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

The backscatter cross section Q for high-frequency irradiated turbulent dielectric media, many mean free paths L₁ wide, is computed. The length L₁ is the distance into the medium over which the mean electric field decreases in amplitude by a factor e^-1. Previous calculations have always been restricted to L L₁. It is found that Q increases from the Born approximation Q = Q₁ for medium width L L₁ to Q = 2Q₁ for L L₁, and the theory is valid as long as L (kL₀) ^5/3 L₁, a significant improvement over the Born approximation, when the macroscale L₀ is much larger than the wavelength 2_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.