A Fast Algorithm for Computation of Electromagnetic Wave Propagation in Half-Space

A new frequency-domain algorithm, the planar Taylor expansion through the fast Fourier transform (FFT) method, has been developed to speed the computation of the Green's function related formulas in the half-space scenario for both the near-field (NF) and the far-field (FF). Two types of Taylor-FFT algorithms are presented in this paper: the spatial Taylor-FFT and the spectral Taylor-FFT. The former is for the computation of the NF and the latter is for the computation of the FF or the Fourier spectrum. The planar Taylor-FFT algorithm has a computational complexity of ${O(N^{2} \log _{2} N^{2})}$ for an ${N\times N}$ computational grid, comparable to the multilevel fast multipole method (MLFMM). What's more important is that, the narrowband property of many electromagnetic fields allows the Taylor-FFT algorithm to use larger sampling spacing, which is limited by the transverse wave number. In addition, the algorithm is free of singularities. An accuracy of $-50~{\rm dB}$ for the planar Taylor-FFT algorithm is easily obtained and an accuracy of $-80~{\rm dB}$ is possible when the algorithm is optimized. The algorithm works particularly well for narrowband fields and quasi-planar geometries.