Maxwell solvers for the simulations of the laser-matter interaction

With the advent of high intensity laser beams, solving the Maxwell equations with a free-dispersive algorithm is becoming essential. Several Maxwell solvers, implemented in Particle-In-Cell codes, have been proposed. We present here some of them by describing their computational stencil in two-dimensional geometry and defining their stability area as well as their numerical dispersion relation. Numerical simulations of Backward Raman amplification and laser wake-field are presented to compare these different solvers.