Unified asymptotic description of Gaussian pulse propagation of arbitrary initial pulse width in a Lorentz-type gain medium

Abstract

An asymptotic approach is utilized in order to obtain a unified description of the propagated field dynamics due to an input Gaussian-modulated harmonic wave of arbitrary initial pulse width in a linear, causally dispersive gain medium, described by the single resonance Lorentz model. The asymptotic method of analysis is applied on the unified, exact integral representation of the propagated field, which is characterized by a unified complex phase function that depends upon the input field and gain medium parameters as well as upon the propagation distance in the medium. In order to apply the asymptotic method, an analysis of the evolution of the saddle point locations, which depend upon the dispersive properties of the gain medium, the temporal width, and the carrier frequency of the input Gaussian pulse as well as upon the propagation distance and of the topography of the real part of the unified phase function in the complex ω plane, must be performed. Upon the subsequent numerical application of the asymptotic method, the predictions of the unified asymptotic approach are found to be in exceptional agreement with the respective results of a purely numerical experiment for all considered initial pulse widths and lead to a unified model of Gaussian pulse propagation in a gain Lorentzian medium. According to this model, the propagated field is composed of pulse components, each being due to the asymptotic contribution of a respective relevant saddle point of the unified phase function. The instantaneous angular frequency of oscillation and the stationary point(s) of the envelope of each such pulse component are then obtained from the real and imaginary parts, respectively, of the corresponding relevant saddle point as it evolves in the complex ω plane. This theoretical approach may then yield particularly useful physical insights into attosecond pulse propagation.