STUDY OF A MATHEMATICAL MODEL FOR STIMULATED RAMAN SCATTERING

We study a semiclassical modelization of the interaction of a laser with a mono-atomic gas. The Maxwell equations are coupled with a three-level version of the Bloch equations. Taking into account the specificities of the laser pulse and of the gas, we introduce small parameters and a dimensionless form of the equations. To describe stimulated Raman scattering, we perform a three-scale WKB expansion in the weakly nonlinear regime of geometric optics. The limit system is of Schrödinger–Bloch type. We prove a global existence result for this system and the convergence of its solution toward the solution of the initial Maxwell–Bloch equations, as the parameter of the WKB expansion goes to 0. We put in evidence Raman instability in the one-dimensional case, both theoretically and numerically.