Self-Modulation, Self-Steepening, and Spectral Development of Light in Small-Scale Trapped Filaments

Phys. Rev. 177, 306 – Published 5 January 1969
T. K. Gustafson, J. P. Taran, H. A. Haus, J. R. Lifsitz, and P. L. Kelley


The spectral broadening associated with light propagating in self-trapped filaments through liquids with large optical Kerr constants is studied. In particular, we treat the influence of a nonzero orientational relaxation time and of linear dispersion upon the phase (and amplitude) development of the light as it interacts with the optically nonlinear medium. Relaxation introduces Stokes-anti-Stokes asymmetry, even in the absence of pulse steepening. The spectrum is compressed, and the degree of interference in various portions of the spectrum is altered. The effect of dispersion is apparently much less important, particularly in the case where propagation distances are short compared with the shock distance. However, dispersion combined with a finite relaxation time does introduce an exponential gain in the forward direction. For a small nonlinearity, the peak gain is equal to the stimulated Rayleigh gain in the backward direction; but it falls off with increasing nonlinearity, because of the Stokes-anti-Stokes interaction.

Spectra computed for a picosecond pulse and for a 100% sinusoidally modulated light beam of infinite extent are compared. Because of its periodicity, the latter possesses a fine structure and is influenced differently by the orientational relaxation.

Comparison of the experimental results with the theoretical calculations for the cases of a zero and a nonzero relaxation time indicates that pulses of the order of 5-10 psec in extent could give rise to the observed spectra. Possible sources of such pulses (or a sequence of such pulses) are discussed.


  • Received 18 July 1968
  • Published in the issue dated January 1969

© 1969 The American Physical Society

Authors & Affiliations

T. K. Gustafson*,† and J. P. Taran‡,§

  • Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

H. A. Haus*

  • Department of Electrical Engineering and Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

J. R. Lifsitz

  • Electronics Research Center, National Aeronautics and Space Administration, Cambridge, Massachusetts 02139

P. L. Kelley§,**

  • Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, Massachusetts 02173

  • *Work supported by the Joint Services Electronics Program [Contract DA28-043-AMC-02536 (E)].
  • Present address: Department of Electrical Engineering, University of California, Berkeley, California 94720.
  • On leave of absence until September 1969 from Département d'Optique, Office National d'Etudes et de Recherches Aérospatiales, France (ONERA). Work supported by ONERA and Délégation Générale á la Recherche Scientifique et Technique, France.
  • §Present address: Department of Physics, University of California, Berkeley, California 94720.
  • **Operated with support from the U. S. Air Force.

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