Dirichlet-to-Neumann Map Method for Diffraction Gratings

The researchers propose to develop two numerical methods for diffraction grating problems. The first method is for multi-layered structures where each layer is z-invariant as in the popular Fourier modal method. Instead of computing the eigenmodes in each layer, they compute the local Dirichlet-to-Neumann (DtN) map M and use M to solve the diffraction grating problems. The second method attempts to overcome the difficulty of existing integral equation methods for evaluating the quasi-periodic Green's function. The researchers develop an integral equation method to calculate the Dirichlet-to-Neumann map Lambda of a bounded homogeneous domain and use it to solve the diffraction grating problem. Only the standard Green's function is needed in our integral equation formulation.