Two techniques in near-to-far-field extrapolation for one-dimensional periodic structure

In order to perform the near-to-far-field extrapolation for one-dimensional periodic structure, the Floquet-mode method is first discussed. The complex amplitudes of each Floquet’s mode are determined based on the Fourier series expansion for the near fields on the output boundary. The far fields are then computed by the superposition of each Floquet's mode. On the other hand, an approach using the periodic Green’s function is also considered. The equivalent electromagnetic currents on the output boundary in near field region are obtained from FDTD computation. The far fields are then extrapolated using the periodic Green's function. This approach is similar to the way commonly applied for near-to-far field extrapolation. Only near fields in a single cell of the periodic structure are us