  Metasurfaces are generally designed by placing scatterers in periodic or
pseudo-periodic grids. We propose and discuss design rules for functional
metasurfaces with randomly placed anisotropic elements. By analyzing the
focusing performance of random metasurface lenses as a function of their
density and the density of the phase-maps used to design them, we find that the
performance of 1D metasurfaces is mostly governed by their density while 2D
metasurfaces strongly depend on both the density and the near-field coupling
configuration of the surface. The proposed approach is used to design
all-polarization random metalenses at near infrared frequencies. Challenges, as
well as opportunities of random metasurfaces compared to periodic ones are
discussed. Our results pave the way to new approaches in the design of
nanophotonic structures and devices from lenses to solar energy concentrators.
