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We study the nonlinear interaction of laser light with vacuum for a large angular aperture at electromagnetic field strengths far below the Schwinger limit. The polarization and magnetization in vacuum irradiated by a focused laser beam clearly differ from those in matter. This is due to the dependence on the Lorentz invariant, which results in a ring-shaped radiation distribution in vacuum. The number of the radiated photons increases nonlinearly with increasing angular aperture.
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Monden et al. (2011) studied this question.
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