Asymptotic description of electromagnetic pulse propagation in active Lorentzian media

The asymptotic description of the propagation of a step-modulated signal of fixed angular frequency omega_c into the half-space z > 0 that is occupied by a single-resonance active Lorentzian medium, which is a classical model of an inverted two-level atom, has been presented. The steepest descent method as an asymptotic technique provides the detailed time evolution of the pulse propagation in a linear, temporally dispersive active Lorentzian medium. The analysis and the numerical results show the relation of the location of the saddle points and the topography of the phase function in the complex omega-plane with the transient portion of the pulse that can be used to control the transient response of the medium