A simple and efficient joint algorithm of finite difference time domain (FDTD) and periodic boundary condition (PBC), called as the direct spectral FDTD method, has been investigated to study three-dimensional (3D) periodic structures with oblique incidence, where both the azimuth angle φ and the elevation angle θ are varying. The number of sampling points for the horizontal wave number can be determined by using an adaptive approach. As numerical results, the transmission and reflection coefficients from split-ring resonators (SRRs) and a dielectric grating slab are computed to validate the accuracy and efficiency of the direct spectral FDTD method. The computed results are in good agreement to the published ones obtained by other methods.
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