A Review of 3-D Green's Functions for Integral Equation Modeling of Electromagnetic Scattering from 1/2/3-D Periodic Structures Using Ewald Transformation

Abstract

This paper reviews 3-D Green's functions (GFs) used in numerical modeling of electromagnetic scattering from periodic structures and presents a consolidated formulation for 1-D, 2-D, and 3-D lattices obtained using Ewald transformation. It includes formulas for the transformed periodic GF sums and their gradient, the expressions for the Ewald splitting parameter, and the singularity extraction. Numerical implementation details that lead to further enhancements in computational speed, accuracy, and numerical stability are also presented.