Generation of High Order Harmonics in Quantum Vacuum for 4π-Dipole Geometry

Abstract High-order harmonic (HOH) generation during the interaction of extremely intense electromagnetic waves in a quantum vacuum is studied within the Heisenberg-Euler formalism. We consider this process in the first nonvanishing order of perturbation theory. The basic expressions are derived for a general geometry, where the polarizations of the various sub-beams forming the focus of the electromagnetic beam are virtually identical. Explicit expressions for HOH generation are obtained for 4π-dipole incoming wave. This beam geometry is optimal for a given incident electromagnetic wave power.