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 that randomly sample a well-defined phase function. 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.
