Coupled dipole method for scatterers with large permittivity

Abstract

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.

The discrete dipole approximation: An overview and recent developments

“…Later it was shown that the DDA also can be derived from the integral equation for the electric field, which is discretized by dividing the scatterer into small cubical subvolumes. This derivation was apparently first performed by Goedecke and O'Brien [7] and further developed by others (see, for instance, [8][9][10][11]). It is important to note that the final equations, produced by both lines of derivation of the DDA are essentially the same.…”

“…This approach is called FCD (filtered coupled dipoles), and a computer code library for evaluation of filtered Green's function is available [45]. Chaumet et al [11] proposed direct integration of the Green's tensor (IT) in Eqs. (12), (13).…”

Elastic metamaterials and dynamic homogenization: a review

“…The retrieval method, which began with electromagnetic metamaterials, was subsequently extended to acoustic metamterials [59]. However, the retrieval method, while simple in principle, produces effective parameters which fail to satisfy basic passivity and causality properties [60] and exhibits other antiresonant artifacts [61][62][63]. An excellent review [64] points out that the majority of metamaterial homogenization studies published in the last decade failed to respect basic causality and passivity properties and in some cases also violated the second law of thermodynamics.…”

Near-Field Properties of Plasmonic Nanostructures With High Aspect Ratio

“…In a similar context, Chaumet et al used a Weyl expansion of the Green's tensor to perform the numerical integration of Eq. (6) in the reciprocal k-space [18]. More recently, Massa and coworkers derived an approximate analytical expression for the polarisability of a cuboidal cell [27].…”

“…Let us mention the regularization scheme proposed by Kottmann and Martin developed for 2D-elements but also transposable to 3D-nanostructures [17]. Instead of regularizing the Green's tensor, Chaumet and coworkers directly computed its integral over the volume of cubic meshes [18]. To this aim, they considered a Weyl expansion of the tensor and performed a numerical integration in the reciprocical k-space.…”