| Summary: | 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.
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