A numerical model for light interaction with a two-level atom medium

The aim of this work is to study the interaction of a laser pulse with a gas described by the Bloch equations. The physical model is derived from the Maxwell–Bloch equations under the assumption that the polarization and the electric field are both oriented in a single direction, and under the slowly varying envelope approximation. The Schrödinger equation is formulated for a two-level atom medium under the rotating wave approximation and dipole interaction. A rigorous asymptotic analysis of the simplified system is performed to point out the different mechanisms associated with the physical model. A numerical approach based on a splitting technique is proposed and successfully performed.