Vacuum Birefringence in a Field of a Plane Electromagnetic Wave

The process of vacuum birefringence in a strong electromagnetic field is investigated, in which a probe photon changes its polarization when passing through a counterpropagating laser beam. To describe this phenomenon, the polarization operator in a field of a plane monochromatic wave is calculated in the leading order with respect to its amplitude. The main objective of this study is to compare the results with the data obtained within the locally constant field approximation (LCFA) approach. In this study, the limits of applicability of LCFA in the case of an external field of the plane wave are established. It is shown that the frequency of the probe photon and the frequency of the external field contribute to the relative error in a symmetric way. At an energy scale of around 0.1-1 MeV, it becomes necessary to accurately describe the spatial and temporal dependence of the field beyond the LCFA approach.