  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.
