Scattering of electromagnetic waves from a half space of densely distributed dielectric scatterers

The scattering of a plane wave obliquely incident on a half space of densely distributed spherical dielectric scatterers is studied. The quasi-crystalline approximation is applied to truncate the hierarchy of multiple scattering equations, and the Percus-Yevick and the Verlet-Weis results are used to represent the pair distribution function. The coherent reflected wave is studied with these approximations. The incoherent scattered wave is calculated with the distorted Born approximation. In the low-frequency limit, closed-form expressions are obtained for the effective propagation constants, the coherent reflected wave, and the bistatic scattering coeficients. Results at higher frequencies are calculated numerically. The advantage of the present approach is that, in the low-frequency limit, it reproduces the effects of specular reflection, Fresnel reflection coefficient, Brewster angle, and Clausius-Mosotti relation. In addition to the classical results, the bistatic scattering coefficients are also calculated. The theory is also applied to match backscattering data from dry snow at microwave frequencies.