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Draine, BT, Flatau PJ.  2008.  Discrete-dipole approximation for periodic targets: theory and tests. Journal of the Optical Society of America a-Optics Image Science and Vision. 25:2693-2703.   10.1364/josaa.25.002693   AbstractWebsite

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. (C) 2008 Optical Society of America

Draine, BT, Flatau PJ.  1994.  Discrete-Dipole Approximation for Scattering Calculations. Journal of the Optical Society of America a-Optics Image Science and Vision. 11:1491-1499.   10.1364/josaa.11.001491   AbstractWebsite

The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two contiguous spheres. It is shown that, for dielectric materials (Absolute value of m less than or similar to 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.