Wave scattering in a randomly inhomogeneous medium with long-range noise correlation function $\sim1/r$

A simplified scalar model of the propagation of light in liquid crystals is considered: a monochromatic plane wave propagating normally to the boundary in a half-space filled with a randomly inhomogeneous medium with a long-range homogeneous isotropic noise correlation function $D(r)\sim1/r$ (Goldstone fluctuations). In the eikonal approximation, which is valid for small scattering angles $\theta$ and not too large depth $z$ of penetration into the medium, the ray intensity $I_p(z,\theta)$ of the scattered light is calculated. The results make it possible to explain why intense spreading of a laser beam in nematics is observed experimentally for the extraordinary mode only at distances several times greater than the damping length of the coherent component.