  Optical signatures of the effective nonlinear couplings among electromagnetic
fields in the quantum vacuum can be conveniently described in terms of
stimulated photon emission processes induced by strong classical, space-time
dependent electromagnetic fields. Recent studies have adopted this approach to
study collisions of Gaussian laser pulses in paraxial approximation. The
present study extends these investigations beyond the paraxial approximation by
using an efficient numerical solver for the classical input fields. This new
numerical code allows for a consistent theoretical description of optical
signatures of QED vacuum nonlinearities in generic electromagnetic fields
governed by Maxwell's equations in the vacuum, such as manifestly non-paraxial
laser pulses. Our code is based on a locally constant field approximation of
the Heisenberg-Euler effective Lagrangian. As this approximation is applicable
for essentially all optical high-intensity laser experiments, our code is
capable of calculating signal photon emission amplitudes in completely generic
input field configurations, limited only by numerical cost.
