  This paper reviews the state of the art of periodic boundary conditions
(PBCs) in Finite-Difference Time-Domain (FDTD) simulations. 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 non-periodic 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.
