电磁波传播与散射的泰勒插值FFT算法
The Taylor Interpolation through FFT Algorithm for Electromagnetic Wave Propagation and Scattering
摘要：
本文提出了用于计算半空间准平面几何结构中电磁波传播的泰勒插值快速傅里叶变换（TI-FFT）算法。有两种类型的TI-FFT算法，即，空间TI-FFT和频谱TI-FFT。前者工作在空间域，后者工作在谱域。结果表明，两种TI-FFT算法的优化计算复杂度相同，对于N = N_x \times N_y计算网格，优化计算复杂度为N_r^{opt} N_o^{opt} O（N log_2 N），其中N_r^{opt}为切片参考平面的优化数目，N_o^{opt}为泰勒级数的优化阶数。分析表明，N_o^{opt}与算法的计算精度γ_{TI}密切相关，表示为N_o^{opt} ~ - ln（γ_{TI}），相邻空间参考平面间的最佳空间切片间距δ_z^{opt}仅取决于电磁波的特征波长λ_c，表示为δ_z^{opt} ~ 1/17 λ_c。平面TI-FFT算法允许采样定理所要求的大采样间隔。此外，该算法不存在奇异性，对窄带光束和准平面几何结构的计算效果特别好。
英文摘要：
The Taylor Interpolation through FFT (TI-FFT) algorithm for the computation of the electromagnetic wave propagation in the quasi-planar geometry within the half-space is proposed in this article. There are two types of TI-FFT algorithm, i.e., the spatial TI-FFT and the spectral TI-FFT. The former works in the spatial domain and the latter works in the spectral domain. It has been shown that the optimized computational complexity is the same for both types of TI-FFT algorithm, which is N_r^{opt} N_o^{opt} O (N log_2 N) for an N = N_x \times N_y computational grid, where N_r^{opt} is the optimized number of slicing reference planes and N_o^{opt} is the optimized order of Taylor series. Detailed analysis shows that N_o^{opt} is closely related to the algorithm's computational accuracy γ_{TI}, which is given as N_o^{opt} ~ - ln(γ_{TI}) and the optimized spatial slicing spacing between two adjacent spatial reference planes δ_z^{opt} only depends on the characteristic wavelength λ_c of the electromagnetic wave, which is given as δ_z^{opt} ~ 1/17 λ_c. The planar TI-FFT algorithm allows a large sampling spacing required by the sampling theorem. What's more, the algorithm is free of singularities and it works particularly well for the narrow-band beam and the quasi-planar geometry.
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