Discrete-dipole approximation for periodic targets: theory and tests

TLDR

The discrete‑dipole approximation (DDA) is a powerful method for calculating absorption and scattering by targets whose sizes are smaller than or comparable to the wavelength of the incident radiation. The authors extend the DDA to singly and doubly periodic targets by generalizing the scattering amplitude and Mueller matrices. They derive generalized scattering matrices for periodic targets and present a method to compute near‑field distributions using the DDA solution, illustrated for infinite slabs. The DDA implementation in DDSCAT accurately reproduces exact scattering for infinite cylinders and slabs, and the near‑field method yields correct field distributions 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 with 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.