Internal and scattered electric fields in the discrete dipole approximation

Abstract

The calculated scattering matrix elements and interior electric fields for a dielectric sphere based on the discrete dipole approximation (DDA) are compared with the exact Mie solution for homogeneous and composite spheres. For homogeneous spheres the macroscopic average field produced at each DDA dipole site by the incident field combined with the field from all DDA sites is found to be approximated by the factor (n12+2)/3 multiplied by the Mie macroscopic field, where n1 is the refractive index. This holds to surprising accuracy, considering the finite wavelength and the small number of dipoles used in the DDA approximation. The approximate relation is most accurate near the center of the sphere and least accurate at the interface. The relation also holds for electric fields within composite spheres, with poorer agreement near each interface, where the refractive index changes. The dependence of this relation on parameters of the model is examined.