Light Scattering by Clusters: the Al-Term Method

This paper concerns the theoretical improvement of the discrete dipole approximation (DDA) to provide scattering properties of clusters of spherical monomers. The first scattering coefficient (al-term) in Mie theory is introduced to determine the dipole polarizability used in the DDA. In the al-term method, a spherical monomer in the cluster is replaced by a single dipole. The accuracy of this method is tested to calculate extinction and scattering cross sections by a single sphere, two-touching spheres and three collinear touching spheres. It is found that when each monomer is replaced by a dipole the al-term method is superior to the different types of DDA, e.g., the Lattice Dispersion Relation (LDR), at least for the target with the volume equivalent size parameter X, 0.2≦X≦2. This method also allows treatment of a relatively large sub-volume element which is replaced by a dipole, i.e. the size parameter of the monomer X_m∼1.5. Furthermore, a great reduction in memory requirement and computing time are achieved, e.g. for two touching spheres the al-term method requires only 6% of the total memory requirement and 0.008% of the total computing time for N=8448 with the LDR.Part of this work was done when the author was in the Institute of Physics, GKSS Research Center, Postfach 1160, D-21494 Geesthacht, Germany