Sauter-Schwinger effect for colliding laser pulses

We study electron-positron pair creation by the electromagnetic field of two colliding laser pulses as described by the vector potential
A(t,r) = [f(ct−x) +f(ct+x)]ey. Employing the world-line instanton technique as well as a generalized WKB approach, we find that the pair creation rate along the symmetry axisx= 0(where one would expect the maximum contribution) displays the same exponential dependence as for a purely time-dependent electric field A(t) = 2f(ct)ey. 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.