Scaling limits for wave pulse transmission and reflection operators

The random paraxial wave equation is revisited to take into account not only random forward scattering, but also random backscattering. In this paper we are interested in the transmitted wave fronts and also wave fronts reflected by a strong interface buried in a random medium. In the weakly heterogeneous regime the reflected and transmitted wave fields are characterized by reflection and transmission operators that are the solutions of Itô-Schrödinger diffusion models. These models allow for the computations of the Wigner distributions and the autocorrelation functions of the reflected and transmitted waves. They also fully take into account the fact that the waves travel through the same medium during the propagation to and from the interface, which induces an increase of the beam radius and of the correlation radius, and also predict the enhanced backscattering effect in the backscattered direction.