Unified Description of Chirped Gaussian Pulse Propagation of Arbitrary Initial Width in a Multiple Resonance Lorentz Medium

摘要

The unified asymptotic approach yields an accurate description of chirped Gaussian pulse propagation in a causally dispersive and absorptive multiple resonance Lorentz medium, and is valid from the slowly-varying envelope to the sub-cycle pulse regimes. The dynamical evolution of the propagated field is directly related to the dynamics of the saddle points of the unified complex phase function. Accordingly, the (total) propagated field is comprised of pulse components each being due to the contribution of a respective relevant saddle point. The instantaneous oscillation frequency and the occurrence/propagation velocity of a stationary point of the envelope, of each such pulse component are intrinsically related with the dynamics of the respective relevant saddle point. Under certain conditions, a stationary point of the envelope of a pulse component occurs when the respective saddle point trajectory intersects the real frequency axis, and it travels with the group velocity at this frequency crossing value.