  We derive analytical expressions for the photon polarization tensor in
circularly polarized Hermite- and Laguerre-Gaussian beams, complementing the
corresponding results for linearly polarized beams obtained recently. As they
are based upon a locally constant field approximation of the one-loop
Heisenberg-Euler effective Lagrangian for quantum electrodynamics (QED) in
constant fields, our results are generically limited to slowly varying
electromagnetic fields, varying on spatial (temporal) scales much larger than
the Compton wavelength (time) of the electron.
