A numerical Maxwell–Schrödinger model for intense laser–matter interaction and propagation

We present in this paper an original ab initio Maxwell–Schrödinger model and a methodology to simulate intense ultrashort laser pulses interacting with a 3D H+2-gas in the nonlinear nonperturbative regime under and beyond Born–Oppenheimer approximation. The model we present is the first one to our knowledge (excepted in [E. Lorin, S. Chelkowski, A. Bandrauk, A Maxwell–Schrödinger model for non-perturbative laser–molecule interaction and some methods of numerical computation, Proceeding CRM, vol. 41, American Mathematics Society, 2007], where a one-dimensional version is presented) to be totally nonperturbative, vectorial and multidimensional, taking into account ionization, and high order nonlinearities going far beyond classical nonlinear Maxwell or Schrödinger models. After a presentation of the model and a short mathematical study, we examine some numerical approximations for its computation. In particular, we focus on the polarization computation allowing an efficient coupling between the Maxwell and time dependent Schrödinger equations (TDSE), and on an efficient parallelization. Examples of numerical computations of high order harmonic generation and of electric field propagation are presented for one molecule and up to 512, thus highlighting cooperative effects in harmonic generation at high order.