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.

Figure 1

Scattering properties of a pseudosphere with $N=2320$ and $\epsilon =n^2=2.25+i$. Relative error (in percent) for the extinction, absorption, and scattering cross sections between different methods and the exact Mie result. The relative error is plotted versus the normalized lattice spacing $\mid n\mid k_0\Delta$, where $k_0$ is the free-space wave vector of the incident light. Dotted line, radiation reaction correction (RR); dash-dotted line, lattice dispersion relation (LDR); dashed line, polarizability is defined by integrating only the diagonal element of the tensor (IDT); solid line, computation is done by integrating all the elements of the field susceptibilities tensor (IT). The curves with the symbol $+$ pertain to calculations using the polarizability defined by Lakhtakia.

Figure 2

Same as Fig. 1 but for $\epsilon =n^2=10+10i$.

Figure 3

Relative error (in percent) for the extinction cross section for $\mid n\mid k_0\Delta =0.02$ versus $\mathrm{Re}\left(\epsilon \right)$ for three different values of $\mathrm{Im}\left(\epsilon \right)$. Solid line, radiation reaction correction (RR); dashed line, computation done by integrating all the elements of the field susceptibility tensor (IT).