An $O(N^{3})$ Algorithm for the Calculation of Far Field Radiation Patterns

We present a new method for computing the near-to-far-field (NTFF) transformation in finite-difference time-domain simulations which has an overall scaling of O(N³) instead of the standard O(N⁴). By mapping the far field with a cartesian coordinate system, the 2-D surface integral can be split into two successive 1-D integrals. For a near field spanned by N_X×N_Y discrete sample points, and a far field spanned by N_θ×N_φ points, the NTFF calculation can then be performed in O(N_θN_XN_Y)+O(N_θN_φN_Y) operations instead of O(N_θN_φN_XN_Y).