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We test current numerical implementations of laser-matter interactions by comparison with exact analytical results. Focussing on photon emission processes, it is found that the numerics accurately reproduce analytical emission spectra in all considered regimes, except for the harmonic structures often singled out as the most significant high intensity/multi-photon effects. We find that this discrepancy originates in the use of the locally constant field approximation., 9 pages, 10 figures

We discuss the theory and phenomenology of pair annihilation, within an ultrashort laser pulse, to a single photon. The signature of this process is the unidirectional emission of single photons with a fixed energy. We show that the cross section is significantly larger than for two-photon pair annihilation in vacuum, with x-ray free-electron laser parameters admitting a much clearer signal than optical beams.