Self-Steepening of Light Pulses

Abstract

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.