  Effective refractive index of disordered all-dielectric metasurfaces
consisting of gallium phosphide (GaP) spheres is studied by means of
three-dimensional finite-difference time-domain (FDTD) simulations at the
wavelength of 532~nm. It is shown that a mixture of the high index
nanoparticles with sizes close to the first magnetic and electric resonances
randomly dispersed on metasurface may possess negative refraction. The
dependence of the metasurface effective refractive index on the nanoparticle
concentration and size is constructed. The feasibility of negative refraction
at large concentrations of the high index resonant spheres is demonstrated. The
negative effective refractive index is exhibited only for a monolayer of GaP
spheres.
