Probing vacuum birefringence by phase-contrast Fourier imaging under fields of high-intensity lasers

In vacuum high-intensity lasers can cause photon-photon interaction via the process of virtual vacuum polarization which may be measured by the phase velocity shift of photons across intense fields. In the optical frequency domain, the photon-photon interaction is polarization-mediated described by the Euler-Heisenberg effective action. This theory predicts the vacuum birefringence or polarization dependence of the phase velocity shift arising from nonlinear properties in quantum electrodynamics (QED). We suggest a method to measure the vacuum birefringence under intense optical laser fields based on the absolute phase velocity shift by phase-contrast Fourier imaging. The method may serve for observing effects even beyond the QED vacuum polarization.