Scattering of electromagnetic waves from rough surfaces: A boundary integral method for low-grazing angles

We present a boundary integral method for the numerical solution of the rigorous problem of wave scattering from rough surfaces under grazing illumination. The model of a locally perturbated plane is adopted: a finite patch of rough surface has its roughness flattened at the edges. The boundary formulation unknowns are the tangential components of the scattered field, defined as the contribution from the rough area. This way, the numerical domain of study is correctly bounded, even with a plane wave as incident field, and the sampled area is made independent of the incidence. This rigorous approach, called the grazing method of moments, is implemented on two-dimensional perfectly conducting surfaces and validated by comparison with a reference numerical solution for surfaces with Gaussian correlation functions. Now, the validity of approximate models at low-grazing-angles can be investigated; the small perturbation method and the small slope approximation are addressed in this paper. Scattering diagrams show how the performances of these methods deteriorate drastically at backward scattering angles as the incidence goes to grazing.