Harmonic generation from laser-driven vacuum

We investigate the feasibility that, in the field of a superstrong standing laser wave, high-order harmonics of the pumping laser are generated from vacuum. Analytical calculations employing adiabatic perturbation theory show that, for laser electric fields larger than Ecr=m²c³/e=1.3×10¹⁶ V/cm, high-order harmonics are generated. The harmonic spectrum shows a wide plateau followed by a cutoff. The cutoff starts approximately at photon energies ωM~√ecEL, with EL being the amplitude of the laser field. In the opposite limit ELEcr, the emission of high harmonics is very unlikely. In this case, a feasibility analysis for the experimental observation of the photon-photon scattering process using x-ray free electron lasers shows that the requirements are much less restrictive than those required to observe electron-positron pair creation.