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
L_{1}
wide, is computed. The length
L_{1}
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 \ll L_{1}
. It is found that
Q
increases from the Born approximation
Q = Q_{1}
for medium width
L \ll L_{1}
to
Q = 2Q_{1}
for
L \gg L_{1}
, and the theory is valid as long as
L \ll (kL_{0})^{5/3} L_{1}
, a significant improvement over the Born approximation, when the macroscale
L_{0}
is much larger than the wavelength
2_{\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.