2025/08/11 by Sasorov, Pavel, Bulanov, Sergei
#FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #Plasma Physics (physics.plasm-ph)
paper · doi:10.48550/arxiv.2508.09214
High order harmonic (HOH) generation by interacting extremely intense electromagnetic waves in the quantum vacuum is investigated within the framework of the Heisenberg-Euler formalism. We consider here the process in the lowest order of a perturbation theory relative to the electromagnetic (EM) beam intensity, giving contribution to the HOH generation. The main expressions are obtained for a general geometry, whyle polarizations of different sub-beams forming the EM beam focus are almost the same. Nevertheless, explicit expressions for the HOH generation are derived for the 4π-dipole in-coming waves and for the two crossing Gaussian beams. The former geometry of the EM beam is optimal at a given EM wave power, whereas the latter one is more realistic from the experimental point of view. We consider also a relationship of our present general results with the results, obtained earlier for the HOH generation during of collision of two plane electromagnetic waves.