Abstract. We present a scheme for the computation of scattering amplitudes for the scattering of electromagnetic waves off perfectly reflective periodic rough surfaces. Our scheme starts with a surface integral equation and is based on the equivalence of Padé approximants to the Liouville–Neumann series solution, and the exact solution of the projection of the problem to finite subspaces. This, we show, implies convergence of the sequence of Padé approximants even in cases where the Liouville–Neumann series may not converge. Next, we show that a novel extension of the projective subspace, motivated by considerations of reciprocity, yields significant enhancement in computational accuracy at negligible computational cost. We present numerical results to illustrate both these points.

Keywords: Padé approximants, rough surface scattering, surface integral

Print publication: Issue 10 (October 2005)
Received 16 March 2005, accepted for publication 11 July 2005
Published 8 September 2005