FDTD far-field scattering amplitudes: Comparison of surface and volume integration methods

The transformation of the near-field to the corresponding far-field is a key step involved in the application of the finite-difference time-domain (FDTD) technique to the scattering of an electromagnetic wave by a dielectric particle. In practice, either a volume-integral method (VIM) or an equivalent surface-integral method (SIM) can be used to calculate the far-field. Previous studies reported in the literature demonstrated that a fine grid resolution is necessary for implementing the FDTD technique with the aforementioned VIM for electromagnetic scattering of plane waves by a dielectric particle with a large refractive index. A fine grid resolution leads to a significant amount of computational effort in terms of computer memory and CPU time, and consequently, substantially limits the applicability of the FDTD technique. In this study, we show that the SIM allows a much coarser grid resolution than that required by the VIM. The physical mechanism associated with the advantages of the SIM is also discussed. Furthermore, it is demonstrated that the same order of numerical errors for the phase function computation can be achieved using the SIM with a grid size of Δs=λ/40 for the two published large refractive indices, namely m=7.1499+i2.914 and 8.2252+i1.6808, whereas the grid size required by the VIM, as reported in the literature, needs to be Δs=λ/143 or λ/165. With the SIM, the scattering properties of particles with complex refractive indices as large as 7.1499+i2.914 can be simulated by the FDTD technique for size parameters up to 20 by using an ordinary desktop computer.