Polarization ratios anomalies of 3D rough surface scattering as second order effects

A detailed analysis of the behaviour of electromagnetic scattering from various corrugated bidimensional surfaces is presented. We show that rigorous electromagnetic computations on two dimensional surfaces can in fact yield HH/VV polarization ratios greater than one, with values consistent with those observed experimentally. We also show that HH/VV ratios greater than one are ubiquitous in the case of surfaces of the form f(x, y)=f/sub 1/(x)+f/sub 2/(y), known as crossed gratings in optics. Theoretically and numerically, these surfaces are shown to produce backscattered returns for which the first order Rice/Valenzuela term vanishes for off axis incidence. The second order term becomes dominant and has the property that HH returns exceed VV returns for a significant range of incident angles. Our approach is based on the methods of O.Bruno and F. Reitich (see J. Opt. Soc. A., vol.10, p.2551-62, 1993) which yield accurate results for a large range of values of the surface height. In particular, these methods can be used well beyond the domain of applicability of the first order theory of S.O. Rice (1951). The error in our calculations is guaranteed to be several orders of magnitude smaller than the computed values. The high order expansions provided by these methods are essential to determining the role played by the second order terms as they show that these terms indeed dominate most of the backscattering returns for the surfaces mentioned. Classically, large HH/VV ratios were sought by means of first order approximations on one dimensional sinusoidal profiles. In that case, we show that the first order terms do not vanish and the first order theories predict the behaviour of the backscattered returns, for small values of the height to period ratio. However, in the case of a two dimensional bisinusoidal surface, strong polarization dependent anomalies appear in the scattering returns as a result of the contributions of second order terms since, in that case, the first order contributions vanish.