  In this study we elaborate on the recent concept of metagratings proposed in
Ra'di et al. [Phys. Rev. Lett. 119, 067404 (2017)] for efficient manipulation
of reflected waves. Basically, a metagrating is a set of 1D arrays of
polarization line currents which are engineered to cancel scattering in
undesirable diffraction orders. We consider a general case of metagratings
composed of N polarization electric line currents per supercell. This
generalization is a necessary step to totally control diffraction patterns. We
show that a metagrating having N equal to the number of plane waves scattered
in the far-field can be used for controlling the diffraction pattern. To
validate the developed theoretical approach, anomalous and multichannel
reflections are demonstrated with 3D full-wave simulations in the microwave
regime at 10 GHz. The results can be interesting for the metamaterials
community as allow one to significantly decrease the number of used elements
and simplify the design of wavefront manipulation devices, what is very
convenient for optical and infra-red frequency ranges. Our findings also may
serve as a way for development of efficient tunable antennas in the microwave
domain.
