Pade approximants for the scattering amplitude in scattering from rough surfaces

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 Pade 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 Pade 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.