An $O(N^3)$ algorithm for the calculation of far field radiation patterns

Abstract

We present a new method for computing the Near-To-Far-Field (NTFF) transformation in FDTD simulations which has an overall scaling of $O(N^3)$ instead of the standard $O(N^4)$. By mapping the far field with a cartesian coordinate system the 2D surface integral can be split into two successive 1D integrals. For a near field spanned by $N_X\times N_Y$ discrete sample points, and a far field spanned by $N_{\theta }\times N_{\varphi }$ points, the calculation can then be performed in $O(N_{\theta }{N}_X{N}_Y)+O(N_{\theta }{N}_{\varphi }{N}_Y)$ operations instead of $O(N_{\theta }{N}_{\varphi }{N}_X{N}_Y)$.

8 pages, 7 figures