Abstract

Modern asymptotic techniques are applied to obtain a rigorous, uniformly valid description of Gaussian pulse propagation of arbitrary initial pulse width in a single- resonance Lorentz medium in the mature dispersion regime. This is a problem of considerable practical importance because of the current experimental capability of generating pulses with widths approaching the femtosecond regime. The description afforded by the standard asymptotic theory is shown to be in excellent agreement with two independent numerical experiments describing the propagation of ultrashort Gaussian-modulated harmonic signals with full widths at half maximum ranging from 0 (δ-function input pulse) to 0.4 fs. A generalization of the asymptotic description to broader pulses of arbitrary initial pulse width is then presented. The proposed theoretical description does not rely upon any quasimonochromatic or slowly varying envelope approximations, generalizing the results of these approaches in the limit of broad pulses, nor does it depend upon any nth-order dispersion approximation. Thus, it rigorously maintains the Kramers-Krönig relations, which are critical to the proper analysis of linear dispersive pulse dynamics.

© 1992 Optical Society of America