  In this article, we provide analytical expressions for the photon
polarization tensor in pulsed Hermite- and Laguerre-Gaussian laser beams. Our
results are based on a locally constant field approximation of the one-loop
Heisenberg-Euler effective Lagrangian for quantum electrodynamics. Hence, by
construction they are limited to slowly varying electromagnetic fields, varying
on spatial and temporal scales significantly larger than the Compton
wavelength/time of the electron. The latter criterion is fulfilled by all laser
beams currently available in the laboratory. Our findings will, e.g., be
relevant for the study of vacuum birefringence experienced by probe photons
brought into collision with a high-intensity laser pulse which can be
represented as a superposition of either Hermite- or Laguerre-Gaussian modes.
