Asymptotic analysis of classical wave localization in multiple-scattering random media

In this work we consider the localization of classical waves propagating in random continuum. We apply the method of proper time for the transfer from the elliptic-type wave equation to the generalized parabolic one. Presenting the solution of the latter equation in the form of the Feynman path integral allows us to estimate the so-called wave correction terms. These corrections are related to coherent backscattering and recurrent multiple-scattering events, i.e., to phenomena that cannot be described within the framework of the conventional theories of radiative transfer or small-angle scattering. We evaluate the wave correction to the mean intensity of a point source located in a statistically homogeneous Gaussian random medium. Our results confirm that there is an essential difference between two- and three-dimensional systems. We consider both isotropic and anisotropic media and show in particular that in the latter case there is a critical value of the anisotropy parameter, below which the system behaves basically as a three-dimensional isotropic medium, i.e., the wave correction is positive for all observation angles. Above this critical value the properties of the medium are similar to those of a layered structure.