A new fast algorithm for calculating near-field propagation between arbitrary smooth surfaces

A new fast algorithm using multilevel Taylor interpolation and the FFT (TI-FFT) has been developed to solve the near-field (NF) propagation problem for the planar scenario. The algorithm speeds the computation by grouping neighborhood regions in the spatial domain or the spectral domain through the Taylor interpolation (TI) method using the FFT technique. The CPU time increases as O(N² log₂ N²) instead of the polynomial time O(N⁴) required for the Stratton-Chu formula for N × N observation points. The multilevel TI-FFT uses a sampling rate above the Nyquist rate as required by the FFT, while the Stratton-Chu formula requires a higher sampling rate because of the fast variation of the phase term. An accuracy of -50 dB for the multilevel TI-FFT algorithm is easily obtained and an accuracy of -70 dB is possible when the algorithm is optimized. The algorithm works particularly well for band-limited beam-like fields and "quasi-planar" surfaces.