  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.
