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An efficient finite-difference time-domain method based on the locally one-dimensional scheme (LOD-FDTD) is developed for the analysis of periodic structures. The Sherman-Morrison formula is used to efficiently solve the cyclic matrix problem resulting from the application of the periodic boundary condition to the implicit LOD scheme. Through the analysis of a photonic band-gap (PBG) structure, numerical results are found to be identical to those of the alternating-direction implicit (ADI) counterpart. The use of dispersion control parameters enables us to use a large time-step size. As a result, the computational time is reduced to sime 50% of that of the traditional explicit FDTD while maintaining acceptable numerical results.