  We study optical wave manipulations through high-index dielectric
metalattices in both diffractionless metasurface and diffractive metagrating
regimes. It is shown that the collective lattice couplings can be employed to
tune the excitation efficiencies of all electric and magnetic multipoles of
various orders supported by each particle within the metalattice. The
interferences of those adjusted multipoles lead to highly asymmetric angular
scattering patterns that are totally different from those of isolated
particles, which subsequently enables flexible beam manipulations, including
perfect reflection, perfect transmission and efficient large-angle beam
steering. The revealed functioning mechanism of manipulated interplays between
lattice couplings and multipolar interferences can shed a new light on both
photonic branches of metasurfaces and metagratings, which can potentially
inspire many advanced applications related to optical beam controls.
