Homogenization Techniques for Improving the Calculations of Scattering by 1-D Fast Oscillating Periodic Surfaces

This paper deals with the efficient computation of scattering problems by fast oscillating periodic surfaces using two-scale expansion homogenization techniques. The proposed method splits the field between an effective field and a boundary layer corrector and applies an asymptotic expansion. Then, the evaluation of these boundary layers leads to the extraction of effective parameters, modeling the effects of the highly oscillating surface on the scattered field. A previous paper has already presented such a technique to deal with TM polarization. First, this paper extends the approach to TE polarization and completes it by pointing out all the key points. Especially it shows the map of the split fields underlining the physical contribution of each term. Second, this paper exposes and compares two different uses of these computed effective parameters. Numerical examples show the validity of the method, especially by justifying the asymptotic expansion ansatz. Computational efficiency is discussed.