In the present study, we consider the effects of vacuum birefringence and
dichroism in strong electromagnetic fields. According to quantum
electrodynamics, the vacuum state exhibits different refractive properties
depending on the probe photon polarization and one also obtains different
probabilities of the photon decay via production of electron-positron pairs.
Here we investigate these two phenomena by means of several different
approaches to computing the polarization operator. The external field is
assumed to be a linearly polarized plane electromagnetic wave of arbitrary
amplitude and frequency. Varying the probe-photon energy and the field
parameters, we thoroughly examine the validity of the locally-constant field
approximation (LCFA) and techniques involving perturbative expansions in terms
of the external-field amplitude. Within the latter approach, we develop a
numerical method based on a direct evaluation of the weak-field Feynman
diagrams, which can be employed for investigating more complex external
backgrounds. It is demonstrated that the polarization operator depends on two
parameters: classical nonlinearity parameter ξ and the product η=ωq0​/m2 of the laser field frequency ω and the photon energy
q0​ (m is the electron mass). The domains of validity of the approximate
techniques in the ξη plane are explicitly identified.Comment: 11 pages, 6 figure