Random backscattering in the parabolic scaling

In this paper we revisit the parabolic approximation for wave propagation in random media by taking into account backscattering. We obtain a system of transport equations for the moments of the components of reflection and transmission operators. In the regime in which forward scattering is strong and backward scattering is weak, we obtain closed form expressions for physically relevant quantities related to the reflected wave, such as the beam width, the spectral width and the mean spatial power profile. In particular, we analyze the enhanced backscattering phenomenon, that is, we show that the mean power reflected from an incident quasi-plane wave has a maximum in the backscattered direction. This enhancement can be observed in a small cone around the backscattered direction and we compute the enhancement factor as well as the shape of the enhanced backscattering cone.