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According to the characteristics of the periodic structures with 2-D-staggered grids, two new effective construction methods dealing with periodic boundaries based on the finite-difference time-domain (FDTD) algorithm are developed in this work. The two proposed staggered periodic boundary conditions (PBC) arrangement methods can be implemented combining the existing boundary data mapping techniques. Applying these arrangements, coordinate change and additional ladder boundary grids can be avoided during the modeling process, so that the simulation accuracy of the FDTD algorithm can be maintained. The performance and the applicable conditions of the two staggered PBC arrangement methods are discussed and compared with the common nonstaggered PBC arrangement method. The validity of the two staggered PBC arrangement methods is verified through the numerical examples of an infinite dielectric slab and Jerusalem cross frequency selective surface with 2-D-staggered girds.