Vacuum birefringence in the field of a plane electromagnetic wave

We study the process of vacuum birefringence in a strong electromagnetic field: a probe photon changes its polarization while traversing a counterpropagating laser beam. To describe this phenomenon, we calculate the polarization tensor in the field of a plane monochromatic wave to leading order with respect to its amplitude. The main goal of the study is to compare the results with the data obtained within the locally constant field approximation (LCFA). Here we identify the domain of the LCFA applicability in the case of a plane-wave external background. It is shown that the frequency of the probe photon and that of the external field are symmetrically involved in the relative uncertainty. The exact treatment of the spatiotemporal dependence beyond the LCFA becomes necessary at the energy scale 0.1–1 MeV.