Self-Steepening of Light Pulses

Phys. Rev. 164, 312 – Published 10 December 1967
F. DeMartini, C. H. Townes, T. K. Gustafson, and P. L. Kelley


The self-steepening, or change in shape, of light pulses due to propagation in a medium with an intensity-dependent index of refraction is investigated. The time required for the pulse to steepen into an optical shock is found, and the time development of the pulses is studied for both zero and nonzero times of relaxation of the index of refraction. Analytic and numerical solutions are given for the pulse development in a number of cases. The frequency spectrum is obtained in the zero-relaxation time limit, and the largest peak intensities are found on the lower-frequency side of the input spectrum. Although the rate of steepening is modified when the decay time of the pulse becomes as short as the relaxation time for the nonlinear part of the index of refraction, the time of decay can become arbitrarily short when there is no dispersion. Estimates are given of the thickness of the optical-shock region and of the frequency spreading allowed by dispersion with the effect of relaxation included. The influence of self-steepening or pulse distortion in nonlinear optical experiments is discussed.


  • Received 19 May 1967
  • Published in the issue dated December 1967

© 1967 The American Physical Society

Authors & Affiliations

F. DeMartini*,† and C. H. Townes*,‡

  • Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts

T. K. Gustafson§

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

P. L. Kelley**

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

  • *Work supported by the National Aeronautics and Space Administration under Contract No. NsG-330 and the U.S. Air Force Cambridge Research Laboratories.
  • Present address: Institut d'Optique, Faculte des Sciences, Orsay, France.
  • Present address: Department of Physics, University of California, Berkeley, California.
  • §Work supported by the Joint Services Electronics Program [Contract No. DA28-043-AMC-02536 (E)].
  • **Operated with support from the U.S. Air Force.

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