  The generalized Breit-Wheeler process, i.e. the emission of $e^+e^-$ pairs
off a probe photon propagating through a polarized short-pulsed electromagnetic
(e.g.\ laser) wave field, is analyzed. We show that the production probability
is determined by the interplay of two dynamical effects. The first one is
related to the shape and duration of the pulse and the second one is the
non-linear dynamics of the interaction of $e^\pm$ with the strong
electromagnetic field. The first effect manifests itself most clearly in the
weak-field regime, where the small field intensity is compensated by the rapid
variation of the electromagnetic field in a limited space-time region, which
intensifies the few-photon events and can enhance the production probability by
orders of magnitude compared to an infinitely long pulse. Therefore, short
pulses may be considered as a powerful amplifier. The non-linear dynamics in
the multi-photon Breit-Wheeler regime plays a decisive role at large field
intensities, where effects of the pulse shape and duration are less important.
In the transition regime, both effects must be taken into account
simultaneously. We provide suitable expressions for the $e^+e^-$ production
probability for kinematic regions which can be used in transport codes.
