  We propose and numerically validate a patch reflectarray modeling approach
suitable for small patches that describes each patch as a pair of polarizable
magnetic dipoles. We introduce an extraction technique to obtain the effective
polarizability of the patch dipoles via full-wave simulations on individual
patches, followed by a beamforming design routine valid under weakly scattering
configurations. This dipole framework serves as an alternative to the ray
tracing model often used in reflectarray designs, in which rays are drawn from
the feed point and scattered off of the patch elements. Whereas the ray tracing
method solves the design problem in terms of phase delays, the dipole framework
presented here has the potential to accurately design and predict beam patterns
using a fully dipolar treatment of empirically characterized patches. We
illustrate this technique by applying it to two modulation strategies: a
variable patch size reflectarray in which the phase can be continuously tuned
(grayscale patch response), and a fixed patch size (binary patch response) in
which on/off modulation is achieved through selective patch electrical
shorting. Methods for incorporating these cases into the dipole design
framework are discussed and the results compared to those from full wave
simulation.
