Sauter-Schwinger effect for colliding laser pulses

Via a combination of analytical and numerical methods, we study electron-positron pair creation by the electromagnetic field ${\bf A}(t,{\bf r})=[f(ct-x)+f(ct+x)]{\bf e}_y$ of two colliding laser pulses. Employing a generalized WKB approach, we find that the pair creation rate along the symmetry plane $x=0$ (where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field ${\bf A}(t)=2f(ct){\bf e}_y$. The pre-factor in front of this exponential does also contain corrections due to focusing or de-focusing effects induced by the spatially inhomogeneous magnetic field. We compare our analytical results to numerical simulations using the Dirac-Heisenberg-Wigner method and find good agreement.