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

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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 <emphasis emphasistype="italic">spatial</emphasis> Taylor-FFT and the <emphasis emphasistype="italic">spectral</emphasis> 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 <formula formulatype="inline"><tex Notation="TeX">${O(N^{2} \log _{2} N^{2})}$</tex></formula> for an <formula formulatype="inline"><tex Notation="TeX">${N\times N}$</tex></formula> 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 <formula formulatype="inline"><tex Notation="TeX">$-50~{\rm dB}$</tex> </formula> for the planar Taylor-FFT algorithm is easily obtained and an accuracy of <formula formulatype="inline"><tex Notation="TeX">$-80~{\rm dB}$</tex> </formula> is possible when the algorithm is optimized. The algorithm works particularly well for narrowband fields and quasi-planar geometries. </para>