  We develop a simple and reliable analytical model that allows describing the
electromagnetic response of all-dielectric metasurfaces consisting of a
single-layer array of high-permittivity spherical particles. By combining Mie
theory with a bi-dimensional homogenization approach, we derive closed-form
expressions of the electric and magnetic surface impedances exhibited by the
metasurface and, thus, its reflection and transmission coefficients. The
effectiveness of the proposed approach is validated through a set of full-wave
simulations. The availability of the analytical model here developed allows a
more in-depth understanding of the complex scattering response of these
electromagnetic structures and enables the design of innovative devices
operating throughout the whole electromagnetic spectrum, including, for
example, unconventional reflectors for antennas, broadband optical mirrors, and
highly efficient nanoantenna reflectarrays.
