Exact Absorbing Boundary Conditions for Periodic Three-Dimensional Structures: Derivation and Implementation in Discontinuous Galerkin Time-Domain Method

A discontinuous Galerkin time-domain method (DGTD) enhanced with exact absorbing boundary conditions (EACs) for characterizing transient electromagnetic interactions on periodic three-dimensional (3-D) gratings is proposed. The EACs are derived rigorously and discretized using a high-order scheme in space and time. The periodic boundary conditions (PBCs) under oblique incidence are also discussed. Implementation of the EACs and PBCs within the DGTD framework is described in detail. Numerical results demonstrate that the accuracy of the discretized EACs matches to that of the discretized Maxwell equations. Additionally, the accuracy and efficiency of the DGTD with the EACs are found to be superior to that of the same DGTD with the perfectly matched layers or approximate absorbing boundary conditions.