Analysis of four-wave mixing of high-power lasers for the detection of   elastic photon-photon scattering
  We derive expressions for the coupling coefficients for electromagnetic four-wave mixing in the non-linear quantum vacuum. An experimental setup for detection of elastic photon-photon scattering is suggested, where three incoming laser pulses collide and generate a fourth wave with a new frequency and direction of propagation. An expression for the number of scattered photons is derived and, using beam parameters for the Astra Gemini system at the Rutherford Appleton Laboratory, it is found that the signal can reach detectable levels. Problems with shot-to-shot reproducibility are reviewed, and the magnitude of the noise arising from competing scattering processes is estimated. It is found that detection of elastic photon-photon scattering may for the first time be achieved. 
J. Lundin, M. Marklund, E. Lundstrom, G. Brodin, J. Collier, R.   Bingham, J.T. Mendonca, P. Norreys