The scattering of an electromagnetic wave from an infinite random surface is studied by the probabilistic method developed in a previous paper. For a vertical polarized plane wave incident on a slightly random and perfectly conductive surface a new stochastic wave solution involving multiple scattering is obtained. The stochastic solution is free from the divergence difficulty as in the small perturbation method but gives an anomaly such that for a grazing angle of incidence the coherent scattering almost disappears and instead the incoherent scattering becomes dominant. In terms of the stochastic solution, a number of statistical properties of the scattering are calculated concretely for a perfectly conductive surface, such as the complex amplitude of the coherent scattering, the variance of the electric field, the optical theorem describing the power relation between the coherent and the incoherent scattering, the angular distribution of the incoherent scattering, the scattering cross section per unit area, and the surface wave flow, which are all illustrated in the figures.
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