Self-Steepening of Optical Pulses
Self-steepening of optical pulses has been well described in the literature (De Martini et al., 1967; Marburger, 1975) and has been invoked to explain certain cases of spectral superbroadening (Yang and Shen, 1984). For intense optical pulses the refractive index depends on the intensity. Thus, the peak of the pulse travels at a speed different from that of the leading and trailing edges, so that ultimately the pulse tries to form a shock at the trailing edge if n 2 is positive or on the leading edge if n 2 is negative. A very similar thing occurs in fluid mechanics. However, all fluids exhibit viscosity and heat flow and these effects combine to prevent the formation of a truly discontinuous shock; they give the final shock structure, which has finite thickness and a definite shape. In the optical case, dispersion will play an analogous role; it brings the process of self-steepening to an end before a true discontinuity can form. It is for this last reason that we feel it to be imperative to include the effects of dispersion in our present study of self-steepening.
KeywordsTravel Wave Solution Optical Pulse Modulational Instability Solitary Wave Solution Gaussian Pulse
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