Finite-Difference Time-Domain Modeling of Periodic Structures: A review of constant wave vector techniques

This article reviews state-of-the-art periodic boundary conditions (PBCs) in finite difference time-domain (FDTD) simulations that operate by enforcing constant wave vector components. The mathematical principles and 3D FDTD implementation details are systematically outlined. Techniques for extracting scattering parameters, Brillouin diagrams, and attenuation constants are presented along with the array scanning method (ASM) used to model the interaction of nonperiodic sources with periodic structures. Through these techniques, the robustness, utility, and efficiency of PBCs are demonstrated and a unified view of the various approaches to the FDTD implementation of PBCs is presented.