Electromagnetic reflection from an extended turbulent medium: Cumulative forward-scatter single-backscatter approximation

Abstract

The backscatter cross sectionQfor high-frequency irradiated turbulent dielectric media, many mean free pathsL_{1}wide, is computed. The lengthL_{1}is the distance into the medium over which the mean electric field decreases in amplitude by a factore^{-1}. Previous calculations have always been restricted toL \ll L_{1}. It is found thatQincreases from the Born approximationQ = Q_{1}for medium widthL \ll L_{1}toQ = 2Q_{1}forL \gg L_{1}, and the theory is valid as long asL \ll (kL_{0})^{5/3} L_{1}, a significant improvement over the Born approximation, when the macroscaleL_{0}is much larger than the wavelength2_{\pi}k^{-1}. The improvement is due to incorporation of the dominant effects of cumulative forward scattering in the local electric field in the medium. A rigorous and a heuristic derivation are given. The transitional behavior is discussed and a simple physical interpretation is given.