Interpolation of Ewald-Accelerated Periodic Green’s Function Representations for Homogeneous or Layered Media

A method is explored and developed for significantly accelerating the computation of the Ewald series representation for periodic homogeneous media Green's functions. The method involves extracting corner singularity terms from the corners of the unit cell, resulting in a smooth regularized Green's function that is amenable to interpolation. The approach can be used to accelerate layered-media problems, where application of Kummer's method splits the spectral (Floquet modal) series representation into a rapidly converging difference series that is regular plus a residual series that contains any spatial singularities present. The residual series corresponds to a homogeneous medium, and can thus be treated with the method proposed here.