  We study the effective theory of soft photons in slowly varying
electromagnetic background fields at one-loop order in QED. This is of
relevance for the study of all-optical signatures of quantum vacuum
nonlinearity in realistic electromagnetic background fields as provided by
high-intensity lasers. The central result derived in this article is a new
analytical expression for the photon polarization tensor in two linearly
polarized counter-propagating pulsed Gaussian laser beams. As we treat the peak
field strengths of both laser beams as free parameters this field configuration
can be considered as interpolating between the limiting cases of a purely
right- or left-moving laser beam (if one of the peak field strengths is set to
zero) and the standing-wave type scenario with two counter-propagating beams of
equal strength.
