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(N² log₂ N²) 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 for the planar Taylor-FFT algorithm is easily obtained and an accuracy of -80 dB is possible when the algorithm is optimized. The algorithm works particularly well for narrowband fields and quasi-planar geometries.