  We investigate a nonlinear response of the physical vacuum by the example of
the third harmonic in radiation of the electron-positron-photon plasma excited
by a strong time dependent electric field at the focus spot of
counterpropagating laser pulses. The investigation was developed within the
framework of the Bogoliubov-Born-Green-Kirkwood-Yvon kinetic theory
nonperturbatively describing vacuum creation of the quasiparticle
electron-positron plasma (EPP) and different channels of its interaction with
the photon subsystem in the single-photon approximation that are opened in the
presence of a strong semiclassical field. We investigate the radiation of EPP
in the annihilation channel on the basis of the well known approximations and
compare the obtained result with the semiclassical radiation of the plasma
oscillations. In the high-frequency range for large adiabaticity parameter the
quantum radiation dominates in comparison with the semiclassical one.
