首先讨论了自由空间中一维周期结构近-远场外推的Floquet模方法,即对FDTD计算所得散射近场中输出边界上散射场进行级数展开,求出各阶Floquet模的复数幅值,再求得远区场.接着介绍了求解一维周期结构远区散射场的周期Green函数方法,即根据FDTD计算所得散射近场中输出边界上散射场,求得等效面电磁流后,再借助周期Green函数进行外推得到远区场.两种方法均仅用一个周期单元内的散射近场进行外推.计算结果验证了上述两种方法外推的有效性.

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 used to calculate far fields in these two methods. The efficiency and applicability of these two schemes are demonstrated by numerical results.