On Fast Computation of Electromagnetic Wave Propagation through FFT

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. The optimized computational complexity of the planar TI-FFT algorithm is N_T ^opt N_T ^opt O(N log₂ N) for an N = N_x times N_y computational grid, where N_T ^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 gamma_TI, which is given as N_O ^opt ~ In gamma_TI and the optimized spatial slicing spacing between two adjacent spatial reference planes only depends on the characteristic wavelength lambda_c of the electromagnetic wave, which is given as delta_ap ^opt ~ 1/17lambda_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.