Maxwell–Schrödinger–Plasma (MASP) model for laser–molecule interactions: Towards an understanding of filamentation with intense ultrashort pulses

We develop in this paper a method for the simulation of intense ultrashort electromagnetic fields propagating in a molecular gas. The electromagnetic field (laser pulse) is modeled using Maxwell’s equations coupled with many time dependent quantum Schrödinger equations modeling the molecular gas thus including an ab initio description of the laser–molecule interaction. This Maxwell–Schrödinger–Plasma, MASP, model allows us to include high harmonics, self-focusing and self-defocusing nonlinearities. At the intensities, we consider that the gas is partially ionized leading to the creation of a free electron plasma which contributes to the pulse defocusing. We then present a series of numerical simulations showing the behavior of the MASP model depending on the gas density, and initial laser intensity. In particular, self-focusing and self-defocusing effects as well as filament-like behaviors are presented and discussed. A scaling theory is developed for large propagations.