Harmonic generation from laser-driven vacuum

We investigate harmonic generation from vacuum in the field of a superstrong standing laser wave. We show analitycally that for laser electric fields larger than E-cr = m(2)c(3)/he = 1.3. 10(16) V/cm high order harmonics of the pumping laser are generated. The harmonic spectrum shows a wide plateau followed by a cut-off at photon energies h omega m similar to root hecE(L) with EL the amplitude of the laser field. In the weak field limit EL << Ecr the emission of high harmonics is very unlikely. This is now the experimentally interesting case and we show that "laser assisted" photon-photon scattering could be observed with optical lasers available today.