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The finite-difference time-domain method based on the locally one-dimensional scheme (LOD-FDTD) is extended to the analysis of periodic structures. The cyclic matrix problem resulting from the application of the periodic boundary condition to the implicit LOD scheme is efficiently solved with the Sherman-Morrison formula. The analysis of a photonic bandgap structure shows that the numerical results are identical to the alternating-direction implicit counterparts. The use of dispersion control parameters enables us to use a large time step size. As a result, the computational time is reduced to Â¿50% of that of the traditional explicit FDTD, while maintaining acceptable numerical accuracy.