A Unified Method to Handle Singularities of Periodic Green's Function in Ewald Transformation

In numerical modeling of electromagnetic (EM) scattering from two-dimensional (2-D) periodic structures using the integral equation method, the Ewald transformation is commonly employed to accelerate the convergence of the periodic Green's function (PGF). while the singularity extraction method can accurately evaluate the PGF at singular point using L'Hôpital's rule, direct numerical computation of integrals involving near-singularities may lead to inaccurate in characterizing periodic structures. In this letter, we propose a unified approach to handle both the singularities and near-singularities in the spatial-domain part of the transformed PGF, enabling more precise evaluation of singular and near-singular integrals. Numerical results demonstrate that the proposed method provides accurate predictions of the EM properties of typical 2-D periodic structures.