  The classical nonlinear laser-plasma interaction theory is corrected. Given
the effects of vacuum polarization (induced by extreme laser) as nonlinear
media response, one-dimensional wave equations of a monochromatic laser field
are derived from the Heisenberg-Euler Lagrangian density and a derivative
correction with the first order quantum electrodynamic (QED) effects. A more
suitable model to formulate the interactions of extreme laser and
high-energy-density plasma is developed. In the results, the enhanced effect of
vacuum polarization will be discussed and shown.
