Instability of Hydromagnetic Waves Along the Magnetic Field in a Cold Plasma , 1968 .

[2]  C. Judice,et al.  RECURRENCE OF NONLINEAR ION ACOUSTIC WAVES. , 1972 .

[3]  R. Leonhardt,et al.  Polarization modulation instability in weakly birefringent fibers. , 1995, Optics letters.

[4]  Govind P. Agrawal,et al.  Nonlinear Fiber Optics , 1989 .

[5]  N. Akhmediev,et al.  Exact first-order solutions of the nonlinear Schrödinger equation , 1987 .

[6]  E. Infeld,et al.  Quantitive theory of the Fermi-Pasta-Ulam recurrence in the nonlinear Schroedinger equation , 1981 .

[7]  S. Ulam,et al.  Studies of nonlinear problems i , 1955 .

[8]  W. Ferguson,et al.  Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train , 1977, Journal of Fluid Mechanics.

[9]  N. S. Bergano,et al.  Polarization multiplexing with solitons , 1992 .

[10]  N. Doran,et al.  Nonlinear-optical loop mirror. , 1988, Optics letters.

[11]  N. Akhmediev,et al.  Modulation instability and periodic solutions of the nonlinear Schrödinger equation , 1986 .

[12]  H. Yuen,et al.  Nonlinear deep water waves: Theory and experiment , 1975 .

[13]  D. Cotter.  Suppression of stimulated Brillouin scattering during transmission of high-power narrowband laser light in monomode fibre , 1982 .

[14]  Warren E. Ferguson,et al.  Relationship between Benjamin–Feir instability and recurrence in the nonlinear Schrödinger equation , 1978 .

[15]  D. Batens,et al.  Theory and Experiment , 1988 .

[16]  M. Jinno,et al.  Nonlinear Sagnac interferometer switch and its applications , 1992 .

[17]  S Wabnitz,et al.  Dynamics of the nonlinear modulational instability in optical fibers. , 1991, Optics letters.

[18]  T. Brooke Benjamin,et al.  The disintegration of wave trains on deep water Part 1. Theory , 1967, Journal of Fluid Mechanics.

[19]  Thomas Brooke Benjamin,et al.  Instability of periodic wavetrains in nonlinear dispersive systems , 1967, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[20]  R. Leonhardt,et al.  Nonlinear dynamics of polarization modulation instability in optical fiber , 1997 .

[21]  N. Doran,et al.  Two-wavelength operation of the nonlinear fiber loop mirror. , 1990, Optics letters.

[22]  R. Stolen,et al.  Parametric amplification and frequency conversion in optical fibers , 1982 .

[23]  Marc Haelterman,et al.  Vector soliton associated with polarization modulational instability in the normal-dispersion regime. , 1994 .

[24]  Stefano Trillo,et al.  Third-order three-wave mixing in single-mode fibers: exact solutions and spatial instability effects , 1991 .

[25]  Hasegawa,et al.  Observation of modulational instability in optical fibers. , 1986, Physical review letters.

[26]  Wabnitz,et al.  Modulational polarization instability of light in a nonlinear birefringent dispersive medium. , 1988, Physical review. A, General physics.

[27]  G. Cappellini,et al.  Energy conversion in degenerate four-photon mixing in birefringent fibers. , 1991, Optics letters.