Light diffraction by a strong standing electromagnetic wave
  The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the probe beam as opposed to the corresponding plane wave scenario. A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light. 
A. Di Piazza, K. Z. Hatsagortsyan, and C. H. Keitel