Coupled dipole method for scatterers with large permittivity

In the coupled dipole method, a three-dimensional scattering object is discretized over a lattice into a set of polarizable units that are coupled self-consistently. Starting from the volume integral equation for the field, we show that performing the integration of the free-space field susceptibility tensor over the lattice cell dramatically improves the accuracy of the method when the permittivity of the object is large. This integration, done without any approximation, allows us to define a prescription for the polarizability used in the coupled dipole method. Our derivation is not restricted to any particular shape of the scatterer or to a cubic discretization lattice.