The discrete dipole approximation for periodic targets I. theory and tests

TL;DR

This paper extends the discrete dipole approximation (DDA) to periodic targets, generalizes scattering matrices, and validates the approach with accuracy tests against exact solutions, also providing a method for near-field calculations.

Contribution

The paper introduces a generalization of DDA for periodic targets and demonstrates its accuracy with new scattering matrices and near-field calculation methods.

Findings

DDA can be extended to singly- and doubly-periodic targets.

The generalized scattering matrices accurately match exact solutions.

The method enables near-field calculations for infinite slabs.

Abstract

The discrete-dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets that have sizes smaller than or comparable to the wavelength of the incident radiation. The DDA can be extended to targets that are singly- or doubly-periodic. We generalize the scattering amplitude matrix and the 4 x 4 Mueller matrix to describe scattering by singly- and doubly-periodic targets, and show how these matrices can be calculated using the DDA. The accuracy of DDA calculations using the open-source code DDSCAT is demonstrated by comparison to exact results for infinite cylinders and infinite slabs. A method for using the DDA solution to obtain fields within and near the target is presented, with results shown for infinite slabs.