The interaction of photons with a slowly varying electromagnetic background

Abstract: The interaction of intense radiation with the quantum vacuum becomes nonlinear as soon as the strengths of the em-fields involved approach the Schwinger critical field. In order to derive nonlinear wave equations in the vacuum we make use of the effective Heisenberg-Euler Lagrangian, which we expand making use of the weak field assumption. That way pair production is neglected and only dispersive nonlinear wave effects are retained. We consider a short laser pulse as a probe traversing a strong em-background. Due to the nonlinear interaction of the probe with the background field the wave front of the probe steepens and high harmonics are generated depending on the initial polarization of the probe. We introduce a numerical scheme capable of solving the underlying wave equations. We show numerical results in one spatial dimension and compare them with an analytical model. The numerical scheme can be extended to multiple spatial dimensions, which will open up the option of complex interacting beam configuration thus lowering the required field strengths for the onset of a strong nonlinear response. First two dimensional simulation results will be discussed.