Abstract

By solving the time-dependent Dirac equation numerically, we calculate the rate of electron–positron pairs that are created from the vacuum by an oscillating field. The data permit us to examine the validity of approximate, but analytical, expressions derived from the WKB-based description. If two characteristic parameters ($E/c^3$ and $\omega /c^2$) are less than 1 or the parameter $\gamma (=\omega c/E)$ is small (tunneling region), this description predicts the true rate well, where $E$ and $\omega$ are the amplitude and frequency of the external field. In the multi-photon region (where $E/c^3$ is small and $\gamma$ is large), perturbative methods become valid.

© 2015 Optical Society of America

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