  Starting from the Heisenberg-Euler effective Lagrangian, we determine the
photon current and photon polarization tensor in inhomogeneous, slowly varying
electromagnetic fields. To this end, we consider background field
configurations varying in both space and time, paying special attention to the
tensor structure. As a main result, we obtain compact analytical expressions
for the photon polarization tensor in realistic Gaussian laser pulses, as
generated in the focal spots of high-intensity lasers. These expressions are of
utmost importance for the investigation of quantum vacuum nonlinearities in
realistic high-intensity laser experiments.
