---
abstract: 'We study the effect of stimulated photon emission from the vacuum in strong space-time dependent electromagnetic fields. We emphasize the viewpoint that the vacuum subjected to macroscopic electromagnetic fields with at least one nonzero electromagnetic field invariant, as, e.g., attainable by superimposing two laser beams, can represent a source term for outgoing photons. We believe that this view is particularly intuitive and allows for a straightforward and intuitive study of optical signatures of quantum vacuum nonlinearity in realistic experiments involving the collision of high-intensity laser pulses, and exemplify this view for the vacuum subjected to a strong standing electromagnetic wave as generated in the focal spot of two counter-propagating, linearly polarized high-intensity laser pulses. Focusing on a comparably simple electromagnetic field profile, which should nevertheless capture the essential features of the electromagnetic fields generated in the focal spots of real high-intensity laser beams, we provide estimates for emission characteristics and the numbers of emitted photons attainable with present and near future high-intensity laser facilities.'
author:
- Felix Karbstein
- Rashid Shaisultanov
title: Stimulated photon emission from the vacuum
---

Introduction {#sec:intro}
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The fluctuations of virtual charged particles in the vacuum of quantum electrodynamics (QED) give rise to 