A modified 1D finite-difference time-domain method is analyzed by using the surface boundary condition (SBC-FDTD) for oblique incidence. The SBC-FDTD iterative formulas are deduced in oblique incidence by TEz and TMz wave. The reflection and transmission coefficients of electromagnetic wave in the 1D photonic crystal (PC) including a graphene sheet are calculated by the SBC-FDTD method. The method is also validated by comparison with the existed analytic methods. Finally, this modified method is applied to simulate 1D graphene photonic crystal (GPC). By changing the position of grapheme sheet in GPC, the electromagnetic gap characterizations of 1D GPC by an oblique incidence plane wave in THz spectral range are studied. The computational results show that the graphene sheet can enhance the absorption in THz because of the localization of light and the surface defect formed by graphene.
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