Enhancement of the computational efficiency of the near-to-far field mapping in the finite-difference method and ray-by-ray method with the fast multi-pole plane wave expansion approach

The finite-difference time-domain (FDTD) and ray-by-ray (RBR) methods are techniques used to calculate the optical properties of nonspherical particles for small-to-moderate and large size parameters, respectively. The former is a rigorous method, and the latter is an approximate geometric-physical optics-hybrid method that takes advantage of both high efficiency of the geometric optics approach and high accuracy of the physical optics approach. In these two methods, the far field is calculated by mapping the near field to the far field with consideration of the phase interference. The mapping computation is more time-consuming than the near-field simulation when multiple scattering directions are involved, particularly in the case of the RBR implementation. To overcome the difficulty, in this study the fast multi-pole method is applied to both FDTD and RBR towards accelerating the far-field calculation, without degrading the accuracy of the simulation results.