  Metagrating is a new concept for wavefront manipulation that, unlike phase
gradient metasurfaces, does not suffer from low efficiency and also has a less
complicated fabrication process. In this paper, a compound metallic grating (a
periodic structure with more than one slit in each period) is proposed for
anomalous reflection. The electromagnetic response of this grating is analyzed
by a proposed analytical method and then a closed-form and analytical
expressions are presented for the reflection coefficients of the higher
diffracted orders. The proposed method is verified by full-wave simulations and
the results are in excellent agreement. Thanks to the geometrical asymmetry of
compound metallic grating, we use it for designing anomalous reflection in the
normal incident. Given analytical expressions for reflection coefficients, a
perfect anomalous reflector is designed via transferring all the incident power
to (-1) diffraction order. The structure designed in this study has an
unprecedented near-to-unitary efficiency of 99.9%. Finally, a multi-element
compound metallic grating is proposed for reflecting the normal incident to
angles of below 30, which is a challenging accomplishment. This excellent
performance of compound metallic grating shows its high potential for microwave
and terahertz wave-front manipulation applications.
