Field-gradient-induced second-harmonic generation in magnetized vacuum

Abstract
The photon-photon scattering in vacuum can give rise to the second-harmonic generation of intense laser radiation in a dc magnetic field in the “box” diagram approximation of quantum electrodynamics if the symmetry of interaction is broken by modulation or/and nonuniformity of optical wave +dc field system in time or/and space. Specific examples considered here are: an optical pulse plane wave or a Gaussian laser beam propagating in uniform or nonuniform dc fields.