Green's functions for planar structures in periodic skewed 2-D lattices using Ewald transformation

In this paper, we apply the Ewald acceleration technique to the efficient evaluation of periodic Green's functions (GFs) for 2-D skewed lattices. We develop the expression for the optimal value of the splitting parameter for 2-D skewed lattices, derive the gradient of the scalar potential GFs and address the extraction of singularity for both vector/scalar potential GF and their curl/gradient. Several numerical implementation issues are also discussed leading to further enhancement in computational speed, accuracy, and numerical stability.