  A thorough theoretical study of the optical properties of periodic Si
nanosphere arrays is undertaken, placing particular emphasis on the synergy
between electric and magnetic Mie resonances, which occur in
high-refractive-index nanoparticles and can lead to a rich variety of phenomena
ranging from perfect reflection to controlled diffraction. By means of
systematic calculations using the layer-multiple-scattering method that we
properly extended so as to describe periodic arrays with many scatterers per
unit cell, in conjunction with finite-element simulations, we optimized
surfaces of Si nanospheres that efficiently channel the transmitted light into
a single, first-order diffraction beam, following simple design rules based on
physical insight. Our results provide compelling evidence that Huygens'
metasurfaces consisting of simple Si nanosphere dimer lattices constitute a
promising platform for large-angle unidirectional deflection of transmitted
light in the visible, at wavelengths shorter than the diffraction edge of the
lattice.
