Parallel implementation of the periodic boundary condition (PBC) in the FDTD for the investigation of spatial filters

Two-dimensional periodic structures, that exhibit spatial filtering characteristics, find a variety of applications in defense as well as communication. Several PBC/FDTD schemes have been proposed for analyzing such structures. By incorporating the PBC, which takes advantage of the periodicity inherent in the geometry as well as the excitation, the simulation of the original problem is reduced to that of a single unit cell, considerably simplifying the process. However, the simulation time may still be extensive because of the multiple reflections that might occur, especially when the periodic structure is comprised of multiple screens, and the waves can bounce back and forth between them. In this paper, we propose an efficient parallel implementation of the PBC/FDTD based on the split-field formulation, which can significantly reduce the total simulation time when multiple processors are used. For truncating the open boundary of the computational domain, the convolutional PML (CPML) has certain advantages over other types of PML, namely that it is numerically-efficient and essentially independent of the material that it terminates. In this work, we propose a stable implementation of CPML in the PBC/FDTD algorithm.