Generalized asymptotic description of the propagated field dynamics in Gaussian pulse propagation in a linear, causally dispersive medium

Abstract

As the initial pulse envelope width of an input Gaussian pulse-modulated harmonic wave is increased above the characteristic relaxation time of a single resonance Lorentz model dielectric, the classical asymptotic description of the propagated field becomes increasingly inaccurate at a fixed propagation distance and must then be generalized in order to become uniformly valid with respect to the initial pulse width. The required generalization results in a modified complex phase function that depends not only upon the dispersive medium parameters and the propagation distance, but also upon the initial pulse width. The resultant modified asymptotic description of Gaussian pulse propagation is shown to be uniformly valid in the initial pulse width. The modified asymptotic description presented here reduces to the classical asymptotic result presented in an earlier paper [Phys. Rev. E 47, 3645 (1993)] in the limit of an input ultrashort Gaussian pulse. In the opposite limit of a very broad input pulse, the modified asymptotic description reduces to that obtained with the well-known quasimonochromatic or slowly varying envelope approximation. Furthermore, the modified asymptotic description provides a clear description of the transition from the ultrashort limit to the quasimonochromatic regime for Gaussian pulse propagation.