Flexible Discretization of Singular Green Functions Using a Composite Spectral Integration Path

Scattering of electromagnetic waves by a dielectric object can be described as an integral equation involving a Green function. These types of problems can be solved using a spatial spectral formulation, which requires sampling of the spectral Green function. To avoid sampling around the singularities on or near the real axis, the spectral Green function is represented on three separate complex paths. Using appropriate selection functions, these paths are recombined such that the original Fourier integrals are retrieved. This composite path method provides a general way to solve domain integral equations involving Green functions with simple singularities with minimal computational overhead.