  In this paper we suggest a simple analytical method for description of
electromagnetic properties of a geometrically regular two-dimensional
subwavelength arrays (metasurfaces) formed by particles with randomly
fluctuating polarizabilities. Such metasurfaces are of topical importance due
to development of mass-scale bottom-up fabrication methods, for which
fluctuations of the particles sizes, shapes, and/or composition are inevitable.
Understanding and prediction of electromagnetic properties of such random
metasurfaces is a challenge. We propose an analytical homogenization method
applicable for normal wave incidence on particles arrays with dominating
electric dipole responses and validate it with numerical point-dipole modeling
using the supercell approach. We demonstrate that fluctuations of particles
polarizabilities lead to increased diffuse scattering despite the subwavelength
lattice constant of the array. The proposed method can be readily extended to
oblique incidence and particles with both electric and magnetic dipole
resonances.
