We present a rigorous theoretical framework for designing full-space spatial power dividers using metagratings. In our study, the current restrictions of spatial power dividing platforms such as reflection-only performance, operating at normal incidence, and small reflection/refraction angles have been totally relaxed. A modal expansion analysis based on Floquet-Bloch (FB) theorem is established so that a discrete set of spatial harmonics is considered in both reflection and transmission sides of a compound metallic grating in which the unknown coefficients are calculated by applying proper boundary conditions. By eliminating the unwanted scattering harmonics, the proposed metagrating has the ability to realize different functionalities from perfect anomalous refraction to reflection-transmission spatial power dividing, without resorting to full-wave numerical optimizations. The numerical simulations confirm well the theoretical predictions. Our findings not only offer possibilities to realize arbitrary spatial power dividers but also reveal a simple alternative for beamforming array antennas.
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