A Maxwell–Schrödinger Model for Non-perturbative Laser-molecule Interaction and Some Methods of Numerical Computation

We present in this paper a numerical Maxwell–Schrödinger model to simulate intense ultrashort laser pulses interacting with a H 2 -gas in the nonlinear non-perturbative regime. After presentation of the model and a short mathematical study, we propose a numerical approach for its computation. In particular we focus on the polarization computation allowing the coupling between the Maxwell and Schrödinger equations, and on the boundary conditions problem for the time dependent Schrödinger equations, TDSE. Some comparisons with existing methods are also addressed.