Increasing the performance of the coupled-dipole approximation: a spectral approach

We show that it is possible to increase the performance of the coupled-dipole approximation (CDA) for scattering by using concepts from sampling theory. In standard CDA, the source in each discretized cell is represented by a point dipole and the corresponding scattered field given by Green´s tensor. In the present approach, the source has a certain spatial extension, and the corresponding Green´s tensor must be redefined. We derive these so-called filtered Green´s tensors for one-dimensional (1-D), two-dimensional (2-D), and three-dimensional (3-D) systems, which forms the basis of our new scheme: the filtered coupled-dipole technique (FCD). By reducing the aliasing phenomena related to the discretization of the scatterer, we obtain with the FCD a more accurate description of the original scatterer. The convergence and accuracy of the FCD is assessed for 1-D, 2-D, and 3-D systems and compared to CDA results. In particular we show that, for a given discretization grid, the scattering cross section obtained with the FCD is more accurate (to a factor of 100). Furthermore, the computational effort required by the FCD is similar to that of the CDA