Effect of fluctuations on the reflectivity near the angle of total internal reflection

Wave propagation in the presence of a rough dielectric interface with total internal reflection is studied theoretically using the Kirchhoff approximation. An approximate expression valid when the surface is smooth enough is obtained for the mean intensity of a point source as a function of propagation range and statistical parameters of a surface. It is shown that if the characteristic angle of incidence is close to the angle of total internal reflection, small irregularities of interface can drastically change the reflectivity and, consequently, the signal level far away from the source. As an example, far beyond the horizon propagation of radiowaves in the presence of elevated irregular reflecting layers in the atmosphere is discussed.