Analysis of the Angular Frequency Dynamics in Chirped Dispersive Pulse Propagation

The unified asymptotic approach yields an accurate description of chirped dispersive pulse propagation of arbitrary initial width. The saddle points of the phase function appearing in the exact integral expression of the propagated field are central to the application of this approach. In fact, the dynamics of these saddle points are mapped into the characteristics of the propagated field. Therefore, an analysis of the dependence of the saddle points on the input field and medium parameters and on the propagation distance provides unique theoretical insight on the propagated field characteristics. Here, the procedure for investigating this dependence is elaborated and applied to describe the angular frequency dynamics of the propagated field; the regions of up and down chirp of the instantaneous oscillation frequency are also identified.